TSTP Solution File: SWW471+7 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SWW471+7 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 13:22:38 EDT 2022
% Result : Unknown 48.27s 47.99s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SWW471+7 : TPTP v8.1.0. Released v5.3.0.
% 0.09/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n015.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 03:08:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 48.27/47.91 ----- Otter 3.3f, August 2004 -----
% 48.27/47.91 The process was started by sandbox on n015.cluster.edu,
% 48.27/47.91 Wed Jul 27 03:08:41 2022
% 48.27/47.91 The command was "./otter". The process ID is 24454.
% 48.27/47.91
% 48.27/47.91 set(prolog_style_variables).
% 48.27/47.91 set(auto).
% 48.27/47.91 dependent: set(auto1).
% 48.27/47.91 dependent: set(process_input).
% 48.27/47.91 dependent: clear(print_kept).
% 48.27/47.91 dependent: clear(print_new_demod).
% 48.27/47.91 dependent: clear(print_back_demod).
% 48.27/47.91 dependent: clear(print_back_sub).
% 48.27/47.91 dependent: set(control_memory).
% 48.27/47.91 dependent: assign(max_mem, 12000).
% 48.27/47.91 dependent: assign(pick_given_ratio, 4).
% 48.27/47.91 dependent: assign(stats_level, 1).
% 48.27/47.91 dependent: assign(max_seconds, 10800).
% 48.27/47.91 clear(print_given).
% 48.27/47.91
% 48.27/47.91 formula_list(usable).
% 48.27/47.91 all A (A=A).
% 48.27/47.91 all X_b X_c (ti(fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool))),big_comm_monoid_big(X_b,X_c))=big_comm_monoid_big(X_b,X_c)).
% 48.27/47.91 all X_b (lattice(X_b)->ti(fun(fun(X_b,bool),X_b),big_lattice_Inf_fin(X_b))=big_lattice_Inf_fin(X_b)).
% 48.27/47.91 all X_b (lattice(X_b)->ti(fun(fun(X_b,bool),X_b),big_lattice_Sup_fin(X_b))=big_lattice_Sup_fin(X_b)).
% 48.27/47.91 all X_b (ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),big_semilattice_big(X_b))=big_semilattice_big(X_b)).
% 48.27/47.91 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)).
% 48.27/47.91 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)).
% 48.27/47.91 all X_a (ti(fun(X_a,X_a),combi(X_a))=combi(X_a)).
% 48.27/47.91 all X_a X_b (ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b))=combk(X_a,X_b)).
% 48.27/47.91 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)).
% 48.27/47.91 ti(fun(pname,option(com)),body_1)=body_1.
% 48.27/47.91 ti(fun(pname,com),body)=body.
% 48.27/47.91 ti(fun(fun(state,bool),fun(com,fun(com,com))),cond)=cond.
% 48.27/47.91 ti(com,skip)=skip.
% 48.27/47.91 ti(fun(com,fun(com,com)),semi)=semi.
% 48.27/47.91 ti(fun(fun(state,bool),fun(com,com)),while)=while.
% 48.27/47.91 ti(fun(com,nat),com_size)=com_size.
% 48.27/47.91 all X_b (ti(fun(fun(X_b,bool),nat),finite_card(X_b))=finite_card(X_b)).
% 48.27/47.91 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)).
% 48.27/47.91 all X_b (ti(fun(fun(X_b,bool),bool),finite_finite_1(X_b))=finite_finite_1(X_b)).
% 48.27/47.91 all X_b (ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b)),finite_fold1(X_b))=finite_fold1(X_b)).
% 48.27/47.91 all X_b (ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool))),finite_fold1Set(X_b))=finite_fold1Set(X_b)).
% 48.27/47.91 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)).
% 48.27/47.91 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)).
% 48.27/47.91 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)).
% 48.27/47.91 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)).
% 48.27/47.91 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)).
% 48.27/47.91 all X_c (minus(X_c)->ti(fun(X_c,fun(X_c,X_c)),minus_minus(X_c))=minus_minus(X_c)).
% 48.27/47.91 all X_b (one(X_b)->ti(X_b,one_one(X_b))=one_one(X_b)).
% 48.27/47.91 all X_a (monoid_add(X_a)->ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a)).
% 48.27/47.91 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)).
% 48.27/47.91 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)).
% 48.27/47.91 all X_a (monoid_mult(X_a)->ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a)).
% 48.27/47.91 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)).
% 48.27/47.91 all X_a (mult_zero(X_a)->ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a)).
% 48.27/47.91 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)).
% 48.27/47.91 all X_a (semiring(X_a)->ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a)).
% 48.27/47.91 all X_b (zero(X_b)->ti(X_b,zero_zero(X_b))=zero_zero(X_b)).
% 48.27/47.91 all X_b (ti(fun(fun(X_b,bool),X_b),the_1(X_b))=the_1(X_b)).
% 48.27/47.91 all X_a (ti(X_a,undefined(X_a))=undefined(X_a)).
% 48.27/47.91 ti(fun(com,hoare_2118899576triple(state)),hoare_Mirabelle_MGT)=hoare_Mirabelle_MGT.
% 48.27/47.91 all X_b (ti(fun(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool)),hoare_1301688828derivs(X_b))=hoare_1301688828derivs(X_b)).
% 48.27/47.91 all X_b (ti(fun(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool)),hoare_902341502valids(X_b))=hoare_902341502valids(X_b)).
% 48.27/47.91 all X_b (ti(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hoare_759811442triple(X_b))=hoare_759811442triple(X_b)).
% 48.27/47.91 all X_c X_b (ti(fun(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b)),hoare_225284258e_case(X_c,X_b))=hoare_225284258e_case(X_c,X_b)).
% 48.27/47.91 all X_c X_b (ti(fun(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b)),hoare_1759541758le_rec(X_c,X_b))=hoare_1759541758le_rec(X_c,X_b)).
% 48.27/47.91 all X_b (ti(fun(fun(X_b,nat),fun(hoare_2118899576triple(X_b),nat)),hoare_2043812435e_size(X_b))=hoare_2043812435e_size(X_b)).
% 48.27/47.91 all X_b (ti(fun(nat,fun(hoare_2118899576triple(X_b),bool)),hoare_1942962616_valid(X_b))=hoare_1942962616_valid(X_b)).
% 48.27/47.91 all X_a (ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a))=if(X_a)).
% 48.27/47.91 all X_a (semilattice_inf(X_a)->ti(fun(X_a,fun(X_a,X_a)),semilattice_inf_inf(X_a))=semilattice_inf_inf(X_a)).
% 48.27/47.91 all X_a (semilattice_sup(X_a)->ti(fun(X_a,fun(X_a,X_a)),semilattice_sup_sup(X_a))=semilattice_sup_sup(X_a)).
% 48.27/47.91 ti(fun(nat,nat),suc)=suc.
% 48.27/47.91 all X_b (ti(fun(X_b,fun(fun(nat,X_b),fun(nat,X_b))),nat_case(X_b))=nat_case(X_b)).
% 48.27/47.91 ti(fun(com,nat),size_size(com))=size_size(com).
% 48.27/47.91 all X_b (ti(fun(hoare_2118899576triple(X_b),nat),size_size(hoare_2118899576triple(X_b)))=size_size(hoare_2118899576triple(X_b))).
% 48.27/47.91 ti(fun(com,fun(state,fun(state,bool))),evalc)=evalc.
% 48.27/47.91 ti(fun(com,fun(state,fun(nat,fun(state,bool)))),evaln)=evaln.
% 48.27/47.91 ti(fun(option(com),com),the(com))=the(com).
% 48.27/47.91 all X_c (bot(X_c)->ti(X_c,bot_bot(X_c))=bot_bot(X_c)).
% 48.27/47.91 all X_a (ord(X_a)->ti(fun(X_a,fun(X_a,bool)),ord_less(X_a))=ord_less(X_a)).
% 48.27/47.91 all X_c (ord(X_c)->ti(fun(X_c,fun(X_c,bool)),ord_less_e_q(X_c))=ord_less_e_q(X_c)).
% 48.27/47.91 all X_b (ti(fun(X_b,fun(fun(X_b,bool),X_b)),partial_flat_lub(X_b))=partial_flat_lub(X_b)).
% 48.27/47.91 all X_b (ti(fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),powp(X_b))=powp(X_b)).
% 48.27/47.91 all X_b (ti(fun(fun(X_b,bool),fun(X_b,bool)),collect(X_b))=collect(X_b)).
% 48.27/47.91 all X_c X_b (ti(fun(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool))),image(X_c,X_b))=image(X_c,X_b)).
% 48.27/47.91 all X_b (ti(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),insert(X_b))=insert(X_b)).
% 48.27/47.91 all X_b (ti(fun(fun(X_b,bool),X_b),the_elem(X_b))=the_elem(X_b)).
% 48.27/47.91 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)).
% 48.27/47.91 ti(bool,fFalse)=fFalse.
% 48.27/47.91 ti(fun(bool,bool),fNot)=fNot.
% 48.27/47.91 ti(bool,fTrue)=fTrue.
% 48.27/47.91 ti(fun(bool,fun(bool,bool)),fconj)=fconj.
% 48.27/47.91 ti(fun(bool,fun(bool,bool)),fdisj)=fdisj.
% 48.27/47.91 all X_a (ti(fun(X_a,fun(X_a,bool)),fe_qual(X_a))=fe_qual(X_a)).
% 48.27/47.91 ti(fun(bool,fun(bool,bool)),fimplies)=fimplies.
% 48.27/47.91 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)).
% 48.27/47.91 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)).
% 48.27/47.91 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)).
% 48.27/47.91 all B_1_1 (hBOOL(ti(bool,B_1_1))<->hBOOL(B_1_1)).
% 48.27/47.91 all X_b (ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b))=member(X_b)).
% 48.27/47.91 ti(fun(hoare_2118899576triple(x_a),bool),g)=g.
% 48.27/47.91 ti(fun(pname,fun(x_a,fun(state,bool))),p)=p.
% 48.27/47.91 ti(fun(pname,bool),procs)=procs.
% 48.27/47.91 ti(fun(pname,fun(x_a,fun(state,bool))),q)=q.
% 48.27/47.91 ti(nat,n)=n.
% 48.27/47.91 all X_b Fun1 Com_1 Fun2 Fun1_2 Com Fun2_2 (hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1),Com_1),Fun2)=hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1_2),Com),Fun2_2)<->Fun1=Fun1_2&Com_1=Com&Fun2=Fun2_2).
% 48.27/47.91 all X_b Ga Ts (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_902341502valids(X_b),Ga),Ts))<-> (all N ((all X (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),bool),member(hoare_2118899576triple(X_b)),X),Ga))->hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N),X))))-> (all X (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),bool),member(hoare_2118899576triple(X_b)),X),Ts))->hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N),X))))))).
% 48.27/47.91 all X_b Ga Pa Qa Procsa (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),semilattice_sup_sup(fun(hoare_2118899576triple(X_b),bool)),Ga),hAPP(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(pname,hoare_2118899576triple(X_b)),fun(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool)),image(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),pname),hoare_759811442triple(X_b)),Pa)),body)),Qa)),Procsa))),hAPP(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(pname,hoare_2118899576triple(X_b)),fun(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool)),image(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),pname),hoare_759811442triple(X_b)),Pa)),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body_1))),Qa)),Procsa)))->hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(pname,hoare_2118899576triple(X_b)),fun(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool)),image(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),pname),hoare_759811442triple(X_b)),Pa)),body)),Qa)),Procsa)))).
% 48.27/47.91 all X_b C_1 A_3 B_2 (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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))-> (-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_2)))).
% 48.27/47.91 all X_b A_3 B_2 X_2 (hBOOL(hAPP(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2),X_2))-> (-hBOOL(hAPP(X_b,bool,A_3,X_2))->hBOOL(hAPP(X_b,bool,B_2,X_2)))).
% 48.27/47.91 all X_b A_3 B_2 X_2 ((-hBOOL(hAPP(X_b,bool,B_2,X_2))->hBOOL(hAPP(X_b,bool,A_3,X_2)))->hBOOL(hAPP(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2),X_2))).
% 48.27/47.91 all X_b A_3 C_1 B_2 ((-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))->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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))).
% 48.27/47.91 all X_b X_c A_3 B_1 F X_2 (ti(X_b,B_1)=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))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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))))).
% 48.27/47.91 all X_c X_b F1 Fun1 Com_1 Fun2 (hAPP(hoare_2118899576triple(X_c),X_b,hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b),hoare_1759541758le_rec(X_c,X_b),F1),hAPP(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hoare_759811442triple(X_c),Fun1),Com_1),Fun2))=hAPP(fun(X_c,fun(state,bool)),X_b,hAPP(com,fun(fun(X_c,fun(state,bool)),X_b),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b)),F1,Fun1),Com_1),Fun2)).
% 48.27/47.91 all X_c X_b F1 Fun1 Com_1 Fun2 (hAPP(hoare_2118899576triple(X_c),X_b,hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b),hoare_225284258e_case(X_c,X_b),F1),hAPP(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hoare_759811442triple(X_c),Fun1),Com_1),Fun2))=hAPP(fun(X_c,fun(state,bool)),X_b,hAPP(com,fun(fun(X_c,fun(state,bool)),X_b),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b)),F1,Fun1),Com_1),Fun2)).
% 48.27/47.91 all X_c X_b F A_3 B_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),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_sup_sup(fun(X_c,bool)),A_3),B_2))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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_2))).
% 48.27/47.91 all X_b X_c (lattice(X_c)-> (all F G X (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)),semilattice_sup_sup(fun(X_b,X_c)),F),G),X)=hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),semilattice_sup_sup(X_c),hAPP(X_b,X_c,F,X)),hAPP(X_b,X_c,G,X))))).
% 48.27/47.91 all X_c X_b (lattice(X_b)-> (all F G X_2 (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)),semilattice_sup_sup(fun(X_c,X_b)),F),G),X_2)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,G,X_2))))).
% 48.27/47.91 all X_b Ga G_1 Ts (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),G_1),Ts))-> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),G_1))->hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts)))).
% 48.27/47.91 all X_a (semilattice_sup(X_a)-> (all X_1 Y Z (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)),Z)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z))))).
% 48.27/47.91 all X_a (lattice(X_a)-> (all X_1 Y Z (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)),Z)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z))))).
% 48.27/47.91 all X_a (semilattice_sup(X_a)-> (all A_1 B C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B)),C)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B),C))))).
% 48.27/47.91 all X_a (semilattice_sup(X_a)-> (all X_1 Y Z (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Z))))).
% 48.27/47.91 all X_a (lattice(X_a)-> (all X_1 Y Z (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Z))))).
% 48.27/47.91 all X_a (semilattice_sup(X_a)-> (all B A_1 C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),C))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B),C))))).
% 48.27/47.91 all X_a (semilattice_sup(X_a)-> (all X_1 Y (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)))).
% 48.27/47.91 all X_a (lattice(X_a)-> (all X_1 Y (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)))).
% 48.27/47.91 all X_a (semilattice_sup(X_a)-> (all A_1 B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B)))).
% 48.27/47.91 all X_a (semilattice_sup(X_a)-> (all X_1 Y (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X_1)))).
% 48.27/47.91 all X_a (lattice(X_a)-> (all X_1 Y (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X_1)))).
% 48.27/47.91 all X_a (semilattice_sup(X_a)-> (all A_1 B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B),A_1)))).
% 48.27/47.91 all X_a (semilattice_sup(X_a)-> (all X_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),X_1)=ti(X_a,X_1)))).
% 48.27/47.91 all X_a (semilattice_sup(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),A_1)=ti(X_a,A_1)))).
% 48.27/47.91 all X_c X_b B_1 F 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),A_3))-> (ti(X_c,B_1)=hAPP(X_b,X_c,F,X_2)->hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),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))))).
% 48.27/47.91 all X_c X_b F 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),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)),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)))).
% 48.27/47.91 all X_b X_c Z_1 F A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z_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 X (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X),A_3))&ti(X_b,Z_1)=hAPP(X_c,X_b,F,X)))).
% 48.27/47.91 all X_b A_3 C_1 B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))->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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))).
% 48.27/47.91 all X_b B_2 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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))).
% 48.27/47.91 all X_b A_3 B_2 X_2 (hBOOL(hAPP(X_b,bool,B_2,X_2))->hBOOL(hAPP(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2),X_2))).
% 48.27/47.91 all X_b B_2 A_3 X_2 (hBOOL(hAPP(X_b,bool,A_3,X_2))->hBOOL(hAPP(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2),X_2))).
% 48.27/47.91 all X_b Pa A_3 B_2 ((all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))->hBOOL(hAPP(X_b,bool,Pa,X))))<-> (all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3))->hBOOL(hAPP(X_b,bool,Pa,X))))& (all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),B_2))->hBOOL(hAPP(X_b,bool,Pa,X))))).
% 48.27/47.91 all X_b Pa A_3 B_2 ((exists X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))&hBOOL(hAPP(X_b,bool,Pa,X))))<-> (exists X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3))&hBOOL(hAPP(X_b,bool,Pa,X))))| (exists X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),B_2))&hBOOL(hAPP(X_b,bool,Pa,X))))).
% 48.27/47.91 all X_b A_3 B_2 C_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),C_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),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)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3))).
% 48.27/47.91 all X_b C_1 A_3 B_2 (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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))<->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_2))).
% 48.27/47.91 all X_b A_3 B_2 C_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),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)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),C_3))).
% 48.27/47.91 all X_b A_3 B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)).
% 48.27/47.91 all X_b A_3 B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),A_3)).
% 48.27/47.91 all X_b A_3 B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_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),fdisj),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(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_2)))).
% 48.27/47.91 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)),semilattice_sup_sup(fun(X_b,bool)),A_3),A_3)=ti(fun(X_b,bool),A_3)).
% 48.27/47.91 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)).
% 48.27/47.91 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)).
% 48.27/47.91 all X_b R_1 S_1 X (hBOOL(hAPP(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)),semilattice_sup_sup(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_1)),X))<->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),R_1),S_1)))).
% 48.27/47.91 all X_b Pa Qa (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)),Qa))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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),Qa))).
% 48.27/47.91 all X_b X_c B_1 F A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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)))-> -(all X (ti(X_b,B_1)=hAPP(X_c,X_b,F,X)-> -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X),A_3))))).
% 48.27/47.91 all X_b N_1 Pa Pn_1 Qa (hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N_1),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn_1))),Qa)))<->hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),hAPP(nat,nat,suc,N_1)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(pname,com,body,Pn_1)),Qa)))).
% 48.27/47.91 all X_b Y_1 (-(all Fun1_1 Com_2 Fun2_1 (Y_1!=hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1_1),Com_2),Fun2_1)))).
% 48.27/47.91 all X_b Pn_1 Ga Pa Qa Procsa (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),semilattice_sup_sup(fun(hoare_2118899576triple(X_b),bool)),Ga),hAPP(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(pname,hoare_2118899576triple(X_b)),fun(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool)),image(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),pname),hoare_759811442triple(X_b)),Pa)),body)),Qa)),Procsa))),hAPP(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(pname,hoare_2118899576triple(X_b)),fun(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool)),image(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),pname),hoare_759811442triple(X_b)),Pa)),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body_1))),Qa)),Procsa)))-> (hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),Pn_1),Procsa))->hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(pname,fun(X_b,fun(state,bool)),Pa,Pn_1)),hAPP(pname,com,body,Pn_1)),hAPP(pname,fun(X_b,fun(state,bool)),Qa,Pn_1))),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))).
% 48.27/47.92 all X_c X_b F G M_5 N_3 (ti(fun(X_b,bool),M_5)=ti(fun(X_b,bool),N_3)-> ((all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),N_3))->hAPP(X_b,X_c,F,X)=hAPP(X_b,X_c,G,X)))->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_5)=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_3))).
% 48.27/47.92 all X_b A_3 X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),powp(X_b),A_3),X))<-> (all Xa (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Xa),X))->hBOOL(hAPP(X_b,bool,A_3,Xa))))).
% 48.27/47.92 all X_b Pa Pn_1 Qa hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),zero_zero(nat)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(pname,com,body,Pn_1)),Qa))).
% 48.27/47.92 all Pname_3 Pname (hAPP(pname,com,body,Pname_3)=hAPP(pname,com,body,Pname)<->ti(pname,Pname_3)=ti(pname,Pname)).
% 48.27/47.92 all Pn S0 S1_2 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn))),S0),S1_2))->hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(pname,com,body,Pn)),S0),S1_2))).
% 48.27/47.92 all P S S1_2 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(pname,com,body,P)),S),S1_2))->hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,P))),S),S1_2))).
% 48.27/47.92 all X_a (lattice(X_a)-> (all X_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),X_1)=ti(X_a,X_1)))).
% 48.27/47.92 all X_b N_1 Ts ((all X (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),bool),member(hoare_2118899576triple(X_b)),X),Ts))->hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),hAPP(nat,nat,suc,N_1)),X))))-> (all X (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),bool),member(hoare_2118899576triple(X_b)),X),Ts))->hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N_1),X))))).
% 48.27/47.92 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))))).
% 48.27/47.92 all X_b A_2 B_1 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_1),A_3)))-> (ti(X_b,A_2)!=ti(X_b,B_1)->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)))).
% 48.27/47.92 all X_b B_1 A_2 B_2 ((-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2))->ti(X_b,A_2)=ti(X_b,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_1),B_2)))).
% 48.27/47.92 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)).
% 48.27/47.92 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))).
% 48.27/47.92 all X_b X (hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X))<->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),bot_bot(fun(X_b,bool))))).
% 48.27/47.92 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))).
% 48.27/47.92 all X_b A_2 B_2 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_2))).
% 48.27/47.92 all X_b A_3 ((all X (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3))))<->ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))).
% 48.27/47.92 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)))).
% 48.27/47.92 all X_b A_3 ((exists X hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3)))<->ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))).
% 48.27/47.92 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)))).
% 48.27/47.92 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)))).
% 48.27/47.92 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)))).
% 48.27/47.92 all X_b X_c F G ((all X (hAPP(X_b,X_c,F,X)=hAPP(X_b,X_c,G,X)))->ti(fun(X_b,X_c),F)=ti(fun(X_b,X_c),G)).
% 48.27/47.92 all 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),A_3))<->hBOOL(hAPP(X_b,bool,A_3,X_2))).
% 48.27/47.92 all X_b Pa (hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)=ti(fun(X_b,bool),Pa)).
% 48.27/47.92 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 (-hBOOL(hAPP(X_b,bool,Pa,X))))).
% 48.27/47.92 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))))).
% 48.27/47.92 all X_b A_2 B_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_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),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_2)))).
% 48.27/47.92 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))).
% 48.27/47.92 all X_b B_1 A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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)))))<->ti(X_b,B_1)=ti(X_b,A_2)).
% 48.27/47.92 all X_b X_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_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_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_2),A_3)).
% 48.27/47.92 all X_b X_2 Y_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_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),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_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),A_3))).
% 48.27/47.92 all X_b A_2 B_1 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_1),A_3)))<->ti(X_b,A_2)=ti(X_b,B_1)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))).
% 48.27/47.92 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 (-hBOOL(hAPP(X_b,bool,Pa,X))))).
% 48.27/47.92 all X_b A_2 B_1 C_1 D (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_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),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),bot_bot(fun(X_b,bool))))<->ti(X_b,A_2)=ti(X_b,C_1)&ti(X_b,B_1)=ti(X_b,D)|ti(X_b,A_2)=ti(X_b,D)&ti(X_b,B_1)=ti(X_b,C_1)).
% 48.27/47.92 all X_b Y_1 A_3 X_2 (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_1),A_3),X_2))<->ti(X_b,Y_1)=ti(X_b,X_2)|hBOOL(hAPP(X_b,bool,A_3,X_2))).
% 48.27/47.92 all X_b B_2 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),A_3))-> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_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_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_2),B_2)<->ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_2)))).
% 48.27/47.92 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))).
% 48.27/47.92 all X_b B_1 A_2 B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2))->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_1),B_2)))).
% 48.27/47.92 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)).
% 48.27/47.92 all X_b B_1 A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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)))))->ti(X_b,B_1)=ti(X_b,A_2)).
% 48.27/47.92 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),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_1),bot_bot(fun(X_b,bool)))->ti(X_b,A_2)=ti(X_b,B_1)).
% 48.27/47.92 all U_1 C S T_3 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C),S),T_3))-> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C),S),U_1))->U_1=T_3)).
% 48.27/47.92 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)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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),bot_bot(fun(X_b,bool)))),A_3)).
% 48.27/47.92 all X_b X 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),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))),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)))).
% 48.27/47.92 all X_b Ga T_4 Ts (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),T_4),Ts)))->hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),T_4),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))&hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts))).
% 48.27/47.92 all X_b Ts Ga T_4 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),T_4),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))-> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts))->hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),T_4),Ts))))).
% 48.27/47.92 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))))).
% 48.27/47.92 all X_c X_b C_1 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),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)))).
% 48.27/47.92 all X_c X_b F A_2 B_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),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_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),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_2))).
% 48.27/47.92 all X_c X_b F 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),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_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),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)).
% 48.27/47.92 all X_b A_3 A_2 B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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_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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))).
% 48.27/47.92 all X_b A_2 B_2 C_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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),B_2)),C_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)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3))).
% 48.27/47.92 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))).
% 48.27/47.92 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))).
% 48.27/47.92 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))).
% 48.27/47.92 all X_b Pa X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),bot_bot(fun(X_b,bool))))->hBOOL(hAPP(X_b,bool,Pa,X))).
% 48.27/47.92 all X_b B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),bot_bot(fun(X_b,bool))),B_2)=ti(fun(X_b,bool),B_2)).
% 48.27/47.92 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)),semilattice_sup_sup(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool)))=ti(fun(X_b,bool),A_3)).
% 48.27/47.92 all X_b A_3 B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)=bot_bot(fun(X_b,bool))<->ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))&ti(fun(X_b,bool),B_2)=bot_bot(fun(X_b,bool))).
% 48.27/47.92 all X_b Ga Pa C_1 Qa C_3 ((hBOOL(C_3)->hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))->hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(bool,fun(X_b,fun(state,bool)),hAPP(fun(X_b,fun(bool,fun(state,bool))),fun(bool,fun(X_b,fun(state,bool))),combc(X_b,bool,fun(state,bool)),hAPP(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(bool,fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(bool,fun(state,bool))),fun(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(bool,fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X_b),combc(state,bool,bool)),hAPP(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),Pa))),C_3)),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))).
% 48.27/47.92 all X_b Ga hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),bot_bot(fun(hoare_2118899576triple(X_b),bool)))).
% 48.27/47.92 all X_a (bounded_lattice_bot(X_a)-> (all X_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),bot_bot(X_a)),X_1)=ti(X_a,X_1)))).
% 48.27/47.92 all X_a (bounded_lattice_bot(X_a)-> (all X_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),bot_bot(X_a))=ti(X_a,X_1)))).
% 48.27/47.92 all X_b (bounded_lattice_bot(X_b)-> (all X_2 Y_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),Y_1)=bot_bot(X_b)<->ti(X_b,X_2)=bot_bot(X_b)&ti(X_b,Y_1)=bot_bot(X_b)))).
% 48.27/47.92 all X_a N_2 T_3 (hBOOL(hAPP(hoare_2118899576triple(X_a),bool,hAPP(nat,fun(hoare_2118899576triple(X_a),bool),hoare_1942962616_valid(X_a),hAPP(nat,nat,suc,N_2)),T_3))->hBOOL(hAPP(hoare_2118899576triple(X_a),bool,hAPP(nat,fun(hoare_2118899576triple(X_a),bool),hoare_1942962616_valid(X_a),N_2),T_3))).
% 48.27/47.92 all X_b A_2 B_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_2)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),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))),B_2)).
% 48.27/47.92 all X_b Ga Pa Pn_1 Qa (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn_1))),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))->hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(pname,com,body,Pn_1)),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))).
% 48.27/47.92 all X_b Pa Pn_1 Qa Ga (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(pname,com,body,Pn_1)),Qa)),Ga)),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn_1))),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))->hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(pname,com,body,Pn_1)),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))).
% 48.27/47.92 all X_b Ga C_1 Qa Pa ((all Z_3 S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_3),S_3))->hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(fun(state,bool),fun(X_b,fun(state,bool)),combk(fun(state,bool),X_b),hAPP(state,fun(state,bool),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fe_qual(state)),S_3))),C_1),hAPP(fun(state,bool),fun(X_b,fun(state,bool)),combk(fun(state,bool),X_b),hAPP(X_b,fun(state,bool),Qa,Z_3)))),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))))->hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))).
% 48.27/47.92 all X_b Pa Ga P_1 C_1 Qa (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),P_1),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))-> ((all Z_3 S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_3),S_3))->hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_3),S_3))))->hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))).
% 48.27/47.92 all X_b Qa Ga Pa C_1 Q_1 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Q_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))-> ((all Z_3 S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_3),S_3))->hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Qa,Z_3),S_3))))->hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))).
% 48.27/47.92 all X_b Fa Fun1 Com_1 Fun2 (hAPP(hoare_2118899576triple(X_b),nat,hAPP(fun(X_b,nat),fun(hoare_2118899576triple(X_b),nat),hoare_2043812435e_size(X_b),Fa),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1),Com_1),Fun2))=zero_zero(nat)).
% 48.27/47.92 all C_1 (hAPP(com,hoare_2118899576triple(state),hoare_Mirabelle_MGT,C_1)=hAPP(fun(state,fun(state,bool)),hoare_2118899576triple(state),hAPP(com,fun(fun(state,fun(state,bool)),hoare_2118899576triple(state)),hAPP(fun(state,fun(state,bool)),fun(com,fun(fun(state,fun(state,bool)),hoare_2118899576triple(state))),hoare_759811442triple(state),fe_qual(state)),C_1),hAPP(com,fun(state,fun(state,bool)),evalc,C_1))).
% 48.27/47.92 all X_b Fun1 Com_1 Fun2 (hAPP(hoare_2118899576triple(X_b),nat,size_size(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1),Com_1),Fun2))=zero_zero(nat)).
% 48.27/47.92 all X_b Qa Pa Ga P_1 C_1 Q_1 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),P_1),C_1),Q_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))-> ((all Z_3 S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_3),S_3))-> (all S_4 ((all Z_4 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_4),S_3))->hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_4),S_4))))->hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Qa,Z_3),S_4))))))->hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))).
% 48.27/47.92 all X_b X_2 (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_2),bot_bot(fun(X_b,bool))))=ti(X_b,X_2)).
% 48.27/47.92 all M (hAPP(nat,nat,suc,M)!=zero_zero(nat)).
% 48.27/47.92 bot_bot(nat)=zero_zero(nat).
% 48.27/47.92 all N_2 (N_2!=hAPP(nat,nat,suc,N_2)).
% 48.27/47.92 all N_2 (hAPP(nat,nat,suc,N_2)!=N_2).
% 48.27/47.92 all Nat Nat_4 (hAPP(nat,nat,suc,Nat)=hAPP(nat,nat,suc,Nat_4)<->Nat=Nat_4).
% 48.27/47.92 all X_1 Y (hAPP(nat,nat,suc,X_1)=hAPP(nat,nat,suc,Y)->X_1=Y).
% 48.27/47.92 all M (zero_zero(nat)!=hAPP(nat,nat,suc,M)).
% 48.27/47.92 all Nat_3 (zero_zero(nat)!=hAPP(nat,nat,suc,Nat_3)).
% 48.27/47.92 all M (hAPP(nat,nat,suc,M)!=zero_zero(nat)).
% 48.27/47.92 all Nat_2 (hAPP(nat,nat,suc,Nat_2)!=zero_zero(nat)).
% 48.27/47.92 all M (zero_zero(nat)!=hAPP(nat,nat,suc,M)).
% 48.27/47.92 all N_2 (N_2!=zero_zero(nat)-> (exists M_2 (N_2=hAPP(nat,nat,suc,M_2)))).
% 48.27/47.92 all N_1 Pa (hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))-> ((all N (hBOOL(hAPP(nat,bool,Pa,N))->hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N)))))->hBOOL(hAPP(nat,bool,Pa,N_1)))).
% 48.27/47.92 all Pa K_1 (hBOOL(hAPP(nat,bool,Pa,K_1))-> ((all N (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N)))->hBOOL(hAPP(nat,bool,Pa,N))))->hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))))).
% 48.27/47.92 all Y (Y!=zero_zero(nat)-> -(all Nat_1 (Y!=hAPP(nat,nat,suc,Nat_1)))).
% 48.27/47.92 all X_b X_c (bot(X_c)-> (all X (hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X)=bot_bot(X_c)))).
% 48.27/47.92 all X_c X_b (bot(X_b)-> (all X_2 (hAPP(X_c,X_b,bot_bot(fun(X_c,X_b)),X_2)=bot_bot(X_b)))).
% 48.27/47.92 all Pn S0 N_2 S1_2 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn))),S0),N_2),S1_2))->hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(pname,com,body,Pn)),S0),hAPP(nat,nat,suc,N_2)),S1_2))).
% 48.27/47.92 all X_b Ga Pa hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),skip),Pa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))).
% 48.27/47.92 all X_b Ga Pa B_1 C_1 hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(fun(state,bool),fun(X_b,fun(state,bool)),hAPP(fun(X_b,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(X_b,fun(state,bool))),combc(X_b,fun(state,bool),fun(state,bool)),hAPP(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),X_b),combs(state,bool,bool)),hAPP(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),Pa))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),B_1))),hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),Pa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))).
% 48.27/47.92 all C_1 N_1 B_1 S_2 (-hBOOL(hAPP(state,bool,B_1,S_2))->hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S_2),N_1),S_2))).
% 48.27/47.92 all S2_1 C_1 N_1 S1 B_1 S0_1 (hBOOL(hAPP(state,bool,B_1,S0_1))-> (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C_1),S0_1),N_1),S1))-> (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S1),N_1),S2_1))->hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S0_1),N_1),S2_1))))).
% 48.27/47.92 all S2_1 C_1 S1 B_1 S0_1 (hBOOL(hAPP(state,bool,B_1,S0_1))-> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S0_1),S1))-> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S1),S2_1))->hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S0_1),S2_1))))).
% 48.27/47.92 all C_1 B_1 S_2 (-hBOOL(hAPP(state,bool,B_1,S_2))->hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S_2),S_2))).
% 48.27/47.92 all S N_2 hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,skip),S),N_2),S)).
% 48.27/47.92 all S N_2 T_3 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,skip),S),N_2),T_3))->T_3=S).
% 48.27/47.92 all S T_3 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,skip),S),T_3))->T_3=S).
% 48.27/47.92 all S hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,skip),S),S)).
% 48.27/47.92 all Fun Com (skip!=hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com)).
% 48.27/47.92 all Fun Com (hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com)!=skip).
% 48.27/47.92 all Fun_1 Com_1 Fun Com (hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1)=hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com)<->Fun_1=Fun&Com_1=Com).
% 48.27/47.92 all C S N_2 S_5 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C),S),N_2),S_5))->hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C),S),hAPP(nat,nat,suc,N_2)),S_5))).
% 48.27/47.92 all C S N_2 T_3 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C),S),N_2),T_3))->hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C),S),T_3))).
% 48.27/47.92 all C_1 S_2 T_4 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S_2),T_4))<-> (exists N hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C_1),S_2),N),T_4)))).
% 48.27/47.92 all Pname Fun_1 Com_1 (hAPP(pname,com,body,Pname)!=hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1)).
% 48.27/47.92 all Fun_1 Com_1 Pname (hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1)!=hAPP(pname,com,body,Pname)).
% 48.27/47.92 all Pname_2 (skip!=hAPP(pname,com,body,Pname_2)).
% 48.27/47.92 all Pname_2 (hAPP(pname,com,body,Pname_2)!=skip).
% 48.27/47.92 all X_b N_1 Pa C_1 Qa (hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N_1),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)))<-> (all Z_3 S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_3),S_3))-> (all S_4 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C_1),S_3),N_1),S_4))->hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Qa,Z_3),S_4))))))).
% 48.27/47.92 all P S N_2 S1_2 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(pname,com,body,P)),S),N_2),S1_2))-> -(all N (N_2=hAPP(nat,nat,suc,N)-> -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,P))),S),N),S1_2))))).
% 48.27/47.92 all B_1 C_1 S_2 T_4 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S_2),T_4))-> ((T_4=S_2->hBOOL(hAPP(state,bool,B_1,S_2)))-> -(hBOOL(hAPP(state,bool,B_1,S_2))-> (all S1_1 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S_2),S1_1))-> -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S1_1),T_4))))))).
% 48.27/47.92 all B_1 C_1 S_2 N_1 T_4 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S_2),N_1),T_4))-> ((T_4=S_2->hBOOL(hAPP(state,bool,B_1,S_2)))-> -(hBOOL(hAPP(state,bool,B_1,S_2))-> (all S1_1 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C_1),S_2),N_1),S1_1))-> -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S1_1),N_1),T_4))))))).
% 48.27/47.92 all C S T_3 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C),S),T_3))-> (exists N hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C),S),N),T_3)))).
% 48.27/47.92 all X_b D R_1 Ga Pa C_1 Qa (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))-> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Qa),D),R_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))->hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(com,com,hAPP(com,fun(com,com),semi,C_1),D)),R_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))).
% 48.27/47.92 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_1(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)))))).
% 48.27/47.92 all X_c X_b Pa Qa Ga P_1 C0 Q_1 U_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),U_2))-> ((all P_2 (hBOOL(hAPP(fun(hoare_2118899576triple(X_c),bool),bool,hAPP(fun(hoare_2118899576triple(X_c),bool),fun(fun(hoare_2118899576triple(X_c),bool),bool),hoare_1301688828derivs(X_c),Ga),hAPP(fun(hoare_2118899576triple(X_c),bool),fun(hoare_2118899576triple(X_c),bool),hAPP(hoare_2118899576triple(X_c),fun(fun(hoare_2118899576triple(X_c),bool),fun(hoare_2118899576triple(X_c),bool)),insert(hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hoare_759811442triple(X_c),hAPP(X_b,fun(X_c,fun(state,bool)),P_1,P_2)),hAPP(X_b,com,C0,P_2)),hAPP(X_b,fun(X_c,fun(state,bool)),Q_1,P_2))),bot_bot(fun(hoare_2118899576triple(X_c),bool)))))->hBOOL(hAPP(fun(hoare_2118899576triple(X_c),bool),bool,hAPP(fun(hoare_2118899576triple(X_c),bool),fun(fun(hoare_2118899576triple(X_c),bool),bool),hoare_1301688828derivs(X_c),Ga),hAPP(fun(hoare_2118899576triple(X_c),bool),fun(hoare_2118899576triple(X_c),bool),hAPP(hoare_2118899576triple(X_c),fun(fun(hoare_2118899576triple(X_c),bool),fun(hoare_2118899576triple(X_c),bool)),insert(hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hoare_759811442triple(X_c),hAPP(X_b,fun(X_c,fun(state,bool)),Pa,P_2)),hAPP(X_b,com,C0,P_2)),hAPP(X_b,fun(X_c,fun(state,bool)),Qa,P_2))),bot_bot(fun(hoare_2118899576triple(X_c),bool)))))))-> (hBOOL(hAPP(fun(hoare_2118899576triple(X_c),bool),bool,hAPP(fun(hoare_2118899576triple(X_c),bool),fun(fun(hoare_2118899576triple(X_c),bool),bool),hoare_1301688828derivs(X_c),Ga),hAPP(fun(X_b,bool),fun(hoare_2118899576triple(X_c),bool),hAPP(fun(X_b,hoare_2118899576triple(X_c)),fun(fun(X_b,bool),fun(hoare_2118899576triple(X_c),bool)),image(X_b,hoare_2118899576triple(X_c)),hAPP(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,hoare_2118899576triple(X_c)),hAPP(fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),fun(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,hoare_2118899576triple(X_c))),combs(X_b,fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_b,com),fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hAPP(fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),fun(fun(X_b,com),fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),combs(X_b,com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hAPP(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),fun(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))))),combb(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),X_b),hoare_759811442triple(X_c)),P_1)),C0)),Q_1)),U_2)))->hBOOL(hAPP(fun(hoare_2118899576triple(X_c),bool),bool,hAPP(fun(hoare_2118899576triple(X_c),bool),fun(fun(hoare_2118899576triple(X_c),bool),bool),hoare_1301688828derivs(X_c),Ga),hAPP(fun(X_b,bool),fun(hoare_2118899576triple(X_c),bool),hAPP(fun(X_b,hoare_2118899576triple(X_c)),fun(fun(X_b,bool),fun(hoare_2118899576triple(X_c),bool)),image(X_b,hoare_2118899576triple(X_c)),hAPP(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,hoare_2118899576triple(X_c)),hAPP(fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),fun(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,hoare_2118899576triple(X_c))),combs(X_b,fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_b,com),fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hAPP(fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),fun(fun(X_b,com),fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),combs(X_b,com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hAPP(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),fun(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))))),combb(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),X_b),hoare_759811442triple(X_c)),Pa)),C0)),Qa)),U_2)))))).
% 48.27/47.92 all C2_1 S2 N2 T2 C1_1 S1_2 N1 T1 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1_1),S1_2),N1),T1))-> (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2_1),S2),N2),T2))-> (exists N (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1_1),S1_2),N),T1))&hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2_1),S2),N),T2)))))).
% 48.27/47.92 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))-> (exists B_3 (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),A_2),B_3)& -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_3))))).
% 48.27/47.92 all C1_1 S2 C0_1 S0 N_2 S1_2 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C0_1),S0),N_2),S1_2))-> (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1_1),S1_2),N_2),S2))->hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),semi,C0_1),C1_1)),S0),N_2),S2)))).
% 48.27/47.92 all C1_1 S2 C0_1 S0 S1_2 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C0_1),S0),S1_2))-> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1_1),S1_2),S2))->hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),semi,C0_1),C1_1)),S0),S2)))).
% 48.27/47.92 all Com1_1 Com2_1 Com1 Com2 (hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1)=hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2)<->Com1_1=Com1&Com2_1=Com2).
% 48.27/47.92 all Com1_2 Com2_2 Pname_2 (hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2)!=hAPP(pname,com,body,Pname_2)).
% 48.27/47.92 all Pname_2 Com1_2 Com2_2 (hAPP(pname,com,body,Pname_2)!=hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2)).
% 48.27/47.92 all Fun Com Com1_1 Com2_1 (hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com)!=hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1)).
% 48.27/47.92 all Com1_1 Com2_1 Fun Com (hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1)!=hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com)).
% 48.27/47.92 all Com1_3 Com2_3 (hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_3),Com2_3)!=skip).
% 48.27/47.92 all Com1_3 Com2_3 (skip!=hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_3),Com2_3)).
% 48.27/47.92 all C1_1 C2_1 S T_3 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),semi,C1_1),C2_1)),S),T_3))-> -(all S1_1 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1_1),S),S1_1))-> -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C2_1),S1_1),T_3))))).
% 48.27/47.92 all C1_1 C2_1 S N_2 T_3 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),semi,C1_1),C2_1)),S),N_2),T_3))-> -(all S1_1 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1_1),S),N_2),S1_1))-> -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2_1),S1_1),N_2),T_3))))).
% 48.27/47.92 all X_c X_b H F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1))->hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(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)))).
% 48.27/47.92 all X_b A_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)))).
% 48.27/47.92 all X_b hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),bot_bot(fun(X_b,bool)))).
% 48.27/47.92 all X_b Qa Pa (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Qa)))->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)),Qa))))).
% 48.27/47.92 all X_b F_1 Ga (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)),semilattice_sup_sup(fun(X_b,bool)),F_1),Ga)))<->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1))&hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),Ga))).
% 48.27/47.92 all X_b Ga F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),Ga))->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)),semilattice_sup_sup(fun(X_b,bool)),F_1),Ga))))).
% 48.27/47.92 all X_b (finite_finite(X_b)-> (all A_3 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)))).
% 48.27/47.92 all X_b (finite_finite(X_b)-> (all A_3 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)))).
% 48.27/47.92 all X_b Pa Qa (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)),Qa))))<->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)))&hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Qa)))).
% 48.27/47.92 all X_b A_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(X_b),A_3))).
% 48.27/47.92 all X_b Pa F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))-> ((all X F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2))-> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),F_2))-> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_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),F_2)))))))->hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1))))).
% 48.27/47.92 all X_b A_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(X_b),A_5))))).
% 48.27/47.92 all X_c X_b F A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(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 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3))& -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)))))))))).
% 48.27/47.92 all X_b A_3 (ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))<-> (exists X B_3 (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),B_3)& -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),B_3))))).
% 48.27/47.92 all X_b B_2 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_1(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_1(X_b),B_2))-> (ti(fun(X_b,bool),B_2)!=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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_1,A_3)),hAPP(fun(X_b,bool),X_b,F_1,B_2))))))).
% 48.27/47.92 all X_b X_2 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_1(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),hAPP(fun(X_b,bool),X_b,F_1,A_3))))).
% 48.27/47.92 all X_c X_b F A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),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)=hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,bool)),fun(fun(X_c,bool),fun(fun(X_b,bool),fun(X_c,bool))),hAPP(fun(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool))),fun(fun(X_b,fun(X_c,bool)),fun(fun(X_c,bool),fun(fun(X_b,bool),fun(X_c,bool)))),finite_fold_image(fun(X_c,bool),X_b),semilattice_sup_sup(fun(X_c,bool))),hAPP(fun(X_c,bool),fun(X_b,fun(X_c,bool)),hAPP(fun(X_b,fun(fun(X_c,bool),fun(X_c,bool))),fun(fun(X_c,bool),fun(X_b,fun(X_c,bool))),combc(X_b,fun(X_c,bool),fun(X_c,bool)),hAPP(fun(X_b,X_c),fun(X_b,fun(fun(X_c,bool),fun(X_c,bool))),hAPP(fun(X_c,fun(fun(X_c,bool),fun(X_c,bool))),fun(fun(X_b,X_c),fun(X_b,fun(fun(X_c,bool),fun(X_c,bool)))),combb(X_c,fun(fun(X_c,bool),fun(X_c,bool)),X_b),insert(X_c)),F)),bot_bot(fun(X_c,bool)))),bot_bot(fun(X_c,bool))),A_3)).
% 48.27/47.92 all X_b Pa F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1))-> (ti(fun(X_b,bool),F_1)!=bot_bot(fun(X_b,bool))-> ((all X 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),bot_bot(fun(X_b,bool))))))-> ((all X F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2))-> (ti(fun(X_b,bool),F_2)!=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),F_2))-> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_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),F_2))))))))->hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)))))).
% 48.27/47.92 all X_b X_2 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_2),X_2)=ti(X_b,X_2)).
% 48.27/47.92 all X_c X_b F G Z_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),F),G),Z_1),bot_bot(fun(X_c,bool)))=ti(X_b,Z_1)).
% 48.27/47.92 all X_b X_2 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_1(X_b),A_3))-> (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_b,hAPP(X_b,fun(X_b,X_b),F,X_2),hAPP(fun(X_b,bool),X_b,F_1,A_3))=hAPP(fun(X_b,bool),X_b,F_1,A_3)))).
% 48.27/47.92 all X_b N_3 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 Y_2 (hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X),Y_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_b,X_b,H,X)),hAPP(X_b,X_b,H,Y_2))))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3))-> (ti(fun(X_b,bool),N_3)!=bot_bot(fun(X_b,bool))->hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,F_1,N_3))=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_3)))))).
% 48.27/47.92 all X_c X_b G A_3 F Z_1 F_1 (hBOOL(hAPP(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool,hAPP(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool)),big_comm_monoid_big(X_b,X_c),F),Z_1),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3))->hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,G),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_1),A_3))& (-hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3))->hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,G),A_3)=ti(X_b,Z_1))).
% 48.27/47.92 all X_b X_2 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_1(X_b),A_3))-> (-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))->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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),hAPP(fun(X_b,bool),X_b,F_1,A_3)))))).
% 48.27/47.92 all X_b X_2 (hAPP(fun(X_b,bool),X_b,the_1(X_b),hAPP(X_b,fun(X_b,bool),fe_qual(X_b),X_2))=ti(X_b,X_2)).
% 48.27/47.92 all X_b A_2 (hAPP(fun(X_b,bool),X_b,the_1(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)).
% 48.27/47.92 all X_b X_2 Y_1 Pa ((hBOOL(Pa)->ti(X_b,X_2)=hAPP(fun(X_b,bool),X_b,the_1(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_2)))),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_1)))))& (-hBOOL(Pa)->ti(X_b,Y_1)=hAPP(fun(X_b,bool),X_b,the_1(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_2)))),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_1)))))).
% 48.27/47.92 all X_c X_b B_2 A_3 F Z_1 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_1),G),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))->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)),semilattice_sup_sup(fun(X_c,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,A_3)),hAPP(fun(X_c,bool),X_b,F_1,B_2))))).
% 48.27/47.92 all X_c X_b X_2 F Z_1 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_1),G),F_1))->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),X_2)=ti(X_b,X_2)).
% 48.27/47.92 all X_c X_b X_2 A_3 F Z_1 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_1),G),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),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))->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_2)),hAPP(fun(X_c,bool),X_b,F_1,A_3))=hAPP(fun(X_c,bool),X_b,F_1,A_3)))).
% 48.27/47.92 all X_c X_b G A_3 F Z_1 F_1 (hBOOL(hAPP(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool,hAPP(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool)),big_comm_monoid_big(X_b,X_c),F),Z_1),F_1))-> (-hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3))->hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,G),A_3)=ti(X_b,Z_1))).
% 48.27/47.92 all X_b X_2 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_2),bot_bot(fun(X_b,bool))))=ti(X_b,X_2)).
% 48.27/47.92 all X_c X_b X_2 A_3 F Z_1 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_1),G),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_2)),hAPP(fun(X_c,bool),X_b,F_1,A_3)))).
% 48.27/47.92 all X_b Pa A_2 (hBOOL(hAPP(X_b,bool,Pa,A_2))-> ((all X (hBOOL(hAPP(X_b,bool,Pa,X))->ti(X_b,X)=ti(X_b,A_2)))->hAPP(fun(X_b,bool),X_b,the_1(X_b),Pa)=ti(X_b,A_2))).
% 48.27/47.92 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_1(X_b),A_3))-> (ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))-> ((all X Y_2 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),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),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)))))))->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)))))).
% 48.27/47.92 all X_c X_b H G A_3 B_2 F Z_1 F_1 (hBOOL(hAPP(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool,hAPP(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool)),big_comm_monoid_big(X_b,X_c),F),Z_1),F_1))-> (ti(fun(X_c,bool),A_3)=ti(fun(X_c,bool),B_2)-> ((all X (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X),B_2))->hAPP(X_c,X_b,H,X)=hAPP(X_c,X_b,G,X)))->hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,H),A_3)=hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,G),B_2)))).
% 48.27/47.92 all X_b Pa A_2 (hBOOL(hAPP(X_b,bool,Pa,A_2))-> ((all X (hBOOL(hAPP(X_b,bool,Pa,X))->ti(X_b,X)=ti(X_b,A_2)))->hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the_1(X_b),Pa))))).
% 48.27/47.92 all X_b A_2 Pa ((exists X (hBOOL(hAPP(X_b,bool,Pa,X))& (all Y_2 (hBOOL(hAPP(X_b,bool,Pa,Y_2))->ti(X_b,Y_2)=ti(X_b,X)))))-> (hBOOL(hAPP(X_b,bool,Pa,A_2))->hAPP(fun(X_b,bool),X_b,the_1(X_b),Pa)=ti(X_b,A_2))).
% 48.27/47.92 all X_b Pa ((exists X (hBOOL(hAPP(X_b,bool,Pa,X))& (all Y_2 (hBOOL(hAPP(X_b,bool,Pa,Y_2))->ti(X_b,Y_2)=ti(X_b,X)))))->hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the_1(X_b),Pa)))).
% 48.27/47.92 all 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),A_3))-> -(all B_3 (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_3)->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_3))))).
% 48.27/47.92 all X_b A_3 ((all Y_2 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),A_3))))->ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all B_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(X_b),B_2))-> (ti(fun(X_b,bool),B_2)!=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),B_2)))))))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (-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))->hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3))))))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)))))).
% 48.27/47.92 all X_b B_2 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_1(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_1(X_b),B_2))-> (ti(fun(X_b,bool),B_2)!=bot_bot(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)=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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_1,A_3)),hAPP(fun(X_b,bool),X_b,F_1,B_2)))))))).
% 48.27/47.92 all X_b B_2 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_1(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))-> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)!=bot_bot(fun(X_b,bool))->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))),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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_1,A_3)),hAPP(fun(X_b,bool),X_b,F_1,B_2)))))).
% 48.27/47.92 all X_b X_2 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_1(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_2),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_2),A_3))=ti(X_b,X_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),X_2),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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),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_2),bot_bot(fun(X_b,bool))))))))).
% 48.27/47.92 all X_b B_2 A_3 X_2 (hBOOL(hAPP(X_b,bool,A_3,X_2))-> (hBOOL(hAPP(X_b,bool,B_2,X_2))->hBOOL(hAPP(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2),X_2)))).
% 48.27/47.92 all X_b B_2 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_2))->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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))))).
% 48.27/47.92 all X_b C_1 A_3 B_2 (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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))-> -(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_2)))).
% 48.27/47.92 all X_b A_3 B_2 X_2 (hBOOL(hAPP(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2),X_2))-> -(hBOOL(hAPP(X_b,bool,A_3,X_2))-> -hBOOL(hAPP(X_b,bool,B_2,X_2)))).
% 48.27/47.92 all X_b B_2 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_2))->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_2))))).
% 48.27/47.92 all X_b C_1 A_3 B_2 (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_2)))-> -(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_2)))).
% 48.27/47.92 all X_b Ga F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),Ga))->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)),semilattice_inf_inf(fun(X_b,bool)),F_1),Ga)))).
% 48.27/47.92 all X_b B_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2)))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all A_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),A_2),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3))=ti(X_b,A_2))))).
% 48.27/47.92 all X_b A_3 B_2 C_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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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_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),C_3))).
% 48.27/47.92 all X_b A_3 B_2 C_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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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_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),C_3))).
% 48.27/47.92 all X_b A_3 B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))=ti(fun(X_b,bool),A_3)).
% 48.27/47.92 all X_b Pa Qa (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)),Qa))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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),Qa))).
% 48.27/47.92 all X_b X_2 A_3 Pa (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))))<->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(X_b,bool,Pa,X_2))).
% 48.27/47.92 all X_b R_1 S_1 X (hBOOL(hAPP(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)),semilattice_inf_inf(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_1)),X))<->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),R_1),S_1)))).
% 48.27/47.92 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)),semilattice_inf_inf(fun(X_b,bool)),A_3),A_3)=ti(fun(X_b,bool),A_3)).
% 48.27/47.92 all X_a (semilattice_inf(X_a)-> (all A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),A_1)=ti(X_a,A_1)))).
% 48.27/47.92 all X_a (semilattice_inf(X_a)-> (all X_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),X_1)=ti(X_a,X_1)))).
% 48.27/47.92 all X_b X_c (minus(X_c)-> (all A_3 B_2 X (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_2),X)=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)),hAPP(X_b,X_c,B_2,X))))).
% 48.27/47.92 all X_b X_c (lattice(X_c)-> (all F G X (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)),semilattice_inf_inf(fun(X_b,X_c)),F),G),X)=hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),semilattice_inf_inf(X_c),hAPP(X_b,X_c,F,X)),hAPP(X_b,X_c,G,X))))).
% 48.27/47.92 all X_b A_3 B_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),B_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(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_2))))).
% 48.27/47.92 all X_b A_3 B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_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(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(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_2)))).
% 48.27/47.92 all X_b A_3 B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),A_3)).
% 48.27/47.92 all X_a (semilattice_inf(X_a)-> (all A_1 B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B),A_1)))).
% 48.27/47.92 all X_a (lattice(X_a)-> (all X_1 Y (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),X_1)))).
% 48.27/47.92 all X_a (semilattice_inf(X_a)-> (all X_1 Y (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),X_1)))).
% 48.27/47.92 all X_b A_3 B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)).
% 48.27/47.92 all X_a (semilattice_inf(X_a)-> (all A_1 B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)))).
% 48.27/47.92 all X_a (lattice(X_a)-> (all X_1 Y (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)))).
% 48.27/47.92 all X_a (semilattice_inf(X_a)-> (all X_1 Y (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)))).
% 48.27/47.92 all X_b A_3 B_2 C_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),C_3))).
% 48.27/47.92 all X_a (semilattice_inf(X_a)-> (all B A_1 C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),C))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B),C))))).
% 48.27/47.92 all X_a (lattice(X_a)-> (all X_1 Y Z (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Z))))).
% 48.27/47.92 all X_a (semilattice_inf(X_a)-> (all X_1 Y Z (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Z))))).
% 48.27/47.92 all X_b C_1 A_3 B_2 (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_2)))<->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_2))).
% 48.27/47.92 all X_b C_1 A_3 B_2 (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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))<->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_2))).
% 48.27/47.92 all X_b C_3 A_3 B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),C_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),B_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)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),C_3),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)),semilattice_inf_inf(fun(X_b,bool)),C_3),B_2))).
% 48.27/47.92 all X_b A_3 B_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)),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_2)),B_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),B_2)).
% 48.27/47.92 all X_b A_3 B_2 C_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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),C_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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)),B_2),C_3))).
% 48.27/47.92 all X_b A_3 B_2 C_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),C_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3))).
% 48.27/47.92 all X_a (semilattice_inf(X_a)-> (all A_1 B C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)),C)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B),C))))).
% 48.27/47.92 all X_a (lattice(X_a)-> (all X_1 Y Z (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)),Z)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))))).
% 48.27/47.92 all X_a (semilattice_inf(X_a)-> (all X_1 Y Z (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)),Z)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))))).
% 48.27/47.92 all X_b A_3 B_2 C_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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_2)),C_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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),C_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3))).
% 48.27/47.92 all X_b A_3 C_3 B_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)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),C_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),C_3)),B_2)).
% 48.27/47.92 all X_c X_b (minus(X_b)-> (all A_3 B_2 X_2 (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_2),X_2)=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_2)),hAPP(X_c,X_b,B_2,X_2))))).
% 48.27/47.92 all X_c X_b (lattice(X_b)-> (all F G X_2 (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)),semilattice_inf_inf(fun(X_c,X_b)),F),G),X_2)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,G,X_2))))).
% 48.27/47.92 all X_b C_1 A_3 B_2 (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_2)))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3))).
% 48.27/47.92 all X_b C_1 A_3 B_2 (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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3))).
% 48.27/47.92 all X_b C_1 A_3 B_2 (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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))).
% 48.27/47.92 all X_b C_1 A_3 B_2 (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_2)))-> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))).
% 48.27/47.92 all X_b A_3 B_2 X_2 (hBOOL(hAPP(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2),X_2))->hBOOL(hAPP(X_b,bool,A_3,X_2))).
% 48.27/47.92 all X_b A_3 B_2 X_2 (hBOOL(hAPP(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2),X_2))->hBOOL(hAPP(X_b,bool,B_2,X_2))).
% 48.27/47.92 all X_a (lattice(X_a)-> (all X_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),X_1)=ti(X_a,X_1)))).
% 48.27/47.92 all X_b A_3 B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)=bot_bot(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_2)=ti(fun(X_b,bool),A_3)).
% 48.27/47.92 all X_b A_3 B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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)),B_2),A_3))=bot_bot(fun(X_b,bool))).
% 48.27/47.92 all X_a (bounded_lattice_bot(X_a)-> (all X_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),bot_bot(X_a)),X_1)=bot_bot(X_a)))).
% 48.27/47.92 all X_a (bounded_lattice_bot(X_a)-> (all X_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),bot_bot(X_a))=bot_bot(X_a)))).
% 48.27/47.92 all X_a (lattice(X_a)-> (all X_1 Y (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y))=ti(X_a,X_1)))).
% 48.27/47.92 all X_a (lattice(X_a)-> (all X_1 Y (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y))=ti(X_a,X_1)))).
% 48.27/47.92 all X_a (distrib_lattice(X_a)-> (all X_1 Y Z (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Z))))).
% 48.27/47.92 all X_a (distrib_lattice(X_a)-> (all X_1 Y Z (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Z))))).
% 48.27/47.92 all X_a (distrib_lattice(X_a)-> (all Y Z X_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)),X_1)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Z),X_1))))).
% 48.27/47.92 all X_a (distrib_lattice(X_a)-> (all Y Z X_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)),X_1)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Z),X_1))))).
% 48.27/47.92 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))).
% 48.27/47.92 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)).
% 48.27/47.92 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))).
% 48.27/47.92 all X_b A_3 B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2)))<->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)))).
% 48.27/47.92 all X_b A_3 X_2 B_2 ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_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)),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),A_3)),B_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),B_2))& (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_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)),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),A_3)),B_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_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),B_2)))).
% 48.27/47.92 all X_b A_3 X_2 B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_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)),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),A_3)),B_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),B_2)).
% 48.27/47.92 all X_b B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),bot_bot(fun(X_b,bool))),B_2)=bot_bot(fun(X_b,bool))).
% 48.27/47.92 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)),semilattice_inf_inf(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool)))=bot_bot(fun(X_b,bool))).
% 48.27/47.92 all X_b A_3 B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)=bot_bot(fun(X_b,bool))<-> (all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3))-> (all Xa (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Xa),B_2))->ti(X_b,X)!=ti(X_b,Xa)))))).
% 48.27/47.92 all X_b A_3 B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),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)),B_2),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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)).
% 48.27/47.92 all X_b B_2 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)),semilattice_sup_sup(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)),B_2),A_3)),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)),semilattice_sup_sup(fun(X_b,bool)),B_2),A_3)).
% 48.27/47.92 all X_b A_3 B_2 C_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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),C_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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),C_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)),B_2),C_3))).
% 48.27/47.92 all X_b B_2 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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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_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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))& (-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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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_2))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))).
% 48.27/47.92 all X_b B_2 A_2 C_3 ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),C_3))->hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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),B_2)),C_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)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3)))& (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),C_3))->hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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),B_2)),C_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3))).
% 48.27/47.92 all X_b A_2 A_3 B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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)),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_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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))).
% 48.27/47.92 all X_b B_2 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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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_2))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)).
% 48.27/47.92 all X_b B_2 A_2 C_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),C_3))->hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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),B_2)),C_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3)).
% 48.27/47.92 all X_b B_2 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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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_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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))).
% 48.27/47.92 all X_b B_2 A_2 C_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),C_3))->hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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),B_2)),C_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)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3))).
% 48.27/47.92 all X_b A_3 B_2 C_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),C_3))).
% 48.27/47.92 all X_b A_3 B_2 C_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),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)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),C_3))).
% 48.27/47.92 all X_b B_2 C_3 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)),semilattice_inf_inf(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)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3)),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)),semilattice_sup_sup(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)),semilattice_inf_inf(fun(X_b,bool)),B_2),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)),semilattice_inf_inf(fun(X_b,bool)),C_3),A_3))).
% 48.27/47.92 all X_b B_2 C_3 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)),semilattice_sup_sup(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)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3)),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)),semilattice_inf_inf(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)),semilattice_sup_sup(fun(X_b,bool)),B_2),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)),semilattice_sup_sup(fun(X_b,bool)),C_3),A_3))).
% 48.27/47.92 all X_b A_3 B_2 C_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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)),semilattice_sup_sup(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),C_3),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)),semilattice_inf_inf(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)),semilattice_inf_inf(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),C_3),A_3))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2),bot_bot(fun(X_b,bool))))=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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_2),A_3))=ti(X_b,X_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),X_2),bot_bot(fun(X_b,bool))))!=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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_2),bot_bot(fun(X_b,bool)))))))))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),bot_bot(fun(X_b,bool))))=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)=ti(X_b,X_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),X_2),bot_bot(fun(X_b,bool))))!=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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_2),bot_bot(fun(X_b,bool))))))))))).
% 48.27/47.92 all X_b A_3 A_2 B_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),B_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)),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_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))))).
% 48.27/47.92 all X_b A_3 A_2 B_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),B_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)),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_2)).
% 48.27/47.92 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)).
% 48.27/47.92 all 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),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_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_2),bot_bot(fun(X_b,bool))))=ti(fun(X_b,bool),A_3)).
% 48.27/47.92 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)).
% 48.27/47.92 all X_b A_3 A_2 B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2))))<->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2)))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all B_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))-> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)!=bot_bot(fun(X_b,bool))->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),B_2))))))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all B_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(X_b),B_2))-> (ti(fun(X_b,bool),B_2)!=bot_bot(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),B_2))))))))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all X_2 (hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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_2),bot_bot(fun(X_b,bool))))=ti(X_b,X_2)))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (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_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3))=hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3))))).
% 48.27/47.92 all X_c X_b Pa F G S_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),hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,X_b)),combs(X_c,X_b,X_b),hAPP(fun(X_c,X_b),fun(X_c,fun(X_b,X_b)),hAPP(fun(X_c,fun(X_b,fun(X_b,X_b))),fun(fun(X_c,X_b),fun(X_c,fun(X_b,X_b))),combs(X_c,X_b,fun(X_b,X_b)),hAPP(fun(X_c,bool),fun(X_c,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_c,bool),fun(X_c,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_c),if(X_b)),Pa)),F)),G)),S_1)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_inf_inf(fun(X_c,bool)),S_1),hAPP(fun(X_c,bool),fun(X_c,bool),collect(X_c),Pa)))),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),G),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_inf_inf(fun(X_c,bool)),S_1),hAPP(fun(X_c,bool),fun(X_c,bool),collect(X_c),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(bool,bool),fun(fun(X_c,bool),fun(X_c,bool)),combb(bool,bool,X_c),fNot),Pa)))))).
% 48.27/47.92 all X_b X_2 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_1(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),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_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),X_2),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_2),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_2),bot_bot(fun(X_b,bool)))))))))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all N_3 H ((all X Y_2 (hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X),Y_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(X_b,X_b,H,X)),hAPP(X_b,X_b,H,Y_2))))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3))-> (ti(fun(X_b,bool),N_3)!=bot_bot(fun(X_b,bool))->hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),N_3))=hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),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_3))))))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))-> ((all X Y_2 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),semilattice_sup_sup(X_b),X),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),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)))))))->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,big_lattice_Sup_fin(X_b),A_3)),A_3))))))).
% 48.27/47.92 all X_b Pa A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(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))))))).
% 48.27/47.92 all X_a (lattice(X_a)-> (all X_1 Y Z ((all X Y_2 Z_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y_2),Z_2))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Z_2))))->hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Z))))).
% 48.27/47.92 all X_a (lattice(X_a)-> (all X_1 Y Z ((all X Y_2 Z_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y_2),Z_2))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Z_2))))->hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Z))))).
% 48.27/47.92 all X_c X_b B_2 A_3 F Z_1 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_1),G),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))-> (hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_inf_inf(fun(X_c,bool)),A_3),B_2)=bot_bot(fun(X_c,bool))->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)),semilattice_sup_sup(fun(X_c,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,A_3)),hAPP(fun(X_c,bool),X_b,F_1,B_2)))))).
% 48.27/47.92 all X_c X_b X_2 A_3 F Z_1 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_1),G),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),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))->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_2)),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_2),bot_bot(fun(X_c,bool))))))))).
% 48.27/47.92 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N_2)=zero_zero(nat)).
% 48.27/47.92 all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat))=M).
% 48.27/47.92 all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M)=zero_zero(nat)).
% 48.27/47.92 all M N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)=zero_zero(nat)-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),M)=zero_zero(nat)->M=N_2)).
% 48.27/47.92 all M N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)).
% 48.27/47.92 all M N_2 K_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N_2)),hAPP(nat,nat,suc,K_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)),K_2)).
% 48.27/47.92 all X_c X_b F Z_1 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_1),G),F_1))->hAPP(fun(X_c,bool),X_b,F_1,bot_bot(fun(X_c,bool)))=ti(X_b,Z_1)).
% 48.27/47.92 all X_c X_b X_2 A_3 F Z_1 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_1),G),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),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))->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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_2)),hAPP(fun(X_c,bool),X_b,F_1,A_3))))).
% 48.27/47.92 all X_c X_b A_3 F Z_1 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_1),G),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(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_1),A_3))).
% 48.27/47.92 all X_c X_b B_2 A_3 F Z_1 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_1),G),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,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)),semilattice_sup_sup(fun(X_c,bool)),A_3),B_2))),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)),semilattice_inf_inf(fun(X_c,bool)),A_3),B_2)))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,A_3)),hAPP(fun(X_c,bool),X_b,F_1,B_2))))).
% 48.27/47.92 all X_c X_b X_2 A_3 F Z_1 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_1),G),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_2)),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_2),bot_bot(fun(X_c,bool)))))))).
% 48.27/47.92 all X_c X_b B_2 A_3 F Z_1 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_1),G),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))-> ((all X (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_inf_inf(fun(X_c,bool)),A_3),B_2)))->hAPP(X_c,X_b,G,X)=ti(X_b,Z_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)),semilattice_sup_sup(fun(X_c,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,A_3)),hAPP(fun(X_c,bool),X_b,F_1,B_2)))))).
% 48.27/47.92 all X_c X_b A_3 F Z_1 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_1),G),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3))-> ((all X (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X),A_3))->hAPP(X_c,X_b,G,X)=ti(X_b,Z_1)))->hAPP(fun(X_c,bool),X_b,F_1,A_3)=ti(X_b,Z_1)))).
% 48.27/47.92 all X_b (group_add(X_b)-> (all A_2 B_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1)=zero_zero(X_b)<->ti(X_b,A_2)=ti(X_b,B_1)))).
% 48.27/47.92 all X_b (ab_group_add(X_b)-> (all A_2 B_1 (ti(X_b,A_2)=ti(X_b,B_1)<->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1)=zero_zero(X_b)))).
% 48.27/47.92 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)))).
% 48.27/47.92 all I J_1 K_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J_1)),K_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),K_2)),J_1)).
% 48.27/47.92 all X_b (zero(X_b)-> (all X_2 (zero_zero(X_b)=ti(X_b,X_2)<->ti(X_b,X_2)=zero_zero(X_b)))).
% 48.27/47.92 all X_b (ab_group_add(X_b)-> (all A_2 B_1 C_1 D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D)-> (ti(X_b,A_2)=ti(X_b,B_1)<->ti(X_b,C_1)=ti(X_b,D))))).
% 48.27/47.92 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)))).
% 48.27/47.92 all I_1 Pa K_1 (hBOOL(hAPP(nat,bool,Pa,K_1))-> ((all N (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N)))->hBOOL(hAPP(nat,bool,Pa,N))))->hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K_1),I_1))))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all B_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(X_b),B_2))-> (ti(fun(X_b,bool),B_2)!=bot_bot(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),B_2))))))))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all B_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))-> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)!=bot_bot(fun(X_b,bool))->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),B_2))))))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2),bot_bot(fun(X_b,bool))))=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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_2),A_3))=ti(X_b,X_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),X_2),bot_bot(fun(X_b,bool))))!=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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_2),bot_bot(fun(X_b,bool)))))))))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),bot_bot(fun(X_b,bool))))=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)=ti(X_b,X_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),X_2),bot_bot(fun(X_b,bool))))!=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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_2),bot_bot(fun(X_b,bool))))))))))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all X_2 (hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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_2),bot_bot(fun(X_b,bool))))=ti(X_b,X_2)))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all A_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),A_2),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3))=ti(X_b,A_2))))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (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_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3))=hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3))))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (-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))->hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3))))))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)))))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all B_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(X_b),B_2))-> (ti(fun(X_b,bool),B_2)!=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),B_2)))))))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all N_3 H ((all X Y_2 (hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X),Y_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(X_b,X_b,H,X)),hAPP(X_b,X_b,H,Y_2))))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3))-> (ti(fun(X_b,bool),N_3)!=bot_bot(fun(X_b,bool))->hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),N_3))=hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),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_3))))))).
% 48.27/47.92 all X_b (lattice(X_b)-> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))-> ((all X Y_2 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),semilattice_inf_inf(X_b),X),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),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)))))))->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,big_lattice_Inf_fin(X_b),A_3)),A_3))))))).
% 48.27/47.92 all M_1 N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,suc,N_1))=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_1),N_1))).
% 48.27/47.92 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)))))).
% 48.27/47.92 all X_b X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2),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_2),bot_bot(fun(X_b,bool))))))).
% 48.27/47.92 all X_b X_c X_2 Z_1 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_2),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_2),Z_1))=hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_2),Z_1)).
% 48.27/47.92 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))).
% 48.27/47.92 all X_b (hAPP(fun(X_b,bool),nat,finite_card(X_b),bot_bot(fun(X_b,bool)))=zero_zero(nat)).
% 48.27/47.92 all X_b A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))->hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=zero_zero(nat)).
% 48.27/47.92 all X_b (semilattice_sup(X_b)->hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),semilattice_sup_sup(X_b)))).
% 48.27/47.92 all X_b (semilattice_inf(X_b)->hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),semilattice_inf_inf(X_b)))).
% 48.27/47.92 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)).
% 48.27/47.92 all X_b F1 F2 Nat (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))=hAPP(nat,X_b,F2,Nat)).
% 48.27/47.92 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_1(X_b),A_3))).
% 48.27/47.92 all X_b X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),A_3))=hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))).
% 48.27/47.92 all X_b X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),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_2),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_2),A_3))=hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))).
% 48.27/47.92 all X_b A_3 B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))->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_2))=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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))).
% 48.27/47.92 all X_b X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),bot_bot(fun(X_b,bool))))))=hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))).
% 48.27/47.92 all X_b A_3 K_1 (hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=hAPP(nat,nat,suc,K_1)<-> (exists B_4 B_3 (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_4),B_3)& -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_4),B_3))&hAPP(fun(X_b,bool),nat,finite_card(X_b),B_3)=K_1& (K_1=zero_zero(nat)->ti(fun(X_b,bool),B_3)=bot_bot(fun(X_b,bool)))))).
% 48.27/47.92 all X_b A_3 K_1 (hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=hAPP(nat,nat,suc,K_1)-> (exists B_4 B_3 (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_4),B_3)& -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_4),B_3))&hAPP(fun(X_b,bool),nat,finite_card(X_b),B_3)=K_1& (K_1=zero_zero(nat)->ti(fun(X_b,bool),B_3)=bot_bot(fun(X_b,bool)))))).
% 48.27/47.92 all X_b X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),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_2),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_2),bot_bot(fun(X_b,bool)))))=hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))).
% 48.27/47.92 all X_b X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),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)))).
% 48.27/47.92 all X_b B_2 A_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2))->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_2)))=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_2))),one_one(nat))))).
% 48.27/47.92 all X_b (one(X_b)-> (all X_2 (one_one(X_b)=ti(X_b,X_2)<->ti(X_b,X_2)=one_one(X_b)))).
% 48.27/47.92 one_one(nat)=hAPP(nat,nat,suc,zero_zero(nat)).
% 48.27/47.92 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N_2)),one_one(nat))=N_2).
% 48.27/47.92 all M N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,N_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N_2)).
% 48.27/47.92 all X_b A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (((exists X hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3)))->one_one(nat)=zero_zero(nat))->hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=zero_zero(nat))).
% 48.27/47.92 all X_a (zero_ne_q_one(X_a)->one_one(X_a)!=zero_zero(X_a)).
% 48.27/47.92 all X_a (zero_ne_q_one(X_a)->zero_zero(X_a)!=one_one(X_a)).
% 48.27/47.92 all X_b X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),bot_bot(fun(X_b,bool)))))))).
% 48.27/47.92 all X_b X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2),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_2),bot_bot(fun(X_b,bool))))))).
% 48.27/47.92 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N_2)=N_2).
% 48.27/47.92 all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),zero_zero(nat))=M).
% 48.27/47.92 all M_1 N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)=zero_zero(nat)<->M_1=zero_zero(nat)&N_1=zero_zero(nat)).
% 48.27/47.92 all M N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)=M->N_2=zero_zero(nat)).
% 48.27/47.92 all M N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N_2))=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2))).
% 48.27/47.92 all M N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N_2)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2))).
% 48.27/47.92 all M N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N_2))).
% 48.27/47.92 all M N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),M)).
% 48.27/47.92 all X_1 Y Z (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X_1),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_1),Z))).
% 48.27/47.92 all M N_2 K_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)),K_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K_2))).
% 48.27/47.92 all K_1 M_1 N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_1)<->M_1=N_1).
% 48.27/47.92 all M_1 K_1 N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K_1)<->M_1=N_1).
% 48.27/47.92 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))))).
% 48.27/47.92 all X_b (cancel_semigroup_add(X_b)-> (all A_2 B_1 C_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),B_1)=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_1)=ti(X_b,C_1)))).
% 48.27/47.92 all X_b (cancel_semigroup_add(X_b)-> (all B_1 A_2 C_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_1),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_1)=ti(X_b,C_1)))).
% 48.27/47.92 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)))).
% 48.27/47.92 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)))).
% 48.27/47.92 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)))).
% 48.27/47.92 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)))).
% 48.27/47.92 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)))).
% 48.27/47.92 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)))).
% 48.27/47.92 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)))).
% 48.27/47.92 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)))).
% 48.27/47.92 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)))).
% 48.27/47.92 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)))).
% 48.27/47.92 all M N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)),N_2)=M).
% 48.27/47.92 all N_2 M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),M)),N_2)=M).
% 48.27/47.92 all I J_1 K_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J_1)),K_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),K_2))).
% 48.27/47.92 all K_2 M N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),N_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)).
% 48.27/47.92 all M K_2 N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)).
% 48.27/47.92 all M_1 N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)=hAPP(nat,nat,suc,zero_zero(nat))<->M_1=hAPP(nat,nat,suc,zero_zero(nat))&N_1=zero_zero(nat)|M_1=zero_zero(nat)&N_1=hAPP(nat,nat,suc,zero_zero(nat))).
% 48.27/47.92 all M_1 N_1 (hAPP(nat,nat,suc,zero_zero(nat))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)<->M_1=hAPP(nat,nat,suc,zero_zero(nat))&N_1=zero_zero(nat)|M_1=zero_zero(nat)&N_1=hAPP(nat,nat,suc,zero_zero(nat))).
% 48.27/47.92 all N_2 M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),M))=zero_zero(nat)).
% 48.27/47.92 all N_2 (hAPP(nat,nat,suc,N_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),one_one(nat))).
% 48.27/47.92 all N_2 (hAPP(nat,nat,suc,N_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N_2)).
% 48.27/47.92 all X_b B_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))->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_b,bool),nat,finite_card(X_b),B_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))),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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))))).
% 48.27/47.92 all X_b B_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))),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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))=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_b,bool),nat,finite_card(X_b),B_2)))).
% 48.27/47.92 all N_2 M ((M=zero_zero(nat)->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)=N_2)& (M!=zero_zero(nat)->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N_2)))).
% 48.27/47.92 all X_b X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),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)))).
% 48.27/47.92 all X_b A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)).
% 48.27/47.92 all X_b A_3 ((hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(X_b),A_3))->hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=zero_zero(nat))).
% 48.27/47.92 all X_b B_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))-> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)=bot_bot(fun(X_b,bool))->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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=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_b,bool),nat,finite_card(X_b),B_2))))).
% 48.27/47.92 all X_b B_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))-> (((exists X hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))))->one_one(nat)=zero_zero(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=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_b,bool),nat,finite_card(X_b),B_2))))).
% 48.27/47.92 all Com1_2 Com2_2 (hAPP(com,nat,com_size,hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,com_size,Com1_2)),hAPP(com,nat,com_size,Com2_2))),hAPP(nat,nat,suc,zero_zero(nat)))).
% 48.27/47.92 all Fun_1 Com_1 (hAPP(com,nat,com_size,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,com_size,Com_1)),hAPP(nat,nat,suc,zero_zero(nat)))).
% 48.27/47.92 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)))).
% 48.27/47.92 all X_b (semiri456707255roduct(X_b)-> (all B_1 A_2 (ti(X_b,B_1)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_1),A_2)<->ti(X_b,A_2)=zero_zero(X_b)))).
% 48.27/47.92 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)))).
% 48.27/47.92 all X_a (comm_semiring_1(X_a)-> (all A_1 C D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),D_1))))).
% 48.27/47.92 all X_a (comm_semiring_1(X_a)-> (all A_1 C D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),D_1)))).
% 48.27/47.92 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))))).
% 48.27/47.92 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)))).
% 48.27/47.92 all X_a (comm_semiring_1(X_a)-> (all A_1 B C D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))))).
% 48.27/47.92 all Pname_1 (hAPP(com,nat,com_size,hAPP(pname,com,body,Pname_1))=zero_zero(nat)).
% 48.27/47.92 hAPP(com,nat,com_size,skip)=zero_zero(nat).
% 48.27/47.92 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)))).
% 48.27/47.92 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)))).
% 48.27/47.92 all X_c X_b B_2 A_3 ((hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))&hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))->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_2))=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_2)))& (-(hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))&hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2)))->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_2))=zero_zero(nat))).
% 48.27/47.92 all Com1_2 Com2_2 (hAPP(com,nat,size_size(com),hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,size_size(com),Com1_2)),hAPP(com,nat,size_size(com),Com2_2))),hAPP(nat,nat,suc,zero_zero(nat)))).
% 48.27/47.92 all Fun_1 Com_1 (hAPP(com,nat,size_size(com),hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,size_size(com),Com_1)),hAPP(nat,nat,suc,zero_zero(nat)))).
% 48.27/47.92 all X_b X_c (comm_monoid_mult(X_c)-> (all G B_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))-> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)=bot_bot(fun(X_b,bool))->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)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=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)),G),one_one(X_c)),B_2))))))).
% 48.27/47.92 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)))).
% 48.27/47.92 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)))).
% 48.27/47.92 all K_2 M N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),N_2))).
% 48.27/47.92 all M N_2 K_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)),K_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_2))).
% 48.27/47.92 all X_b (semiri456707255roduct(X_b)-> (all W Y_1 X_2 Z_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),W),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),Z_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),W),Z_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),Y_1))<->ti(X_b,W)=ti(X_b,X_2)|ti(X_b,Y_1)=ti(X_b,Z_1)))).
% 48.27/47.92 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)))).
% 48.27/47.92 all X_a (comm_semiring_1(X_a)-> (all A_1 M B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),M))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),M)))).
% 48.27/47.92 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))))).
% 48.27/47.92 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))))).
% 48.27/47.92 all X_b (semiri456707255roduct(X_b)-> (all C_1 D A_2 B_1 (ti(X_b,A_2)!=ti(X_b,B_1)&ti(X_b,C_1)!=ti(X_b,D)<->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_1),D))!=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)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_1),C_1))))).
% 48.27/47.92 all X_a (comm_semiring_1(X_a)-> (all X_1 Y Z (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),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_1),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Z))))).
% 48.27/47.92 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)))).
% 48.27/47.92 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)))).
% 48.27/47.92 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)))).
% 48.27/47.92 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))))).
% 48.27/47.92 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)))).
% 48.27/47.92 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))))).
% 48.27/47.92 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)))).
% 48.27/47.92 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)))))).
% 48.27/47.92 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))))).
% 48.27/47.92 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))))).
% 48.27/47.92 all M_1 N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)=one_one(nat)<->M_1=one_one(nat)&N_1=one_one(nat)).
% 48.27/47.93 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),one_one(nat))=N_2).
% 48.27/47.93 all M_1 N_1 (one_one(nat)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)<->M_1=one_one(nat)&N_1=one_one(nat)).
% 48.27/47.93 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N_2)=N_2).
% 48.27/47.93 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),N_2)=zero_zero(nat)).
% 48.27/47.93 all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),zero_zero(nat))=zero_zero(nat)).
% 48.27/47.93 all M_1 N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)=zero_zero(nat)<->M_1=zero_zero(nat)|N_1=zero_zero(nat)).
% 48.27/47.93 all K_1 M_1 N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1)<->M_1=N_1|K_1=zero_zero(nat)).
% 48.27/47.93 all M_1 K_1 N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K_1)<->M_1=N_1|K_1=zero_zero(nat)).
% 48.27/47.93 all K_1 M_1 N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_1)<->M_1=N_1).
% 48.27/47.93 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)))).
% 48.27/47.93 all X_a (ab_sem1668676832m_mult(X_a)-> (all X_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)=ti(X_a,X_1)))).
% 48.27/47.93 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)))).
% 48.27/47.93 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))))).
% 48.27/47.93 all M N_2 K_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)),K_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_2))).
% 48.27/47.93 all K_2 M N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),N_2))).
% 48.27/47.93 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)))).
% 48.27/47.93 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)))).
% 48.27/47.93 all X_b (ring_n68954251visors(X_b)-> (all A_2 B_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_1)=zero_zero(X_b)<->ti(X_b,A_2)=zero_zero(X_b)|ti(X_b,B_1)=zero_zero(X_b)))).
% 48.27/47.93 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))))).
% 48.27/47.93 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)))).
% 48.27/47.93 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)))).
% 48.27/47.93 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)))).
% 48.27/47.93 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)))).
% 48.27/47.93 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)))).
% 48.27/47.93 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)))).
% 48.27/47.93 all X_b X_c A_3 B_2 (hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite_1(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_2)))->hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))).
% 48.27/47.93 all X_b X_c A_3 B_2 (hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite_1(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_2)))->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))).
% 48.27/47.93 all X_c X_b B_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))->hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite_1(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_2))))).
% 48.27/47.93 all X_b X_c A_3 B_2 (hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite_1(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_2)))<->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))&hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))).
% 48.27/47.93 all X_b (linord581940658strict(X_b)-> (all X_2 Y_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),X_2),X_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_1),Y_1))=zero_zero(X_b)<->ti(X_b,X_2)=zero_zero(X_b)&ti(X_b,Y_1)=zero_zero(X_b)))).
% 48.27/47.93 all X_a (semiri456707255roduct(X_a)-> (all C D_1 A_1 B R_2 (ti(X_a,R_2)!=zero_zero(X_a)-> (ti(X_a,A_1)=ti(X_a,B)&ti(X_a,C)!=ti(X_a,D_1)->hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_2),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_2),D_1)))))).
% 48.27/47.93 all X_b (ring(X_b)-> (all A_2 E C_1 B_1 D (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_1),E)),D)<->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_1),A_2)),E)),D)))).
% 48.27/47.93 all X_b (ring(X_b)-> (all A_2 E C_1 B_1 D (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_1),E)),D)<->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_1)),E)),C_1)=ti(X_b,D)))).
% 48.27/47.93 all X_a (comm_semiring_1(X_a)-> (all M (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),M)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),M)))).
% 48.27/47.93 all X_a (comm_semiring_1(X_a)-> (all M A_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M)))).
% 48.27/47.93 all X_a (comm_semiring_1(X_a)-> (all A_1 M (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),M)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M)))).
% 48.27/47.93 all M_1 N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)=hAPP(nat,nat,suc,zero_zero(nat))<->M_1=hAPP(nat,nat,suc,zero_zero(nat))&N_1=hAPP(nat,nat,suc,zero_zero(nat))).
% 48.27/47.93 all M N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,M)),N_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2))).
% 48.27/47.93 all M N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,suc,N_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2))).
% 48.27/47.93 all M N_2 (M=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2)->N_2=one_one(nat)|M=zero_zero(nat)).
% 48.27/47.93 all X_b X_c (ab_semigroup_mult(X_c)-> (all G Z_1 A_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_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),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_1),A_3)))))).
% 48.27/47.93 all Pname_1 (hAPP(com,nat,size_size(com),hAPP(pname,com,body,Pname_1))=zero_zero(nat)).
% 48.27/47.93 all X_b X_c (comm_monoid_mult(X_c)-> (all G H A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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))))).
% 48.27/47.93 hAPP(com,nat,size_size(com),skip)=zero_zero(nat).
% 48.27/47.93 all N_2 M ((M=zero_zero(nat)->hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2)=zero_zero(nat))& (M!=zero_zero(nat)->hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N_2)))).
% 48.27/47.93 all X_c X_b B_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))->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_2))=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_2)))).
% 48.27/47.93 all X_b X_c (comm_monoid_mult(X_c)-> (all G B_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))->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)),G),one_one(X_c)),B_2))=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)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_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),one_one(X_c)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))))))).
% 48.27/47.93 all X_b X_c (comm_monoid_mult(X_c)-> (all F T_5 S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),T_5))-> ((all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),S_1),T_5)))->hAPP(X_b,X_c,F,X)=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)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),S_1),T_5))=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)),F),one_one(X_c)),S_1)),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)),T_5))))))).
% 48.27/47.93 all X_b X_c (comm_monoid_mult(X_c)-> (all F S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1))-> ((all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),S_1))->hAPP(X_b,X_c,F,X)=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_1)=one_one(X_c))))).
% 48.27/47.93 all X_b X_c (ab_semigroup_mult(X_c)-> (all Z_1 G H A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> ((all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3))->hAPP(X_b,X_c,G,X)=hAPP(X_b,X_c,H,X)))->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_1),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_1),A_3))))).
% 48.27/47.93 all X_c X_b A_3 B_2 (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_2)=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_2)=bot_bot(fun(X_c,bool))).
% 48.27/47.93 all M N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),M)).
% 48.27/47.93 all M N_2 K_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2)),K_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_2))).
% 48.27/47.93 all I U_1 J_1 K_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U_1)),K_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_1)),U_1)),K_2)).
% 48.27/47.93 all K_1 M_1 N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1)<->K_1=zero_zero(nat)|M_1=N_1).
% 48.27/47.93 all X_c X_b X_d (comm_monoid_mult(X_d)-> (all E G F H K_1 T_5 S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1))-> ((all Y_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Y_2),T_5))->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_1,Y_2)),S_1))&hAPP(X_b,X_c,H,hAPP(X_c,X_b,K_1,Y_2))=ti(X_c,Y_2)))-> ((all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),S_1))->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)),T_5))&hAPP(X_c,X_b,K_1,hAPP(X_b,X_c,H,X))=ti(X_b,X)&hAPP(X_c,X_d,G,hAPP(X_b,X_c,H,X))=hAPP(X_b,X_d,F,X)))->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_1)=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_5)))))).
% 48.27/47.93 all X_c X_b (comm_monoid_mult(X_b)-> (all H G S_1 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_1(X_c),S_1))-> ((all X (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X),S_1))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_c,X_b,H,X)),hAPP(X_c,X_b,G,X)))))->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_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)),G),E),S_1))))))))).
% 48.27/47.93 all X_b (ab_semigroup_mult(X_b)-> (all B_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(X_b),B_2))-> (ti(fun(X_b,bool),B_2)!=bot_bot(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),B_2))))))))).
% 48.27/47.93 all Fun_1 Com1_1 Com2_1 (hAPP(com,nat,size_size(com),hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,size_size(com),Com1_1)),hAPP(com,nat,size_size(com),Com2_1))),hAPP(nat,nat,suc,zero_zero(nat)))).
% 48.27/47.93 all Fun_1 Com1_1 Com2_1 (hAPP(com,nat,com_size,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,com_size,Com1_1)),hAPP(com,nat,com_size,Com2_1))),hAPP(nat,nat,suc,zero_zero(nat)))).
% 48.27/47.93 all X_b X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))).
% 48.27/47.93 all X_a (preorder(X_a)-> (all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),X_1)))).
% 48.27/47.93 all K_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(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_1)))).
% 48.27/47.93 all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N_2)).
% 48.27/47.93 all B_1 C1 C2 S_2 N_1 T_4 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C1),C2)),S_2),N_1),T_4))-> ((hBOOL(hAPP(state,bool,B_1,S_2))-> -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1),S_2),N_1),T_4)))-> -(-hBOOL(hAPP(state,bool,B_1,S_2))-> -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2),S_2),N_1),T_4))))).
% 48.27/47.93 all C1 C0 N_1 S1 B_1 S_2 (hBOOL(hAPP(state,bool,B_1,S_2))-> (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C0),S_2),N_1),S1))->hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C0),C1)),S_2),N_1),S1)))).
% 48.27/47.93 all C0 C1 N_1 S1 B_1 S_2 (-hBOOL(hAPP(state,bool,B_1,S_2))-> (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1),S_2),N_1),S1))->hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C0),C1)),S_2),N_1),S1)))).
% 48.27/47.93 all C0 C1 S1 B_1 S_2 (-hBOOL(hAPP(state,bool,B_1,S_2))-> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1),S_2),S1))->hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C0),C1)),S_2),S1)))).
% 48.27/47.93 all C1 C0 S1 B_1 S_2 (hBOOL(hAPP(state,bool,B_1,S_2))-> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C0),S_2),S1))->hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C0),C1)),S_2),S1)))).
% 48.27/47.93 all B_1 C1 C2 S_2 T_4 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C1),C2)),S_2),T_4))-> ((hBOOL(hAPP(state,bool,B_1,S_2))-> -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1),S_2),T_4)))-> -(-hBOOL(hAPP(state,bool,B_1,S_2))-> -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C2),S_2),T_4))))).
% 48.27/47.93 all Pname Fun_1 Com1_1 Com2_1 (hAPP(pname,com,body,Pname)!=hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1)).
% 48.27/47.93 all Fun_1 Com1_1 Com2_1 Pname (hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1)!=hAPP(pname,com,body,Pname)).
% 48.27/47.93 all X_a (linorder(X_a)-> (all X_1 Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))))).
% 48.27/47.93 all X_b X_c (ord(X_c)-> (all X_2 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_2)),hAPP(X_b,X_c,G,X_2)))))).
% 48.27/47.93 all X_a (order(X_a)-> (all Z Y X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))-> (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_1)))))).
% 48.27/47.93 all X_a (order(X_a)-> (all Y X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))->ti(X_a,X_1)=ti(X_a,Y))))).
% 48.27/47.93 all X_a (preorder(X_a)-> (all Z X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),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_1),Z)))))).
% 48.27/47.93 all X_a (order(X_a)-> (all X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))->ti(X_a,X_1)=ti(X_a,Y))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 all X_b (order(X_b)-> (all Y_1 X_2 (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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),Y_1))<->ti(X_b,X_2)=ti(X_b,Y_1))))).
% 48.27/47.93 all X_b X_c (ord(X_c)-> (all X_2 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_2)),hAPP(X_b,X_c,G,X_2)))))).
% 48.27/47.93 all X_a (preorder(X_a)-> (all X_1 Y (X_1=Y->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))))).
% 48.27/47.93 all X_b (order(X_b)-> (all X_2 Y_1 (ti(X_b,X_2)=ti(X_b,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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_1),X_2))))).
% 48.27/47.93 all X_a (linorder(X_a)-> (all X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))))).
% 48.27/47.93 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 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)),hAPP(X_b,X_c,G,X))))))).
% 48.27/47.93 all Fun_1 Com1_1 Com2_1 Fun Com1 Com2 (hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1)=hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun),Com1),Com2)<->Fun_1=Fun&Com1_1=Com1&Com2_1=Com2).
% 48.27/47.93 all M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M))->M=N_2)).
% 48.27/47.93 all K_2 I J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),K_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),K_2)))).
% 48.27/47.93 all M N_2 (M=N_2->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))).
% 48.27/47.93 all M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M))).
% 48.27/47.93 all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),N_2)).
% 48.27/47.93 all M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M)),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))).
% 48.27/47.93 all M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,suc,N_2)))-> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))->M=hAPP(nat,nat,suc,N_2))).
% 48.27/47.93 all M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,suc,N_2)))).
% 48.27/47.93 all N_1 M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_1)),hAPP(nat,nat,suc,M_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M_1))).
% 48.27/47.93 all M_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,suc,N_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))|M_1=hAPP(nat,nat,suc,N_1)).
% 48.27/47.93 all M_1 N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_1)),M_1))).
% 48.27/47.93 all N_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_2)),N_2))).
% 48.27/47.93 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),zero_zero(nat)))<->N_1=zero_zero(nat)).
% 48.27/47.93 all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N_2)).
% 48.27/47.93 all X_a (lattice(X_a)-> (all X_1 Y 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),semilattice_inf_inf(X_a),X_1),Y)),X_1)))).
% 48.27/47.93 all X_a (semilattice_inf(X_a)-> (all X_1 Y 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),semilattice_inf_inf(X_a),X_1),Y)),X_1)))).
% 48.27/47.93 all X_a (lattice(X_a)-> (all X_1 Y 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),semilattice_inf_inf(X_a),X_1),Y)),Y)))).
% 48.27/47.93 all X_a (semilattice_inf(X_a)-> (all X_1 Y 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),semilattice_inf_inf(X_a),X_1),Y)),Y)))).
% 48.27/47.93 all X_b (semilattice_inf(X_b)-> (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))<->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X_2),Y_1)=ti(X_b,X_2)))).
% 48.27/47.93 all X_b (semilattice_inf(X_b)-> (all X_2 Y_1 Z_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),Y_1),Z_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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),Z_1))))).
% 48.27/47.93 all X_a (semilattice_inf(X_a)-> (all B A_1 X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),X_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)),X_1))))).
% 48.27/47.93 all X_a (semilattice_inf(X_a)-> (all A_1 B X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),X_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)),X_1))))).
% 48.27/47.93 all X_a (semilattice_inf(X_a)-> (all X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))->hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)=ti(X_a,X_1)))).
% 48.27/47.93 all X_a (semilattice_inf(X_a)-> (all Y X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))->hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)=ti(X_a,Y)))).
% 48.27/47.93 all X_a (semilattice_inf(X_a)-> (all B X_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B))))))).
% 48.27/47.93 all X_a (semilattice_inf(X_a)-> (all Z X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Z))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))))))).
% 48.27/47.93 all X_a (semilattice_inf(X_a)-> (all B D_1 A_1 C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),C))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),D_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),C),D_1))))))).
% 48.27/47.93 all X_a (semilattice_inf(X_a)-> (all X_1 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)))-> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),A_1))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),B)))))).
% 48.27/47.93 all X_a (lattice(X_a)-> (all X_1 Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y))))).
% 48.27/47.93 all X_a (semilattice_sup(X_a)-> (all X_1 Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y))))).
% 48.27/47.93 all X_a (lattice(X_a)-> (all Y X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y))))).
% 48.27/47.93 all X_a (semilattice_sup(X_a)-> (all Y X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y))))).
% 48.27/47.93 all X_b (semilattice_sup(X_b)-> (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))<->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),Y_1)=ti(X_b,Y_1)))).
% 48.27/47.93 all X_b (semilattice_sup(X_b)-> (all X_2 Y_1 Z_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),semilattice_sup_sup(X_b),X_2),Y_1)),Z_1))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),Z_1))&hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_1),Z_1))))).
% 48.27/47.93 all X_a (semilattice_sup(X_a)-> (all B X_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B)))))).
% 48.27/47.93 all X_a (semilattice_sup(X_a)-> (all A_1 X_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B)))))).
% 48.27/47.93 all X_a (semilattice_sup(X_a)-> (all X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))->hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)=ti(X_a,Y)))).
% 48.27/47.93 all X_a (semilattice_sup(X_a)-> (all Y X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))->hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)=ti(X_a,X_1)))).
% 48.27/47.93 all X_a (semilattice_sup(X_a)-> (all B A_1 X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),X_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),X_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B)),X_1)))))).
% 48.27/47.93 all X_a (semilattice_sup(X_a)-> (all Z Y X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Z),X_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)),X_1)))))).
% 48.27/47.93 all X_a (semilattice_sup(X_a)-> (all B D_1 A_1 C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),C))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),D_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),C),D_1))))))).
% 48.27/47.93 all X_a (semilattice_sup(X_a)-> (all A_1 B X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B)),X_1))-> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),X_1))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),X_1)))))).
% 48.27/47.93 all X_b (ordered_ab_group_add(X_b)-> (all A_2 B_1 C_1 D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D)-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_1))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C_1),D)))))).
% 48.27/47.93 all M C S N_2 T_3 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C),S),N_2),T_3))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M))->hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C),S),M),T_3)))).
% 48.27/47.93 all M N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)),M)).
% 48.27/47.93 all L M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M)))).
% 48.27/47.93 all L M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),L)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),L)))).
% 48.27/47.93 all I N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),N_2))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),I))=I).
% 48.27/47.93 all N_1 K_1 M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K_1)<->M_1=N_1))).
% 48.27/47.93 all N_2 K_2 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),M))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),N_2))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),K_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2))).
% 48.27/47.93 all N_1 K_1 M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))))).
% 48.27/47.93 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))))).
% 48.27/47.93 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))))).
% 48.27/47.93 all X_a (ordere779506340up_add(X_a)-> (all C D_1 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 all X_b (ordere236663937imp_le(X_b)-> (all C_1 A_2 B_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),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B_1)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_1))))).
% 48.27/47.93 all X_b (ordere236663937imp_le(X_b)-> (all A_2 C_1 B_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),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_1),C_1)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_1))))).
% 48.27/47.93 all M K_2 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)),N_2))-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),N_2)))).
% 48.27/47.93 all M K_2 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))).
% 48.27/47.93 all M K_2 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),N_2))).
% 48.27/47.93 all K_2 L I J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),L))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),L))))).
% 48.27/47.93 all K_2 I J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),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),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),K_2)))).
% 48.27/47.93 all M I J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J_1)))).
% 48.27/47.93 all M I J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),M)))).
% 48.27/47.93 all K_1 M_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))).
% 48.27/47.93 all M_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))<-> (exists K (N_1=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K)))).
% 48.27/47.93 all N_2 M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),M))).
% 48.27/47.93 all N_2 M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2))).
% 48.27/47.93 all N_1 (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)),N_1)))=hAPP(nat,nat,suc,N_1)).
% 48.27/47.93 all M_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M_1)),N_1))<->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_1)),N_1))).
% 48.27/47.93 all X_b (semilattice_inf(X_b)-> (all X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),semilattice_inf_inf(X_b)),A_3)))<-> (all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),X))))))))).
% 48.27/47.93 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)))).
% 48.27/47.93 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)))).
% 48.27/47.93 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)))).
% 48.27/47.93 all X_b (semilattice_inf(X_b)-> (all A_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),semilattice_inf_inf(X_b)),A_3)),A_2)))))).
% 48.27/47.93 all K_2 L I J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),L))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),L))))).
% 48.27/47.93 all K_2 I J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),I)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),J_1)))).
% 48.27/47.93 all K_2 I J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),K_2)))).
% 48.27/47.93 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M)))).
% 48.27/47.93 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M))).
% 48.27/47.93 all Fun_1 Com1_1 Com2_1 Fun Com (hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1)!=hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com)).
% 48.27/47.93 all Fun Com Fun_1 Com1_1 Com2_1 (hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com)!=hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1)).
% 48.27/47.93 all Fun Com1 Com2 Com1_1 Com2_1 (hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun),Com1),Com2)!=hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1)).
% 48.27/47.93 all Com1_1 Com2_1 Fun Com1 Com2 (hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1)!=hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun),Com1),Com2)).
% 48.27/47.93 all Fun Com1 Com2 (hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun),Com1),Com2)!=skip).
% 48.27/47.93 all Fun Com1 Com2 (skip!=hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun),Com1),Com2)).
% 48.27/47.93 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))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 all X_b (ordere216010020id_add(X_b)-> (all Y_1 X_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),X_2))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),Y_1))-> (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),X_2),Y_1)=zero_zero(X_b)<->ti(X_b,X_2)=zero_zero(X_b)&ti(X_b,Y_1)=zero_zero(X_b)))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 all X_a (ordered_semiring(X_a)-> (all C D_1 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1))))))))).
% 48.27/47.93 all X_a (ordered_semiring(X_a)-> (all C D_1 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1))))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 all X_b (linord581940658strict(X_b)-> (all A_2 B_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),A_2),B_1)),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_1),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_1))))).
% 48.27/47.93 all X_b (linord581940658strict(X_b)-> (all A_2 B_1 (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_1)))<->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_1))|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_1),zero_zero(X_b)))))).
% 48.27/47.93 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))))).
% 48.27/47.93 all X_b (ordered_ab_group_add(X_b)-> (all A_2 B_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_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),minus_minus(X_b),A_2),B_1)),zero_zero(X_b)))))).
% 48.27/47.93 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)))).
% 48.27/47.93 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)))).
% 48.27/47.93 all X_a (lattice(X_a)-> (all X_1 Y Z 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),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Z))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)))))).
% 48.27/47.93 all X_a (lattice(X_a)-> (all X_1 Y Z 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),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Z)))))).
% 48.27/47.93 all M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)=zero_zero(nat)).
% 48.27/47.93 all M_1 N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)=zero_zero(nat)<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))).
% 48.27/47.93 all N_2 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N_2)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2))).
% 48.27/47.93 all K_1 M_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))).
% 48.27/47.93 all I K_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),J_1))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_2)),J_1)).
% 48.27/47.93 all J_2 K_1 I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)),I_1))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)))).
% 48.27/47.93 all M K_2 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),M)),K_2)))).
% 48.27/47.93 all N_2 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2))=M).
% 48.27/47.93 all I K_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),J_1))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_1)),K_2)).
% 48.27/47.93 all I_1 K_1 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_2)))).
% 48.27/47.93 all N_2 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)),N_2)=M).
% 48.27/47.93 all K_1 I_1 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)=K_1<->J_2=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),I_1))).
% 48.27/47.93 all I K_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),J_1))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_1)),K_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2))).
% 48.27/47.93 all I K_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),J_1))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2)),I)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),I)),K_2)).
% 48.27/47.93 all I K_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),J_1))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),I)),K_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2)),I)).
% 48.27/47.93 all X_b F A_2 (hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),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,A_2)).
% 48.27/47.93 all X_b A_2 G F (G=hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F)->hAPP(fun(X_b,bool),X_b,G,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,A_2)).
% 48.27/47.93 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_1(X_b),A_3))->hAPP(fun(X_b,bool),X_b,F_1,A_3)=hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_3))).
% 48.27/47.93 all X_b (linord581940658strict(X_b)-> (all X_2 Y_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),X_2),X_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_1),Y_1))),zero_zero(X_b)))<->ti(X_b,X_2)=zero_zero(X_b)&ti(X_b,Y_1)=zero_zero(X_b)))).
% 48.27/47.93 all X_a (linordered_ring(X_a)-> (all X_1 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_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y)))))).
% 48.27/47.93 all X_a (linordered_idom(X_a)-> (all Y X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))-> (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_1),Y)),X_1))))))).
% 48.27/47.93 all X_a (linordered_idom(X_a)-> (all Y X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))-> (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_1)),X_1))))))).
% 48.27/47.93 all X_b (ordered_ring(X_b)-> (all A_2 E C_1 B_1 D (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_1),E)),D)))<->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_1)),E)),C_1)),D))))).
% 48.27/47.93 all X_b (ordered_ring(X_b)-> (all A_2 E C_1 B_1 D (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_1),E)),D)))<->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_1),A_2)),E)),D)))))).
% 48.27/47.93 all X_b X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2),A_3))))).
% 48.27/47.93 all M_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1))).
% 48.27/47.93 all X_c X_b F A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)))).
% 48.27/47.93 all M K_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),J_1))->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_1),K_2))),M)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,J_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),M))).
% 48.27/47.93 all M K_2 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),J_1))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)),hAPP(nat,nat,suc,J_1))).
% 48.27/47.93 all U M_1 N_1 J_2 I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U)),M_1)),N_1)))).
% 48.27/47.93 all U_1 M N_2 J_1 I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),I))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U_1)),N_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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J_1)),U_1)),M)),N_2)).
% 48.27/47.93 all U M_1 N_1 J_2 I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_1))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_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),I_1),J_2)),U)),M_1)=N_1)).
% 48.27/47.93 all U M_1 N_1 I_1 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_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),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N_1))))).
% 48.27/47.93 all U_1 M N_2 I J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J_1))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U_1)),N_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I)),U_1)),N_2))).
% 48.27/47.93 all U M_1 N_1 I_1 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N_1))).
% 48.27/47.93 all X_b (lattice(X_b)-> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))->hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)=hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),semilattice_sup_sup(X_b)),A_3)))).
% 48.27/47.93 all X_b (lattice(X_b)-> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))->hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)=hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),semilattice_inf_inf(X_b)),A_3)))).
% 48.27/47.93 all X_a (linord1278240602ring_1(X_a)-> (all V U_1 Y X_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),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_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1))))))))).
% 48.27/47.93 all X_b A_3 B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2))),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_2))))).
% 48.27/47.93 all X_b (lattice(X_b)-> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3))))))).
% 48.27/47.93 all X_b (ab_semigroup_mult(X_b)-> (all X_2 A_3 (ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))->hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3))))))).
% 48.27/47.93 all X_b (ab_sem1668676832m_mult(X_b)-> (all X_2 A_3 (ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))->hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3)))))).
% 48.27/47.93 all X_b (ab_sem1668676832m_mult(X_b)-> (all B_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(X_b),B_2))-> (ti(fun(X_b,bool),B_2)!=bot_bot(fun(X_b,bool))->hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),B_2)))))))).
% 48.27/47.93 all X_b (ab_sem1668676832m_mult(X_b)-> (all N_3 H ((all X Y_2 (hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X),Y_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,H,X)),hAPP(X_b,X_b,H,Y_2))))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3))-> (ti(fun(X_b,bool),N_3)!=bot_bot(fun(X_b,bool))->hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),N_3))=hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),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_3))))))).
% 48.27/47.93 all X_b (ab_semigroup_mult(X_b)-> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))-> ((all X Y_2 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),X),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),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)))))))->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,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3)),A_3))))))).
% 48.27/47.93 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),big_semilattice_big(X_b),F),F_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))->hAPP(fun(X_b,bool),X_b,F_1,A_3)=hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_3))).
% 48.27/47.93 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)).
% 48.27/47.93 all X_b A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))->hBOOL(hAPP(fun(fun(X_b,bool),bool),bool,finite_finite_1(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))))).
% 48.27/47.93 all X_b X_c B_2 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_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 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_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),AA)))).
% 48.27/47.93 all X_c X_b F A_3 B_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),B_2))->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_2)))).
% 48.27/47.93 all X_b A_3 B_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),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),A_3)).
% 48.27/47.93 all X_b A_3 B_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),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),B_2)).
% 48.27/47.93 all X_b A_3 B_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),B_2))->hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)=ti(fun(X_b,bool),A_3)).
% 48.27/47.93 all X_b B_2 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_2),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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)=ti(fun(X_b,bool),B_2)).
% 48.27/47.93 all X_b B_2 C_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)),C_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)),C_3),B_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)),C_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))))).
% 48.27/47.93 all X_b B_2 D_2 A_3 C_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),C_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_2),D_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),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),C_3),D_2))))).
% 48.27/47.93 all X_b A_3 B_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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))).
% 48.27/47.93 all X_b B_2 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_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))).
% 48.27/47.93 all X_b A_3 B_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),B_2))<->hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)=ti(fun(X_b,bool),B_2)).
% 48.27/47.93 all X_b A_3 B_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),B_2))->hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)=ti(fun(X_b,bool),B_2)).
% 48.27/47.93 all X_b B_2 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_2),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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)=ti(fun(X_b,bool),A_3)).
% 48.27/47.93 all X_b B_2 A_3 C_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),C_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_2),C_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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),C_3)))).
% 48.27/47.93 all X_b B_2 D_2 A_3 C_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),C_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_2),D_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),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),C_3),D_2))))).
% 48.27/47.93 all X_b A_3 B_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),B_2))->hBOOL(hAPP(fun(fun(X_b,bool),bool),bool,hAPP(fun(fun(X_b,bool),bool),fun(fun(fun(X_b,bool),bool),bool),ord_less_e_q(fun(fun(X_b,bool),bool)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),powp(X_b),A_3)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),powp(X_b),B_2)))).
% 48.27/47.93 all X_b B_2 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_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_2))).
% 48.27/47.93 all X_b X_2 A_3 B_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),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)),B_2))<->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_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),B_2))).
% 48.27/47.93 all X_b B_2 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),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_2),B_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),B_2)))).
% 48.27/47.93 all X_b B_1 A_3 B_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),B_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),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_1),B_2)))).
% 48.27/47.93 all X_b A_2 C_3 D_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)),C_3),D_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),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),C_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),D_2)))).
% 48.27/47.93 all X_b Ga G_1 Ts (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),G_1),Ts))-> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),ord_less_e_q(fun(hoare_2118899576triple(X_b),bool)),G_1),Ga))->hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts)))).
% 48.27/47.93 all X_b Ts Ga Ts_1 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts_1))-> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),ord_less_e_q(fun(hoare_2118899576triple(X_b),bool)),Ts),Ts_1))->hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts)))).
% 48.27/47.93 all X_b Ts Ga (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),ord_less_e_q(fun(hoare_2118899576triple(X_b),bool)),Ts),Ga))->hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts))).
% 48.27/47.93 all X_b A_3 B_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),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),A_3)).
% 48.27/47.93 all X_b D_2 B_2 A_3 C_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),C_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)),D_2),B_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),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_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)),C_3),D_2))))).
% 48.27/47.93 all X_b C_3 A_3 B_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),B_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_2),C_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)),B_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)),C_3),A_3))=ti(fun(X_b,bool),A_3))).
% 48.27/47.93 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))).
% 48.27/47.93 all X_b A_3 B_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),B_2))-> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)))).
% 48.27/47.93 all X_b A_3 B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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),B_2))->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)))).
% 48.27/47.93 all X_b A_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)),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),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_2),bot_bot(fun(X_b,bool)))).
% 48.27/47.93 all X_c X_b B_2 F A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_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),A_3)))->hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2)))).
% 48.27/47.93 all X_b X_c F A_3 B_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_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)),semilattice_inf_inf(fun(X_c,bool)),A_3),B_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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_2)))).
% 48.27/47.93 all X_b A_3 B_2 C_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),C_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_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_3),A_3))).
% 48.27/47.93 all X_b X_c F A_3 B_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),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_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),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_2)))).
% 48.27/47.93 all X_b A_3 B_2 C_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),B_2)),C_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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3)))).
% 48.27/47.93 all X_b A_3 B_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),B_2))->hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),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)),B_2),A_3))=ti(fun(X_b,bool),B_2)).
% 48.27/47.93 all X_c X_b B_2 A_3 F Z_1 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_1),G),F_1))-> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(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_2),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_2)),hAPP(fun(X_c,bool),X_b,F_1,A_3))=hAPP(fun(X_c,bool),X_b,F_1,A_3)))).
% 48.27/47.93 all X_b A_3 X_2 B_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),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_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(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_2),bot_bot(fun(X_b,bool))))),B_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(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_2)))).
% 48.27/47.93 all X_b A_3 X_2 B_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),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_2),bot_bot(fun(X_b,bool))))),B_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(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_2),B_2))))).
% 48.27/47.93 all X_b A_3 B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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),B_2))->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_2))))).
% 48.27/47.93 all X_b A_3 B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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),B_2))-> (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_2)),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_2)))).
% 48.27/47.93 all X_b B_2 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_1(X_b),A_3))-> (ti(fun(X_b,bool),B_2)!=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_2),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_2)),hAPP(fun(X_b,bool),X_b,F_1,A_3))=hAPP(fun(X_b,bool),X_b,F_1,A_3))))).
% 48.27/47.93 all X_b A_3 B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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_2),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_2))=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_2)))).
% 48.27/47.93 all X_b (lattice(X_b)-> (all B_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (ti(fun(X_b,bool),B_2)!=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_2),A_3))->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),B_2)),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3))=hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)))))).
% 48.27/47.93 all X_b (lattice(X_b)-> (all B_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (ti(fun(X_b,bool),B_2)!=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_2),A_3))->hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),B_2)),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3))=hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)))))).
% 48.27/47.93 all X_b (order(X_b)-> (all N_1 N_4 F ((all N hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(nat,X_b,F,N)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N)))))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),N_4))->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,N_4))))))).
% 48.27/47.93 all X_b Pa A_3 F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2))-> (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_2))-> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_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),A_4),F_2))))))))->hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)))))).
% 48.27/47.93 all X_b A_3 B_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),B_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_2),A_3))->ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_2))).
% 48.27/47.93 all X_b C_1 A_3 B_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),B_2))-> (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_2)))).
% 48.27/47.93 all X_b A_3 B_2 (ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_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),B_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_2),A_3)))).
% 48.27/47.93 all X_b C_3 A_3 B_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),B_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_2),C_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),C_3)))).
% 48.27/47.93 all X_b X_2 A_3 B_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),B_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_2)))).
% 48.27/47.93 all X_b B_2 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),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_2))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)))).
% 48.27/47.93 all X_b X_2 Pa Qa (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),Qa))-> (hBOOL(hAPP(X_b,bool,Pa,X_2))->hBOOL(hAPP(X_b,bool,Qa,X_2)))).
% 48.27/47.93 all X_b X_2 A_3 B_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),B_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_2)))).
% 48.27/47.93 all X_b A_3 B_2 (ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_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_2),A_3))).
% 48.27/47.93 all X_b A_3 B_2 (ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_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),B_2))).
% 48.27/47.93 all X_b Qa Pa X_2 (hBOOL(hAPP(X_b,bool,Pa,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)),Pa),Qa))->hBOOL(hAPP(X_b,bool,Qa,X_2)))).
% 48.27/47.93 all X_b A_3 B_2 (ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_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),B_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_2),A_3))).
% 48.27/47.93 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)).
% 48.27/47.93 all X_b R_1 S_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,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_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)),R_1),S_1))).
% 48.27/47.93 all X_b B_2 A_3 ((all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),B_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),B_2))).
% 48.27/47.93 all X_c X_b F A_3 B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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_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 C_2 (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_2),A_3))&hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),C_2))&ti(fun(X_b,bool),B_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),C_2))))).
% 48.27/47.93 all X_b Qa Pa A_3 B_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),B_2))-> ((all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3))-> (hBOOL(hAPP(X_b,bool,Pa,X))->hBOOL(hAPP(X_b,bool,Qa,X)))))->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)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Qa)))))).
% 48.27/47.93 all N_2 M_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_2)),M_4))-> (exists M_2 (M_4=hAPP(nat,nat,suc,M_2)))).
% 48.27/47.93 all Pa N_1 M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_1)),M_3))-> ((all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M_2))->hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,M_2)))))->hBOOL(hAPP(nat,bool,Pa,M_3)))).
% 48.27/47.93 all X_c X_b F B_2 A_3 ((all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),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)),B_2))))->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_2))).
% 48.27/47.93 all X_b X_c (ord(X_c)-> (all F G ((all X 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)),hAPP(X_b,X_c,G,X))))->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))))).
% 48.27/47.93 all N_3 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3))<-> (exists M_2 all X (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X),N_3))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),M_2))))).
% 48.27/47.93 all U F ((all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),hAPP(nat,nat,F,N))))->hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(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))))).
% 48.27/47.93 all Z X_1 Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_1),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)))).
% 48.27/47.93 all Y X_1 Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_1),Z))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)))).
% 48.27/47.93 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),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_1),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_1),A_3)=ti(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),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_1),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_1),A_3)=hAPP(fun(X_b,bool),X_b,the_1(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_1),bot_bot(fun(X_b,bool)))))))).
% 48.27/47.93 all X_b F A_3 (hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_3)=hAPP(fun(X_b,bool),X_b,the_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_3))).
% 48.27/47.93 all X_b F A_3 X_2 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_3),X_2))->ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))).
% 48.27/47.93 all X_b F X_2 (-hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),bot_bot(fun(X_b,bool))),X_2))).
% 48.27/47.93 all X_b F A_2 B_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),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))<->ti(X_b,A_2)=ti(X_b,B_1)).
% 48.27/47.93 all X_b F A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))-> (exists X1 hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_3),X1))))).
% 48.27/47.93 all X_b X_2 A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))-> (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(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_2),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))).
% 48.27/47.93 all N_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),zero_zero(nat)))).
% 48.27/47.93 all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,N_2))).
% 48.27/47.93 all M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N_2)))).
% 48.27/47.93 all K_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(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_1)))).
% 48.27/47.93 all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_2))).
% 48.27/47.93 all Pa I_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(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))))).
% 48.27/47.93 all N_3 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3))<-> (exists M_2 all X (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X),N_3))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),M_2))))).
% 48.27/47.93 all X_a (order(X_a)-> (all Z Y X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))-> (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_1)))))).
% 48.27/47.93 all X_a (preorder(X_a)-> (all Z X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),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_1),Z)))))).
% 48.27/47.93 all X_a (order(X_a)-> (all Z Y X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1))-> (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_1)))))).
% 48.27/47.93 all X_a (preorder(X_a)-> (all Z X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),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_1),Z)))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 all X_a (order(X_a)-> (all X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))|ti(X_a,X_1)=ti(X_a,Y)))).
% 48.27/47.93 all X_b (linorder(X_b)-> (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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1))<->ti(X_b,X_2)=ti(X_b,Y_1))))).
% 48.27/47.93 all X_a (preorder(X_a)-> (all X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))))).
% 48.27/47.93 all X_a (linorder(X_a)-> (all Y X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 all X_b (linorder(X_b)-> (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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),Y_1))<->ti(X_b,X_2)=ti(X_b,Y_1))))).
% 48.27/47.93 all X_a (linorder(X_a)-> (all Y X_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))))).
% 48.27/47.93 all X_a (linorder(X_a)-> (all X_1 Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))))).
% 48.27/47.93 all X_b (order(X_b)-> (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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1))|ti(X_b,X_2)=ti(X_b,Y_1)))).
% 48.27/47.93 all X_b (preorder(X_b)-> (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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),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))))).
% 48.27/47.93 all X_b (order(X_b)-> (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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),Y_1))&ti(X_b,X_2)!=ti(X_b,Y_1)))).
% 48.27/47.93 all X_a (linorder(X_a)-> (all X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1))))).
% 48.27/47.93 all X_b (linorder(X_b)-> (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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2))))).
% 48.27/47.93 all X_b (linorder(X_b)-> (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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_1),X_2))))).
% 48.27/47.93 all M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))|M=N_2->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))).
% 48.27/47.93 all M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))-> (M!=N_2->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2)))).
% 48.27/47.93 all M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))).
% 48.27/47.93 all M_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))|M_1=N_1).
% 48.27/47.93 all M_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))&M_1!=N_1).
% 48.27/47.93 all X_b A_3 F N_1 (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)),N_1)))->hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))).
% 48.27/47.93 all X_a (ordere223160158up_add(X_a)-> (all C D_1 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))))))).
% 48.27/47.93 all X_a (ordere223160158up_add(X_a)-> (all C D_1 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))))))).
% 48.27/47.93 all M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M)),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))).
% 48.27/47.93 all M_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M_1)))<->N_1=M_1)).
% 48.27/47.93 all M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M)),N_2))).
% 48.27/47.93 all M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N_2)))).
% 48.27/47.93 all M_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M_1)),N_1))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))).
% 48.27/47.93 all M_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))).
% 48.27/47.93 all N_1 M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_1)),M_1))).
% 48.27/47.93 all N_1 K_1 M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))))).
% 48.27/47.93 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))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 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))))).
% 48.27/47.93 all I 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),I),J_1)),I))).
% 48.27/47.93 all J_1 I (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),I)),I))).
% 48.27/47.93 all K_1 M_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))).
% 48.27/47.93 all M I J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),M)))).
% 48.27/47.93 all M I J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J_1)))).
% 48.27/47.93 all K_2 I J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),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),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),K_2)))).
% 48.27/47.93 all K_2 L I J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),L))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),L))))).
% 48.27/47.93 all M N_2 K_2 L (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),L))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),L)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),N_2)->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2)))).
% 48.27/47.93 all I J_1 K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_1)),K_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K_2))).
% 48.27/47.93 all X_b (ordere236663937imp_le(X_b)-> (all A_2 C_1 B_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),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_1),C_1)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1))))).
% 48.27/47.93 all X_b (ordere236663937imp_le(X_b)-> (all C_1 A_2 B_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),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B_1)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 all X_a (ordere223160158up_add(X_a)-> (all C D_1 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))))))).
% 48.27/47.93 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))))).
% 48.27/47.93 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))))).
% 48.27/47.93 all L M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M))))).
% 48.27/47.93 all N_2 J_1 K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),K_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),N_2)),K_2))).
% 48.27/47.93 all X_b (ordered_ab_group_add(X_b)-> (all A_2 B_1 C_1 D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D)-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),D)))))).
% 48.27/47.93 all X_a (semilattice_sup(X_a)-> (all A_1 X_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B)))))).
% 48.27/47.93 all X_a (semilattice_sup(X_a)-> (all B X_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B)))))).
% 48.27/47.93 all X_a (semilattice_inf(X_a)-> (all A_1 B X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),X_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)),X_1))))).
% 48.27/47.93 all X_a (semilattice_inf(X_a)-> (all B A_1 X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),X_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)),X_1))))).
% 48.27/47.93 all N_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),zero_zero(nat)))).
% 48.27/47.93 all N_1 (N_1!=zero_zero(nat)<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))).
% 48.27/47.93 all N_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),zero_zero(nat)))).
% 48.27/47.93 all M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))->N_2!=zero_zero(nat)).
% 48.27/47.93 all N_2 (N_2!=zero_zero(nat)->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2))).
% 48.27/47.93 all M_1 N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M_1)))).
% 48.27/47.93 all M_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))|M_1=N_1).
% 48.27/47.93 all M_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))).
% 48.27/47.93 all N_1 M_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M_1)))<->N_1=M_1)).
% 48.27/47.93 all N_2 M (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M)))->M=N_2)).
% 48.27/47.93 all M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N_2)))).
% 48.27/47.93 all M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))-> (hAPP(nat,nat,suc,M)!=N_2->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N_2)))).
% 48.27/47.93 all K_2 I J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),K_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I)),K_2)))).
% 48.27/47.93 all M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N_2)))-> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))->M=N_2)).
% 48.27/47.93 all M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))).
% 48.27/47.93 all M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N_2)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))).
% 48.27/47.93 all N_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),N_2))).
% 48.27/47.93 all M_1 N_1 (M_1!=N_1<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1))).
% 48.27/47.93 all X_1 Y (X_1!=Y-> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X_1)))).
% 48.27/47.93 all N_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),N_2))).
% 48.27/47.93 all N_2 M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M))->M!=N_2).
% 48.27/47.93 all S T_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3))->S!=T_3).
% 48.27/47.93 all Pa M_1 N_1 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N_1),M_1)))-> ((M_1=N_1->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N_1),M_1)))-> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N_1),M_1)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N_1),M_1))))).
% 48.27/47.93 all X_a (preorder(X_a)-> (all X_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),X_1))))).
% 48.27/47.93 all X_b (linorder(X_b)-> (all X_2 Y_1 (ti(X_b,X_2)!=ti(X_b,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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2))))).
% 48.27/47.93 all X_b (linorder(X_b)-> (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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2))|ti(X_b,X_2)=ti(X_b,Y_1)))).
% 48.27/47.93 all X_a (linorder(X_a)-> (all X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))|ti(X_a,X_1)=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1))))).
% 48.27/47.93 all X_b (linorder(X_b)-> (all Y_1 X_2 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2))-> (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1))<->ti(X_b,X_2)=ti(X_b,Y_1))))).
% 48.27/47.93 all X_a (linorder(X_a)-> (all X_1 Y (ti(X_a,X_1)!=ti(X_a,Y)-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1)))))).
% 48.27/47.93 all X_a (order(X_a)-> (all X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))->ti(X_a,X_1)!=ti(X_a,Y)))).
% 48.27/47.93 all X_a (preorder(X_a)-> (all X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1))))).
% 48.27/47.93 all X_a (preorder(X_a)-> (all X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1))))).
% 48.27/47.93 all X_a (order(X_a)-> (all X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))->ti(X_a,X_1)!=ti(X_a,Y)))).
% 48.27/47.93 all X_a (order(X_a)-> (all X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))->ti(X_a,Y)!=ti(X_a,X_1)))).
% 48.27/47.93 all X_b (preorder(X_b)-> (all Pa 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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2))->hBOOL(Pa))))).
% 48.27/47.93 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))))).
% 48.27/47.93 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))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 all X_a (preorder(X_a)-> (all Z X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),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_1),Z)))))).
% 48.27/47.93 all X_a (order(X_a)-> (all Z Y X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1))-> (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_1)))))).
% 48.27/47.93 all X_a (preorder(X_a)-> (all X_1 Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1))))).
% 48.27/47.93 all X_a (linorder(X_a)-> (all X_1 Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))-> (ti(X_a,X_1)!=ti(X_a,Y)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1)))))).
% 48.27/47.93 all X_a (linordered_idom(X_a)-> (all X_1 Y (ti(X_a,X_1)!=ti(X_a,Y)-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1)))))).
% 48.27/47.93 all I_1 J_2 K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_2))).
% 48.27/47.93 all M N_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2))=M).
% 48.27/47.93 all K_1 M_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))).
% 48.27/47.93 all M N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)),hAPP(nat,nat,suc,M))).
% 48.27/47.93 all M_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))).
% 48.27/47.93 all K_1 M_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))).
% 48.27/47.93 all M_1 K_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))).
% 48.27/47.93 all K_2 I J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),K_2))))).
% 48.27/47.93 all K_2 I J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),I)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),J_1))))).
% 48.27/47.93 all M_1 N_1 K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1)<->M_1=N_1)).
% 48.27/47.93 all M_1 N_1 K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)))).
% 48.27/47.93 all M N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)),M)))).
% 48.27/47.93 all N_1 M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))).
% 48.27/47.93 all I M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),M)))).
% 48.27/47.93 all I M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),I)))).
% 48.27/47.93 all M_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))<-> (exists K (N_1=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K))))).
% 48.27/47.93 all M_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))).
% 48.27/47.93 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))<-> (exists M_2 (N_1=hAPP(nat,nat,suc,M_2)))).
% 48.27/47.93 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat))))<->N_1=zero_zero(nat)).
% 48.27/47.93 all M_1 N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1)))<->M_1=zero_zero(nat)| (exists J (M_1=hAPP(nat,nat,suc,J)&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),N_1))))).
% 48.27/47.93 all X_a (linordered_semidom(X_a)-> (all N_2 M (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),N_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M),N_2))))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 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)))).
% 48.27/47.93 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)))).
% 48.27/47.93 all X_b (ordered_ab_group_add(X_b)-> (all A_2 B_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_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),minus_minus(X_b),A_2),B_1)),zero_zero(X_b)))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 all X_b (linord581940658strict(X_b)-> (all A_2 B_1 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_1)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_1),A_2)))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 all X_b (linord581940658strict(X_b)-> (all A_2 B_1 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_1)))<->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1)))))).
% 48.27/47.93 all X_b (linord581940658strict(X_b)-> (all C_1 A_2 B_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_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_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_1),A_2))))).
% 48.27/47.93 all X_b (linord581940658strict(X_b)-> (all A_2 C_1 B_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),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_1),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_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_1),A_2))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 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))))).
% 48.27/47.93 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)))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 all N_1 (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)),N_1)))=N_1).
% 48.27/47.93 all X (hAPP(nat,fun(nat,bool),ord_less(nat),X)=hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,X))).
% 48.27/47.93 all Z X_1 Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)))).
% 48.27/47.93 all Y X_1 Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Z))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)))).
% 48.27/47.93 all X_1 Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_1),Y))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 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))))))).
% 48.27/47.93 bounded_lattice(bool).
% 48.27/47.93 all T_2 T_1 (bounded_lattice(T_1)->bounded_lattice(fun(T_2,T_1))).
% 48.27/47.93 all T_2 T_1 (bounded_lattice(T_1)->bounded_lattice_bot(fun(T_2,T_1))).
% 48.27/47.93 all T_2 T_1 (lattice(T_1)->semilattice_sup(fun(T_2,T_1))).
% 48.27/47.93 all T_2 T_1 (lattice(T_1)->semilattice_inf(fun(T_2,T_1))).
% 48.27/47.93 all T_2 T_1 (distrib_lattice(T_1)->distrib_lattice(fun(T_2,T_1))).
% 48.27/47.93 all T_2 T_1 (preorder(T_1)->preorder(fun(T_2,T_1))).
% 48.27/47.93 all T_2 T_1 (finite_finite(T_1)&finite_finite(T_2)->finite_finite(fun(T_2,T_1))).
% 48.27/47.93 all T_2 T_1 (lattice(T_1)->lattice(fun(T_2,T_1))).
% 48.27/47.93 all T_2 T_1 (order(T_1)->order(fun(T_2,T_1))).
% 48.27/47.93 all T_2 T_1 (ord(T_1)->ord(fun(T_2,T_1))).
% 48.27/47.93 all T_2 T_1 (bot(T_1)->bot(fun(T_2,T_1))).
% 48.27/47.93 all T_2 T_1 (minus(T_1)->minus(fun(T_2,T_1))).
% 48.27/47.93 semiri456707255roduct(nat).
% 48.27/47.93 ordere223160158up_add(nat).
% 48.27/47.93 ordere236663937imp_le(nat).
% 48.27/47.93 linord893533164strict(nat).
% 48.27/47.93 linord20386208strict(nat).
% 48.27/47.93 ordere779506340up_add(nat).
% 48.27/47.93 ordere216010020id_add(nat).
% 48.27/47.93 cancel146912293up_add(nat).
% 48.27/47.93 ordere453448008miring(nat).
% 48.27/47.93 ordere1490568538miring(nat).
% 48.27/47.93 cancel_semigroup_add(nat).
% 48.27/47.93 linordered_semidom(nat).
% 48.27/47.93 semilattice_sup(nat).
% 48.27/47.93 semilattice_inf(nat).
% 48.27/47.93 distrib_lattice(nat).
% 48.27/47.93 ab_semigroup_mult(nat).
% 48.27/47.93 comm_monoid_mult(nat).
% 48.27/47.93 ab_semigroup_add(nat).
% 48.27/47.93 ordered_semiring(nat).
% 48.27/47.93 no_zero_divisors(nat).
% 48.27/47.93 comm_monoid_add(nat).
% 48.27/47.93 comm_semiring_1(nat).
% 48.27/47.93 comm_semiring(nat).
% 48.27/47.93 zero_ne_q_one(nat).
% 48.27/47.93 preorder(nat).
% 48.27/47.93 linorder(nat).
% 48.27/47.93 monoid_mult(nat).
% 48.27/47.93 monoid_add(nat).
% 48.27/47.93 lattice(nat).
% 48.27/47.93 mult_zero(nat).
% 48.27/47.93 order(nat).
% 48.27/47.93 semiring(nat).
% 48.27/47.93 ord(nat).
% 48.27/47.93 bot(nat).
% 48.27/47.93 minus(nat).
% 48.27/47.93 zero(nat).
% 48.27/47.93 one(nat).
% 48.27/47.93 bounded_lattice_bot(bool).
% 48.27/47.93 semilattice_sup(bool).
% 48.27/47.93 semilattice_inf(bool).
% 48.27/47.93 distrib_lattice(bool).
% 48.27/47.93 preorder(bool).
% 48.27/47.93 finite_finite(bool).
% 48.27/47.93 lattice(bool).
% 48.27/47.93 order(bool).
% 48.27/47.93 ord(bool).
% 48.27/47.93 bot(bool).
% 48.27/47.93 minus(bool).
% 48.27/47.93 all T_2 T_1 (finite_finite(T_1)&finite_finite(T_2)->finite_finite(sum_sum(T_2,T_1))).
% 48.27/47.93 all T A (ti(T,ti(T,A))=ti(T,A)).
% 48.27/47.93 all X_a X_1 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_1),Y)=ti(X_a,X_1)).
% 48.27/47.95 all X_a X_1 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_1),Y)=ti(X_a,Y)).
% 48.27/47.95 all P (ti(bool,P)=fTrue|ti(bool,P)=fFalse).
% 48.27/47.95 all P (-hBOOL(hAPP(bool,bool,fNot,P))| -hBOOL(P)).
% 48.27/47.95 all P (hBOOL(P)|hBOOL(hAPP(bool,bool,fNot,P))).
% 48.27/47.95 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))).
% 48.27/47.95 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)).
% 48.27/47.95 all X_a P (hAPP(X_a,X_a,combi(X_a),P)=ti(X_a,P)).
% 48.27/47.95 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)).
% 48.27/47.95 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))).
% 48.27/47.95 all Q P (-hBOOL(P)| -hBOOL(Q)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))).
% 48.27/47.95 all P Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))|hBOOL(P)).
% 48.27/47.95 all P Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))|hBOOL(Q)).
% 48.27/47.95 all Q P (-hBOOL(P)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q))).
% 48.27/47.95 all P Q (-hBOOL(Q)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q))).
% 48.27/47.95 all P Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q))|hBOOL(P)|hBOOL(Q)).
% 48.27/47.95 -hBOOL(fFalse).
% 48.27/47.95 all P (ti(bool,P)=fTrue|ti(bool,P)=fFalse).
% 48.27/47.95 all X_a X_1 Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fe_qual(X_a),X_1),Y))|ti(X_a,X_1)=ti(X_a,Y)).
% 48.27/47.95 all X_a X_1 Y (ti(X_a,X_1)!=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fe_qual(X_a),X_1),Y))).
% 48.27/47.95 all Q P (hBOOL(P)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q))).
% 48.27/47.95 all P Q (-hBOOL(Q)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q))).
% 48.27/47.95 all P Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q))| -hBOOL(P)|hBOOL(Q)).
% 48.27/47.95 all N ((all X (hBOOL(hAPP(fun(hoare_2118899576triple(x_a),bool),bool,hAPP(hoare_2118899576triple(x_a),fun(fun(hoare_2118899576triple(x_a),bool),bool),member(hoare_2118899576triple(x_a)),X),hAPP(fun(hoare_2118899576triple(x_a),bool),fun(hoare_2118899576triple(x_a),bool),hAPP(fun(hoare_2118899576triple(x_a),bool),fun(fun(hoare_2118899576triple(x_a),bool),fun(hoare_2118899576triple(x_a),bool)),semilattice_sup_sup(fun(hoare_2118899576triple(x_a),bool)),g),hAPP(fun(pname,bool),fun(hoare_2118899576triple(x_a),bool),hAPP(fun(pname,hoare_2118899576triple(x_a)),fun(fun(pname,bool),fun(hoare_2118899576triple(x_a),bool)),image(pname,hoare_2118899576triple(x_a)),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_2118899576triple(x_a)),hAPP(fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_2118899576triple(x_a))),combs(pname,fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)),hAPP(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hAPP(fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),fun(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),combs(pname,com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),hAPP(fun(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))))),combb(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),pname),hoare_759811442triple(x_a)),p)),body)),q)),procs))))->hBOOL(hAPP(hoare_2118899576triple(x_a),bool,hAPP(nat,fun(hoare_2118899576triple(x_a),bool),hoare_1942962616_valid(x_a),N),X))))-> (all X (hBOOL(hAPP(fun(hoare_2118899576triple(x_a),bool),bool,hAPP(hoare_2118899576triple(x_a),fun(fun(hoare_2118899576triple(x_a),bool),bool),member(hoare_2118899576triple(x_a)),X),hAPP(fun(pname,bool),fun(hoare_2118899576triple(x_a),bool),hAPP(fun(pname,hoare_2118899576triple(x_a)),fun(fun(pname,bool),fun(hoare_2118899576triple(x_a),bool)),image(pname,hoare_2118899576triple(x_a)),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_2118899576triple(x_a)),hAPP(fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_2118899576triple(x_a))),combs(pname,fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)),hAPP(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hAPP(fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),fun(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),combs(pname,com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),hAPP(fun(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))))),combb(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),pname),hoare_759811442triple(x_a)),p)),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body_1))),q)),procs)))->hBOOL(hAPP(hoare_2118899576triple(x_a),bool,hAPP(nat,fun(hoare_2118899576triple(x_a),bool),hoare_1942962616_valid(x_a),N),X))))).
% 48.27/47.95 -((all X (hBOOL(hAPP(fun(hoare_2118899576triple(x_a),bool),bool,hAPP(hoare_2118899576triple(x_a),fun(fun(hoare_2118899576triple(x_a),bool),bool),member(hoare_2118899576triple(x_a)),X),g))->hBOOL(hAPP(hoare_2118899576triple(x_a),bool,hAPP(nat,fun(hoare_2118899576triple(x_a),bool),hoare_1942962616_valid(x_a),n),X))))-> (all X (hBOOL(hAPP(fun(hoare_2118899576triple(x_a),bool),bool,hAPP(hoare_2118899576triple(x_a),fun(fun(hoare_2118899576triple(x_a),bool),bool),member(hoare_2118899576triple(x_a)),X),hAPP(fun(pname,bool),fun(hoare_2118899576triple(x_a),bool),hAPP(fun(pname,hoare_2118899576triple(x_a)),fun(fun(pname,bool),fun(hoare_2118899576triple(x_a),bool)),image(pname,hoare_2118899576triple(x_a)),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_2118899576triple(x_a)),hAPP(fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_2118899576triple(x_a))),combs(pname,fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)),hAPP(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hAPP(fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),fun(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),combs(pname,com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),hAPP(fun(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))))),combb(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),pname),hoare_759811442triple(x_a)),p)),body)),q)),procs)))->hBOOL(hAPP(hoare_2118899576triple(x_a),bool,hAPP(nat,fun(hoare_2118899576triple(x_a),bool),hoare_1942962616_valid(x_a),n),X))))).
% 48.27/47.95 end_of_list.
% 48.27/47.95
% 48.27/47.95 -------> usable clausifies to:
% 48.27/47.95
% 48.27/47.95 list(usable).
% 48.27/47.95 0 [] A=A.
% 48.27/47.95 0 [] ti(fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool))),big_comm_monoid_big(X_b,X_c))=big_comm_monoid_big(X_b,X_c).
% 48.27/47.95 0 [] -lattice(X_b)|ti(fun(fun(X_b,bool),X_b),big_lattice_Inf_fin(X_b))=big_lattice_Inf_fin(X_b).
% 48.27/47.95 0 [] -lattice(X_b)|ti(fun(fun(X_b,bool),X_b),big_lattice_Sup_fin(X_b))=big_lattice_Sup_fin(X_b).
% 48.27/47.95 0 [] ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),big_semilattice_big(X_b))=big_semilattice_big(X_b).
% 48.27/47.95 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).
% 48.27/47.95 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).
% 48.27/47.95 0 [] ti(fun(X_a,X_a),combi(X_a))=combi(X_a).
% 48.27/47.95 0 [] ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b))=combk(X_a,X_b).
% 48.27/47.95 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).
% 48.27/47.95 0 [] ti(fun(pname,option(com)),body_1)=body_1.
% 48.27/47.95 0 [] ti(fun(pname,com),body)=body.
% 48.27/47.95 0 [] ti(fun(fun(state,bool),fun(com,fun(com,com))),cond)=cond.
% 48.27/47.95 0 [] ti(com,skip)=skip.
% 48.27/47.95 0 [] ti(fun(com,fun(com,com)),semi)=semi.
% 48.27/47.95 0 [] ti(fun(fun(state,bool),fun(com,com)),while)=while.
% 48.27/47.95 0 [] ti(fun(com,nat),com_size)=com_size.
% 48.27/47.95 0 [] ti(fun(fun(X_b,bool),nat),finite_card(X_b))=finite_card(X_b).
% 48.27/47.95 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).
% 48.27/47.95 0 [] ti(fun(fun(X_b,bool),bool),finite_finite_1(X_b))=finite_finite_1(X_b).
% 48.27/47.95 0 [] ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b)),finite_fold1(X_b))=finite_fold1(X_b).
% 48.27/47.95 0 [] ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool))),finite_fold1Set(X_b))=finite_fold1Set(X_b).
% 48.27/47.95 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).
% 48.27/47.95 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).
% 48.27/47.95 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).
% 48.27/47.95 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).
% 48.27/47.95 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).
% 48.27/47.95 0 [] -minus(X_c)|ti(fun(X_c,fun(X_c,X_c)),minus_minus(X_c))=minus_minus(X_c).
% 48.27/47.95 0 [] -one(X_b)|ti(X_b,one_one(X_b))=one_one(X_b).
% 48.27/47.95 0 [] -monoid_add(X_a)|ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a).
% 48.27/47.95 0 [] -cancel_semigroup_add(X_b)|ti(fun(X_b,fun(X_b,X_b)),plus_plus(X_b))=plus_plus(X_b).
% 48.27/47.95 0 [] -ab_semigroup_add(X_a)|ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a).
% 48.27/47.95 0 [] -monoid_mult(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a).
% 48.27/47.95 0 [] -no_zero_divisors(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a).
% 48.27/47.95 0 [] -mult_zero(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a).
% 48.27/47.95 0 [] -ab_semigroup_mult(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a).
% 48.27/47.95 0 [] -semiring(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a).
% 48.27/47.95 0 [] -zero(X_b)|ti(X_b,zero_zero(X_b))=zero_zero(X_b).
% 48.27/47.95 0 [] ti(fun(fun(X_b,bool),X_b),the_1(X_b))=the_1(X_b).
% 48.27/47.95 0 [] ti(X_a,undefined(X_a))=undefined(X_a).
% 48.27/47.95 0 [] ti(fun(com,hoare_2118899576triple(state)),hoare_Mirabelle_MGT)=hoare_Mirabelle_MGT.
% 48.27/47.95 0 [] ti(fun(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool)),hoare_1301688828derivs(X_b))=hoare_1301688828derivs(X_b).
% 48.27/47.95 0 [] ti(fun(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool)),hoare_902341502valids(X_b))=hoare_902341502valids(X_b).
% 48.27/47.95 0 [] ti(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hoare_759811442triple(X_b))=hoare_759811442triple(X_b).
% 48.27/47.95 0 [] ti(fun(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b)),hoare_225284258e_case(X_c,X_b))=hoare_225284258e_case(X_c,X_b).
% 48.27/47.95 0 [] ti(fun(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b)),hoare_1759541758le_rec(X_c,X_b))=hoare_1759541758le_rec(X_c,X_b).
% 48.27/47.95 0 [] ti(fun(fun(X_b,nat),fun(hoare_2118899576triple(X_b),nat)),hoare_2043812435e_size(X_b))=hoare_2043812435e_size(X_b).
% 48.27/47.95 0 [] ti(fun(nat,fun(hoare_2118899576triple(X_b),bool)),hoare_1942962616_valid(X_b))=hoare_1942962616_valid(X_b).
% 48.27/47.95 0 [] ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a))=if(X_a).
% 48.27/47.95 0 [] -semilattice_inf(X_a)|ti(fun(X_a,fun(X_a,X_a)),semilattice_inf_inf(X_a))=semilattice_inf_inf(X_a).
% 48.27/47.95 0 [] -semilattice_sup(X_a)|ti(fun(X_a,fun(X_a,X_a)),semilattice_sup_sup(X_a))=semilattice_sup_sup(X_a).
% 48.27/47.95 0 [] ti(fun(nat,nat),suc)=suc.
% 48.27/47.95 0 [] ti(fun(X_b,fun(fun(nat,X_b),fun(nat,X_b))),nat_case(X_b))=nat_case(X_b).
% 48.27/47.95 0 [] ti(fun(com,nat),size_size(com))=size_size(com).
% 48.27/47.95 0 [] ti(fun(hoare_2118899576triple(X_b),nat),size_size(hoare_2118899576triple(X_b)))=size_size(hoare_2118899576triple(X_b)).
% 48.27/47.95 0 [] ti(fun(com,fun(state,fun(state,bool))),evalc)=evalc.
% 48.27/47.95 0 [] ti(fun(com,fun(state,fun(nat,fun(state,bool)))),evaln)=evaln.
% 48.27/47.95 0 [] ti(fun(option(com),com),the(com))=the(com).
% 48.27/47.95 0 [] -bot(X_c)|ti(X_c,bot_bot(X_c))=bot_bot(X_c).
% 48.27/47.95 0 [] -ord(X_a)|ti(fun(X_a,fun(X_a,bool)),ord_less(X_a))=ord_less(X_a).
% 48.27/47.95 0 [] -ord(X_c)|ti(fun(X_c,fun(X_c,bool)),ord_less_e_q(X_c))=ord_less_e_q(X_c).
% 48.27/47.95 0 [] ti(fun(X_b,fun(fun(X_b,bool),X_b)),partial_flat_lub(X_b))=partial_flat_lub(X_b).
% 48.27/47.95 0 [] ti(fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),powp(X_b))=powp(X_b).
% 48.27/47.95 0 [] ti(fun(fun(X_b,bool),fun(X_b,bool)),collect(X_b))=collect(X_b).
% 48.27/47.95 0 [] ti(fun(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool))),image(X_c,X_b))=image(X_c,X_b).
% 48.27/47.95 0 [] ti(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),insert(X_b))=insert(X_b).
% 48.27/47.95 0 [] ti(fun(fun(X_b,bool),X_b),the_elem(X_b))=the_elem(X_b).
% 48.27/47.95 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).
% 48.27/47.95 0 [] ti(bool,fFalse)=fFalse.
% 48.27/47.95 0 [] ti(fun(bool,bool),fNot)=fNot.
% 48.27/47.95 0 [] ti(bool,fTrue)=fTrue.
% 48.27/47.95 0 [] ti(fun(bool,fun(bool,bool)),fconj)=fconj.
% 48.27/47.95 0 [] ti(fun(bool,fun(bool,bool)),fdisj)=fdisj.
% 48.27/47.95 0 [] ti(fun(X_a,fun(X_a,bool)),fe_qual(X_a))=fe_qual(X_a).
% 48.27/47.95 0 [] ti(fun(bool,fun(bool,bool)),fimplies)=fimplies.
% 48.27/47.95 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).
% 48.27/47.95 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).
% 48.27/47.95 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).
% 48.27/47.95 0 [] -hBOOL(ti(bool,B_1_1))|hBOOL(B_1_1).
% 48.27/47.95 0 [] hBOOL(ti(bool,B_1_1))| -hBOOL(B_1_1).
% 48.27/47.95 0 [] ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b))=member(X_b).
% 48.27/47.95 0 [] ti(fun(hoare_2118899576triple(x_a),bool),g)=g.
% 48.27/47.95 0 [] ti(fun(pname,fun(x_a,fun(state,bool))),p)=p.
% 48.27/47.95 0 [] ti(fun(pname,bool),procs)=procs.
% 48.27/47.95 0 [] ti(fun(pname,fun(x_a,fun(state,bool))),q)=q.
% 48.27/47.95 0 [] ti(nat,n)=n.
% 48.27/47.95 0 [] hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1),Com_1),Fun2)!=hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1_2),Com),Fun2_2)|Fun1=Fun1_2.
% 48.27/47.95 0 [] hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1),Com_1),Fun2)!=hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1_2),Com),Fun2_2)|Com_1=Com.
% 48.27/47.95 0 [] hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1),Com_1),Fun2)!=hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1_2),Com),Fun2_2)|Fun2=Fun2_2.
% 48.27/47.95 0 [] hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1),Com_1),Fun2)=hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1_2),Com),Fun2_2)|Fun1!=Fun1_2|Com_1!=Com|Fun2!=Fun2_2.
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_902341502valids(X_b),Ga),Ts))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),bool),member(hoare_2118899576triple(X_b)),$f1(X_b,Ga,Ts,N)),Ga))| -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),bool),member(hoare_2118899576triple(X_b)),X),Ts))|hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N),X)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_902341502valids(X_b),Ga),Ts))| -hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N),$f1(X_b,Ga,Ts,N)))| -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),bool),member(hoare_2118899576triple(X_b)),X),Ts))|hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N),X)).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_902341502valids(X_b),Ga),Ts))| -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),bool),member(hoare_2118899576triple(X_b)),X3),Ga))|hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),$f3(X_b,Ga,Ts)),X3)).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_902341502valids(X_b),Ga),Ts))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),bool),member(hoare_2118899576triple(X_b)),$f2(X_b,Ga,Ts)),Ts)).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_902341502valids(X_b),Ga),Ts))| -hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),$f3(X_b,Ga,Ts)),$f2(X_b,Ga,Ts))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),semilattice_sup_sup(fun(hoare_2118899576triple(X_b),bool)),Ga),hAPP(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(pname,hoare_2118899576triple(X_b)),fun(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool)),image(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),pname),hoare_759811442triple(X_b)),Pa)),body)),Qa)),Procsa))),hAPP(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(pname,hoare_2118899576triple(X_b)),fun(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool)),image(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),pname),hoare_759811442triple(X_b)),Pa)),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body_1))),Qa)),Procsa)))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(pname,hoare_2118899576triple(X_b)),fun(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool)),image(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),pname),hoare_759811442triple(X_b)),Pa)),body)),Qa)),Procsa))).
% 48.27/47.95 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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))|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_2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2),X_2))|hBOOL(hAPP(X_b,bool,A_3,X_2))|hBOOL(hAPP(X_b,bool,B_2,X_2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(X_b,bool,B_2,X_2))|hBOOL(hAPP(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2),X_2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(X_b,bool,A_3,X_2))|hBOOL(hAPP(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2),X_2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))|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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))).
% 48.27/47.95 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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))).
% 48.27/47.95 0 [] ti(X_b,B_1)!=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))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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))).
% 48.27/47.95 0 [] hAPP(hoare_2118899576triple(X_c),X_b,hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b),hoare_1759541758le_rec(X_c,X_b),F1),hAPP(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hoare_759811442triple(X_c),Fun1),Com_1),Fun2))=hAPP(fun(X_c,fun(state,bool)),X_b,hAPP(com,fun(fun(X_c,fun(state,bool)),X_b),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b)),F1,Fun1),Com_1),Fun2).
% 48.27/47.95 0 [] hAPP(hoare_2118899576triple(X_c),X_b,hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b),hoare_225284258e_case(X_c,X_b),F1),hAPP(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hoare_759811442triple(X_c),Fun1),Com_1),Fun2))=hAPP(fun(X_c,fun(state,bool)),X_b,hAPP(com,fun(fun(X_c,fun(state,bool)),X_b),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b)),F1,Fun1),Com_1),Fun2).
% 48.27/47.95 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(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_sup_sup(fun(X_c,bool)),A_3),B_2))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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_2)).
% 48.27/47.95 0 [] -lattice(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)),semilattice_sup_sup(fun(X_b,X_c)),F),G),X)=hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),semilattice_sup_sup(X_c),hAPP(X_b,X_c,F,X)),hAPP(X_b,X_c,G,X)).
% 48.27/47.95 0 [] -lattice(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)),semilattice_sup_sup(fun(X_c,X_b)),F),G),X_2)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,G,X_2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),G_1),Ts))| -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),G_1))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts)).
% 48.27/47.95 0 [] -semilattice_sup(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)),Z)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)).
% 48.27/47.95 0 [] -lattice(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)),Z)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)).
% 48.27/47.95 0 [] -semilattice_sup(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B)),C)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B),C)).
% 48.27/47.95 0 [] -semilattice_sup(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Z)).
% 48.27/47.95 0 [] -lattice(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Z)).
% 48.27/47.95 0 [] -semilattice_sup(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),C))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B),C)).
% 48.27/47.95 0 [] -semilattice_sup(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y).
% 48.27/47.95 0 [] -lattice(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y).
% 48.27/47.95 0 [] -semilattice_sup(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B).
% 48.27/47.95 0 [] -semilattice_sup(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X_1).
% 48.27/47.95 0 [] -lattice(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X_1).
% 48.27/47.95 0 [] -semilattice_sup(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B),A_1).
% 48.27/47.95 0 [] -semilattice_sup(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),X_1)=ti(X_a,X_1).
% 48.27/47.95 0 [] -semilattice_sup(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),A_1)=ti(X_a,A_1).
% 48.27/47.95 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(X_c,B_1)!=hAPP(X_b,X_c,F,X_2)|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),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))).
% 48.27/47.95 0 [] -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)),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))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z_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(X_c,fun(fun(X_c,bool),bool),member(X_c),$f4(X_b,X_c,Z_1,F,A_3)),A_3)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z_1),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))|ti(X_b,Z_1)=hAPP(X_c,X_b,F,$f4(X_b,X_c,Z_1,F,A_3)).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z_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(X_c,fun(fun(X_c,bool),bool),member(X_c),X),A_3))|ti(X_b,Z_1)!=hAPP(X_c,X_b,F,X).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))|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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))).
% 48.27/47.95 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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))).
% 48.27/47.95 0 [] -hBOOL(hAPP(X_b,bool,B_2,X_2))|hBOOL(hAPP(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2),X_2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(X_b,bool,A_3,X_2))|hBOOL(hAPP(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2),X_2)).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f5(X_b,Pa,A_3,B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3))|hBOOL(hAPP(X_b,bool,Pa,X)).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f5(X_b,Pa,A_3,B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X4),B_2))|hBOOL(hAPP(X_b,bool,Pa,X4)).
% 48.27/47.95 0 [] -hBOOL(hAPP(X_b,bool,Pa,$f5(X_b,Pa,A_3,B_2)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3))|hBOOL(hAPP(X_b,bool,Pa,X)).
% 48.27/47.95 0 [] -hBOOL(hAPP(X_b,bool,Pa,$f5(X_b,Pa,A_3,B_2)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X4),B_2))|hBOOL(hAPP(X_b,bool,Pa,X4)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X5),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))|hBOOL(hAPP(X_b,bool,Pa,X5))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f6(X_b,Pa,A_3,B_2)),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f7(X_b,Pa,A_3,B_2)),B_2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X5),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))|hBOOL(hAPP(X_b,bool,Pa,X5))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f6(X_b,Pa,A_3,B_2)),A_3))| -hBOOL(hAPP(X_b,bool,Pa,$f7(X_b,Pa,A_3,B_2))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X5),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))|hBOOL(hAPP(X_b,bool,Pa,X5))| -hBOOL(hAPP(X_b,bool,Pa,$f6(X_b,Pa,A_3,B_2)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f7(X_b,Pa,A_3,B_2)),B_2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X5),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))|hBOOL(hAPP(X_b,bool,Pa,X5))| -hBOOL(hAPP(X_b,bool,Pa,$f6(X_b,Pa,A_3,B_2)))| -hBOOL(hAPP(X_b,bool,Pa,$f7(X_b,Pa,A_3,B_2))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))| -hBOOL(hAPP(X_b,bool,Pa,X))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f8(X_b,Pa,A_3,B_2)),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f9(X_b,Pa,A_3,B_2)),B_2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))| -hBOOL(hAPP(X_b,bool,Pa,X))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f8(X_b,Pa,A_3,B_2)),A_3))|hBOOL(hAPP(X_b,bool,Pa,$f9(X_b,Pa,A_3,B_2))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))| -hBOOL(hAPP(X_b,bool,Pa,X))|hBOOL(hAPP(X_b,bool,Pa,$f8(X_b,Pa,A_3,B_2)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f9(X_b,Pa,A_3,B_2)),B_2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))| -hBOOL(hAPP(X_b,bool,Pa,X))|hBOOL(hAPP(X_b,bool,Pa,$f8(X_b,Pa,A_3,B_2)))|hBOOL(hAPP(X_b,bool,Pa,$f9(X_b,Pa,A_3,B_2))).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f10(X_b,Pa,A_3,B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X6),A_3))| -hBOOL(hAPP(X_b,bool,Pa,X6)).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f10(X_b,Pa,A_3,B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X7),B_2))| -hBOOL(hAPP(X_b,bool,Pa,X7)).
% 48.27/47.95 0 [] hBOOL(hAPP(X_b,bool,Pa,$f10(X_b,Pa,A_3,B_2)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X6),A_3))| -hBOOL(hAPP(X_b,bool,Pa,X6)).
% 48.27/47.95 0 [] hBOOL(hAPP(X_b,bool,Pa,$f10(X_b,Pa,A_3,B_2)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X7),B_2))| -hBOOL(hAPP(X_b,bool,Pa,X7)).
% 48.27/47.95 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),C_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),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)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3)).
% 48.27/47.95 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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))|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_2)).
% 48.27/47.95 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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)).
% 48.27/47.95 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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)).
% 48.27/47.95 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),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)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),C_3)).
% 48.27/47.95 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2).
% 48.27/47.95 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),A_3).
% 48.27/47.95 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_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),fdisj),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(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_2))).
% 48.27/47.95 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),A_3)=ti(fun(X_b,bool),A_3).
% 48.27/47.95 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).
% 48.27/47.95 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).
% 48.27/47.95 0 [] -hBOOL(hAPP(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)),semilattice_sup_sup(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_1)),X))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),R_1),S_1))).
% 48.27/47.95 0 [] hBOOL(hAPP(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)),semilattice_sup_sup(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_1)),X))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),R_1),S_1))).
% 48.27/47.95 0 [] 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)),Qa))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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),Qa)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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(X_b,B_1)=hAPP(X_c,X_b,F,$f11(X_b,X_c,B_1,F,A_3)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_1),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),$f11(X_b,X_c,B_1,F,A_3)),A_3)).
% 48.27/47.95 0 [] -hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N_1),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn_1))),Qa)))|hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),hAPP(nat,nat,suc,N_1)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(pname,com,body,Pn_1)),Qa))).
% 48.27/47.95 0 [] hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N_1),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn_1))),Qa)))| -hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),hAPP(nat,nat,suc,N_1)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(pname,com,body,Pn_1)),Qa))).
% 48.27/47.95 0 [] Y_1=hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),$f14(X_b,Y_1)),$f13(X_b,Y_1)),$f12(X_b,Y_1)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),semilattice_sup_sup(fun(hoare_2118899576triple(X_b),bool)),Ga),hAPP(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(pname,hoare_2118899576triple(X_b)),fun(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool)),image(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),pname),hoare_759811442triple(X_b)),Pa)),body)),Qa)),Procsa))),hAPP(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(pname,hoare_2118899576triple(X_b)),fun(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool)),image(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),pname),hoare_759811442triple(X_b)),Pa)),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body_1))),Qa)),Procsa)))| -hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),Pn_1),Procsa))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(pname,fun(X_b,fun(state,bool)),Pa,Pn_1)),hAPP(pname,com,body,Pn_1)),hAPP(pname,fun(X_b,fun(state,bool)),Qa,Pn_1))),bot_bot(fun(hoare_2118899576triple(X_b),bool))))).
% 48.27/47.95 0 [] ti(fun(X_b,bool),M_5)!=ti(fun(X_b,bool),N_3)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f15(X_c,X_b,F,G,M_5,N_3)),N_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),M_5)=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_3).
% 48.27/47.95 0 [] ti(fun(X_b,bool),M_5)!=ti(fun(X_b,bool),N_3)|hAPP(X_b,X_c,F,$f15(X_c,X_b,F,G,M_5,N_3))!=hAPP(X_b,X_c,G,$f15(X_c,X_b,F,G,M_5,N_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),M_5)=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_3).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),powp(X_b),A_3),X))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Xa),X))|hBOOL(hAPP(X_b,bool,A_3,Xa)).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),powp(X_b),A_3),X))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f16(X_b,A_3,X)),X)).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),powp(X_b),A_3),X))| -hBOOL(hAPP(X_b,bool,A_3,$f16(X_b,A_3,X))).
% 48.27/47.95 0 [] hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),zero_zero(nat)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(pname,com,body,Pn_1)),Qa))).
% 48.27/47.95 0 [] hAPP(pname,com,body,Pname_3)!=hAPP(pname,com,body,Pname)|ti(pname,Pname_3)=ti(pname,Pname).
% 48.27/47.95 0 [] hAPP(pname,com,body,Pname_3)=hAPP(pname,com,body,Pname)|ti(pname,Pname_3)!=ti(pname,Pname).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn))),S0),S1_2))|hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(pname,com,body,Pn)),S0),S1_2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(pname,com,body,P)),S),S1_2))|hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,P))),S),S1_2)).
% 48.27/47.95 0 [] -lattice(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),X_1)=ti(X_a,X_1).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),bool),member(hoare_2118899576triple(X_b)),$f17(X_b,N_1,Ts)),Ts))| -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),bool),member(hoare_2118899576triple(X_b)),X),Ts))|hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N_1),X)).
% 48.27/47.95 0 [] -hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),hAPP(nat,nat,suc,N_1)),$f17(X_b,N_1,Ts)))| -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),bool),member(hoare_2118899576triple(X_b)),X),Ts))|hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N_1),X)).
% 48.27/47.95 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)))).
% 48.27/47.95 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_1),A_3)))|ti(X_b,A_2)=ti(X_b,B_1)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2))|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_1),B_2))).
% 48.27/47.95 0 [] ti(X_b,A_2)!=ti(X_b,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_1),B_2))).
% 48.27/47.95 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).
% 48.27/47.95 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)).
% 48.27/47.95 0 [] -hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),bot_bot(fun(X_b,bool)))).
% 48.27/47.95 0 [] hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),bot_bot(fun(X_b,bool)))).
% 48.27/47.95 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)).
% 48.27/47.95 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_2))).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f18(X_b,A_3)),A_3))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3))|ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool)).
% 48.27/47.95 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),fe_qual(X_b),A_2))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3))|ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool)).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f19(X_b,A_3)),A_3))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool)).
% 48.27/47.95 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))).
% 48.27/47.95 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))).
% 48.27/47.95 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)).
% 48.27/47.95 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))).
% 48.27/47.95 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)).
% 48.27/47.95 0 [] hAPP(X_b,X_c,F,$f20(X_b,X_c,F,G))!=hAPP(X_b,X_c,G,$f20(X_b,X_c,F,G))|ti(fun(X_b,X_c),F)=ti(fun(X_b,X_c),G).
% 48.27/47.95 0 [] -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(X_b,bool,A_3,X_2)).
% 48.27/47.95 0 [] 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(X_b,bool,A_3,X_2)).
% 48.27/47.95 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)=ti(fun(X_b,bool),Pa).
% 48.27/47.95 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)).
% 48.27/47.95 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,$f21(X_b,Pa))).
% 48.27/47.95 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)))).
% 48.27/47.95 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_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),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_2))).
% 48.27/47.95 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)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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)))))|ti(X_b,B_1)=ti(X_b,A_2).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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)))))|ti(X_b,B_1)!=ti(X_b,A_2).
% 48.27/47.95 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),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),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),A_3).
% 48.27/47.95 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),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),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_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),A_3)).
% 48.27/47.95 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_1),A_3)))|ti(X_b,A_2)=ti(X_b,B_1)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)).
% 48.27/47.95 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_1),A_3)))|ti(X_b,A_2)!=ti(X_b,B_1).
% 48.27/47.95 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_1),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)).
% 48.27/47.95 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)).
% 48.27/47.95 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,$f22(X_b,Pa))).
% 48.27/47.95 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_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),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),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).
% 48.27/47.95 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_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),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),bot_bot(fun(X_b,bool))))|ti(X_b,A_2)=ti(X_b,C_1)|ti(X_b,B_1)=ti(X_b,C_1).
% 48.27/47.95 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_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),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),bot_bot(fun(X_b,bool))))|ti(X_b,B_1)=ti(X_b,D)|ti(X_b,A_2)=ti(X_b,D).
% 48.27/47.95 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_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),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),bot_bot(fun(X_b,bool))))|ti(X_b,B_1)=ti(X_b,D)|ti(X_b,B_1)=ti(X_b,C_1).
% 48.27/47.95 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_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),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),bot_bot(fun(X_b,bool))))|ti(X_b,A_2)!=ti(X_b,C_1)|ti(X_b,B_1)!=ti(X_b,D).
% 48.27/47.95 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_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),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),bot_bot(fun(X_b,bool))))|ti(X_b,A_2)!=ti(X_b,D)|ti(X_b,B_1)!=ti(X_b,C_1).
% 48.27/47.95 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_1),A_3),X_2))|ti(X_b,Y_1)=ti(X_b,X_2)|hBOOL(hAPP(X_b,bool,A_3,X_2)).
% 48.27/47.95 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_1),A_3),X_2))|ti(X_b,Y_1)!=ti(X_b,X_2).
% 48.27/47.95 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_1),A_3),X_2))| -hBOOL(hAPP(X_b,bool,A_3,X_2)).
% 48.27/47.95 0 [] 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_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_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_2),B_2)|ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_2).
% 48.27/47.95 0 [] 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_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_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_2),B_2)|ti(fun(X_b,bool),A_3)!=ti(fun(X_b,bool),B_2).
% 48.27/47.95 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)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2))|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_1),B_2))).
% 48.27/47.95 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).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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)))))|ti(X_b,B_1)=ti(X_b,A_2).
% 48.27/47.95 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_1),bot_bot(fun(X_b,bool)))|ti(X_b,A_2)=ti(X_b,B_1).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C),S),T_3))| -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C),S),U_1))|U_1=T_3.
% 48.27/47.95 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)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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),bot_bot(fun(X_b,bool)))),A_3).
% 48.27/47.95 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),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))),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))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),T_4),Ts)))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),T_4),bot_bot(fun(hoare_2118899576triple(X_b),bool))))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),T_4),Ts)))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),T_4),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))| -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),T_4),Ts))).
% 48.27/47.95 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)).
% 48.27/47.95 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))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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))).
% 48.27/47.95 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_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),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_2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_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),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).
% 48.27/47.95 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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_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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)).
% 48.27/47.95 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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),B_2)),C_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)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3)).
% 48.27/47.95 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)).
% 48.27/47.95 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)).
% 48.27/47.95 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)).
% 48.27/47.95 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)).
% 48.27/47.95 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)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),bot_bot(fun(X_b,bool))))|hBOOL(hAPP(X_b,bool,Pa,X)).
% 48.27/47.95 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),bot_bot(fun(X_b,bool))),B_2)=ti(fun(X_b,bool),B_2).
% 48.27/47.95 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool)))=ti(fun(X_b,bool),A_3).
% 48.27/47.95 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)!=bot_bot(fun(X_b,bool))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool)).
% 48.27/47.95 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)!=bot_bot(fun(X_b,bool))|ti(fun(X_b,bool),B_2)=bot_bot(fun(X_b,bool)).
% 48.27/47.95 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)=bot_bot(fun(X_b,bool))|ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool))|ti(fun(X_b,bool),B_2)!=bot_bot(fun(X_b,bool)).
% 48.27/47.95 0 [] hBOOL(C_3)|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(bool,fun(X_b,fun(state,bool)),hAPP(fun(X_b,fun(bool,fun(state,bool))),fun(bool,fun(X_b,fun(state,bool))),combc(X_b,bool,fun(state,bool)),hAPP(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(bool,fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(bool,fun(state,bool))),fun(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(bool,fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X_b),combc(state,bool,bool)),hAPP(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),Pa))),C_3)),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(bool,fun(X_b,fun(state,bool)),hAPP(fun(X_b,fun(bool,fun(state,bool))),fun(bool,fun(X_b,fun(state,bool))),combc(X_b,bool,fun(state,bool)),hAPP(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(bool,fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(bool,fun(state,bool))),fun(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(bool,fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X_b),combc(state,bool,bool)),hAPP(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),Pa))),C_3)),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),bot_bot(fun(hoare_2118899576triple(X_b),bool)))).
% 48.27/47.95 0 [] -bounded_lattice_bot(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),bot_bot(X_a)),X_1)=ti(X_a,X_1).
% 48.27/47.95 0 [] -bounded_lattice_bot(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),bot_bot(X_a))=ti(X_a,X_1).
% 48.27/47.95 0 [] -bounded_lattice_bot(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),Y_1)!=bot_bot(X_b)|ti(X_b,X_2)=bot_bot(X_b).
% 48.27/47.95 0 [] -bounded_lattice_bot(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),Y_1)!=bot_bot(X_b)|ti(X_b,Y_1)=bot_bot(X_b).
% 48.27/47.95 0 [] -bounded_lattice_bot(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),Y_1)=bot_bot(X_b)|ti(X_b,X_2)!=bot_bot(X_b)|ti(X_b,Y_1)!=bot_bot(X_b).
% 48.27/47.95 0 [] -hBOOL(hAPP(hoare_2118899576triple(X_a),bool,hAPP(nat,fun(hoare_2118899576triple(X_a),bool),hoare_1942962616_valid(X_a),hAPP(nat,nat,suc,N_2)),T_3))|hBOOL(hAPP(hoare_2118899576triple(X_a),bool,hAPP(nat,fun(hoare_2118899576triple(X_a),bool),hoare_1942962616_valid(X_a),N_2),T_3)).
% 48.27/47.95 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_2)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),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))),B_2).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn_1))),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(pname,com,body,Pn_1)),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(pname,com,body,Pn_1)),Qa)),Ga)),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn_1))),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(pname,com,body,Pn_1)),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))).
% 48.27/47.95 0 [] hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,$f24(X_b,Ga,C_1,Qa,Pa)),$f23(X_b,Ga,C_1,Qa,Pa)))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(fun(state,bool),fun(X_b,fun(state,bool)),combk(fun(state,bool),X_b),hAPP(state,fun(state,bool),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fe_qual(state)),$f23(X_b,Ga,C_1,Qa,Pa)))),C_1),hAPP(fun(state,bool),fun(X_b,fun(state,bool)),combk(fun(state,bool),X_b),hAPP(X_b,fun(state,bool),Qa,$f24(X_b,Ga,C_1,Qa,Pa))))),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),P_1),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))|hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,$f26(X_b,Pa,Ga,P_1,C_1,Qa)),$f25(X_b,Pa,Ga,P_1,C_1,Qa)))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),P_1),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))| -hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,$f26(X_b,Pa,Ga,P_1,C_1,Qa)),$f25(X_b,Pa,Ga,P_1,C_1,Qa)))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Q_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))|hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,$f28(X_b,Qa,Ga,Pa,C_1,Q_1)),$f27(X_b,Qa,Ga,Pa,C_1,Q_1)))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Q_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))| -hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Qa,$f28(X_b,Qa,Ga,Pa,C_1,Q_1)),$f27(X_b,Qa,Ga,Pa,C_1,Q_1)))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))).
% 48.27/47.95 0 [] hAPP(hoare_2118899576triple(X_b),nat,hAPP(fun(X_b,nat),fun(hoare_2118899576triple(X_b),nat),hoare_2043812435e_size(X_b),Fa),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1),Com_1),Fun2))=zero_zero(nat).
% 48.27/47.95 0 [] hAPP(com,hoare_2118899576triple(state),hoare_Mirabelle_MGT,C_1)=hAPP(fun(state,fun(state,bool)),hoare_2118899576triple(state),hAPP(com,fun(fun(state,fun(state,bool)),hoare_2118899576triple(state)),hAPP(fun(state,fun(state,bool)),fun(com,fun(fun(state,fun(state,bool)),hoare_2118899576triple(state))),hoare_759811442triple(state),fe_qual(state)),C_1),hAPP(com,fun(state,fun(state,bool)),evalc,C_1)).
% 48.27/47.95 0 [] hAPP(hoare_2118899576triple(X_b),nat,size_size(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1),Com_1),Fun2))=zero_zero(nat).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),P_1),C_1),Q_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))|hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,$f31(X_b,Qa,Pa,Ga,P_1,C_1,Q_1)),$f30(X_b,Qa,Pa,Ga,P_1,C_1,Q_1)))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),P_1),C_1),Q_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))| -hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_4),$f30(X_b,Qa,Pa,Ga,P_1,C_1,Q_1)))|hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_4),$f29(X_b,Qa,Pa,Ga,P_1,C_1,Q_1)))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),P_1),C_1),Q_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))| -hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Qa,$f31(X_b,Qa,Pa,Ga,P_1,C_1,Q_1)),$f29(X_b,Qa,Pa,Ga,P_1,C_1,Q_1)))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))).
% 48.27/47.95 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_2),bot_bot(fun(X_b,bool))))=ti(X_b,X_2).
% 48.27/47.95 0 [] hAPP(nat,nat,suc,M)!=zero_zero(nat).
% 48.27/47.95 0 [] bot_bot(nat)=zero_zero(nat).
% 48.27/47.95 0 [] N_2!=hAPP(nat,nat,suc,N_2).
% 48.27/47.95 0 [] hAPP(nat,nat,suc,N_2)!=N_2.
% 48.27/47.95 0 [] hAPP(nat,nat,suc,Nat)!=hAPP(nat,nat,suc,Nat_4)|Nat=Nat_4.
% 48.27/47.95 0 [] hAPP(nat,nat,suc,Nat)=hAPP(nat,nat,suc,Nat_4)|Nat!=Nat_4.
% 48.27/47.95 0 [] hAPP(nat,nat,suc,X_1)!=hAPP(nat,nat,suc,Y)|X_1=Y.
% 48.27/47.95 0 [] zero_zero(nat)!=hAPP(nat,nat,suc,M).
% 48.27/47.95 0 [] zero_zero(nat)!=hAPP(nat,nat,suc,Nat_3).
% 48.27/47.95 0 [] hAPP(nat,nat,suc,M)!=zero_zero(nat).
% 48.27/47.95 0 [] hAPP(nat,nat,suc,Nat_2)!=zero_zero(nat).
% 48.27/47.95 0 [] zero_zero(nat)!=hAPP(nat,nat,suc,M).
% 48.27/47.95 0 [] N_2=zero_zero(nat)|N_2=hAPP(nat,nat,suc,$f32(N_2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))|hBOOL(hAPP(nat,bool,Pa,$f33(N_1,Pa)))|hBOOL(hAPP(nat,bool,Pa,N_1)).
% 48.27/47.95 0 [] -hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,$f33(N_1,Pa))))|hBOOL(hAPP(nat,bool,Pa,N_1)).
% 48.27/47.95 0 [] -hBOOL(hAPP(nat,bool,Pa,K_1))|hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,$f34(Pa,K_1))))|hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))).
% 48.27/47.95 0 [] -hBOOL(hAPP(nat,bool,Pa,K_1))| -hBOOL(hAPP(nat,bool,Pa,$f34(Pa,K_1)))|hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))).
% 48.27/47.95 0 [] Y=zero_zero(nat)|Y=hAPP(nat,nat,suc,$f35(Y)).
% 48.27/47.95 0 [] -bot(X_c)|hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X)=bot_bot(X_c).
% 48.27/47.95 0 [] -bot(X_b)|hAPP(X_c,X_b,bot_bot(fun(X_c,X_b)),X_2)=bot_bot(X_b).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn))),S0),N_2),S1_2))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(pname,com,body,Pn)),S0),hAPP(nat,nat,suc,N_2)),S1_2)).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),skip),Pa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(fun(state,bool),fun(X_b,fun(state,bool)),hAPP(fun(X_b,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(X_b,fun(state,bool))),combc(X_b,fun(state,bool),fun(state,bool)),hAPP(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),X_b),combs(state,bool,bool)),hAPP(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),Pa))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),B_1))),hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),Pa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))).
% 48.27/47.95 0 [] hBOOL(hAPP(state,bool,B_1,S_2))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S_2),N_1),S_2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,B_1,S0_1))| -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C_1),S0_1),N_1),S1))| -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S1),N_1),S2_1))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S0_1),N_1),S2_1)).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,B_1,S0_1))| -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S0_1),S1))| -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S1),S2_1))|hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S0_1),S2_1)).
% 48.27/47.95 0 [] hBOOL(hAPP(state,bool,B_1,S_2))|hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S_2),S_2)).
% 48.27/47.95 0 [] hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,skip),S),N_2),S)).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,skip),S),N_2),T_3))|T_3=S.
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,skip),S),T_3))|T_3=S.
% 48.27/47.95 0 [] hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,skip),S),S)).
% 48.27/47.95 0 [] skip!=hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com).
% 48.27/47.95 0 [] hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com)!=skip.
% 48.27/47.95 0 [] hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1)!=hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com)|Fun_1=Fun.
% 48.27/47.95 0 [] hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1)!=hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com)|Com_1=Com.
% 48.27/47.95 0 [] hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1)=hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com)|Fun_1!=Fun|Com_1!=Com.
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C),S),N_2),S_5))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C),S),hAPP(nat,nat,suc,N_2)),S_5)).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C),S),N_2),T_3))|hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C),S),T_3)).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S_2),T_4))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C_1),S_2),$f36(C_1,S_2,T_4)),T_4)).
% 48.27/47.95 0 [] hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S_2),T_4))| -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C_1),S_2),N),T_4)).
% 48.27/47.95 0 [] hAPP(pname,com,body,Pname)!=hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1).
% 48.27/47.95 0 [] hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1)!=hAPP(pname,com,body,Pname).
% 48.27/47.95 0 [] skip!=hAPP(pname,com,body,Pname_2).
% 48.27/47.95 0 [] hAPP(pname,com,body,Pname_2)!=skip.
% 48.27/47.95 0 [] -hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N_1),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)))| -hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_3),S_3))| -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C_1),S_3),N_1),S_4))|hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Qa,Z_3),S_4)).
% 48.27/47.95 0 [] hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N_1),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)))|hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,$f39(X_b,N_1,Pa,C_1,Qa)),$f38(X_b,N_1,Pa,C_1,Qa))).
% 48.27/47.95 0 [] hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N_1),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C_1),$f38(X_b,N_1,Pa,C_1,Qa)),N_1),$f37(X_b,N_1,Pa,C_1,Qa))).
% 48.27/47.95 0 [] hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N_1),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)))| -hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Qa,$f39(X_b,N_1,Pa,C_1,Qa)),$f37(X_b,N_1,Pa,C_1,Qa))).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(pname,com,body,P)),S),N_2),S1_2))|N_2=hAPP(nat,nat,suc,$f40(P,S,N_2,S1_2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(pname,com,body,P)),S),N_2),S1_2))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,P))),S),$f40(P,S,N_2,S1_2)),S1_2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S_2),T_4))|T_4=S_2|hBOOL(hAPP(state,bool,B_1,S_2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S_2),T_4))|T_4=S_2|hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S_2),$f41(B_1,C_1,S_2,T_4))).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S_2),T_4))|T_4=S_2|hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),$f41(B_1,C_1,S_2,T_4)),T_4)).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S_2),T_4))| -hBOOL(hAPP(state,bool,B_1,S_2))|hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S_2),$f41(B_1,C_1,S_2,T_4))).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S_2),T_4))| -hBOOL(hAPP(state,bool,B_1,S_2))|hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),$f41(B_1,C_1,S_2,T_4)),T_4)).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S_2),N_1),T_4))|T_4=S_2|hBOOL(hAPP(state,bool,B_1,S_2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S_2),N_1),T_4))|T_4=S_2|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C_1),S_2),N_1),$f42(B_1,C_1,S_2,N_1,T_4))).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S_2),N_1),T_4))|T_4=S_2|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),$f42(B_1,C_1,S_2,N_1,T_4)),N_1),T_4)).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S_2),N_1),T_4))| -hBOOL(hAPP(state,bool,B_1,S_2))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C_1),S_2),N_1),$f42(B_1,C_1,S_2,N_1,T_4))).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S_2),N_1),T_4))| -hBOOL(hAPP(state,bool,B_1,S_2))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),$f42(B_1,C_1,S_2,N_1,T_4)),N_1),T_4)).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C),S),T_3))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C),S),$f43(C,S,T_3)),T_3)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))| -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Qa),D),R_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(com,com,hAPP(com,fun(com,com),semi,C_1),D)),R_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))).
% 48.27/47.95 0 [] hAPP(fun(X_b,bool),X_b,the_elem(X_b),X_3)=hAPP(fun(X_b,bool),X_b,the_1(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))))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),U_2))|hBOOL(hAPP(fun(hoare_2118899576triple(X_c),bool),bool,hAPP(fun(hoare_2118899576triple(X_c),bool),fun(fun(hoare_2118899576triple(X_c),bool),bool),hoare_1301688828derivs(X_c),Ga),hAPP(fun(hoare_2118899576triple(X_c),bool),fun(hoare_2118899576triple(X_c),bool),hAPP(hoare_2118899576triple(X_c),fun(fun(hoare_2118899576triple(X_c),bool),fun(hoare_2118899576triple(X_c),bool)),insert(hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hoare_759811442triple(X_c),hAPP(X_b,fun(X_c,fun(state,bool)),P_1,$f44(X_c,X_b,Pa,Qa,Ga,P_1,C0,Q_1,U_2))),hAPP(X_b,com,C0,$f44(X_c,X_b,Pa,Qa,Ga,P_1,C0,Q_1,U_2))),hAPP(X_b,fun(X_c,fun(state,bool)),Q_1,$f44(X_c,X_b,Pa,Qa,Ga,P_1,C0,Q_1,U_2)))),bot_bot(fun(hoare_2118899576triple(X_c),bool)))))| -hBOOL(hAPP(fun(hoare_2118899576triple(X_c),bool),bool,hAPP(fun(hoare_2118899576triple(X_c),bool),fun(fun(hoare_2118899576triple(X_c),bool),bool),hoare_1301688828derivs(X_c),Ga),hAPP(fun(X_b,bool),fun(hoare_2118899576triple(X_c),bool),hAPP(fun(X_b,hoare_2118899576triple(X_c)),fun(fun(X_b,bool),fun(hoare_2118899576triple(X_c),bool)),image(X_b,hoare_2118899576triple(X_c)),hAPP(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,hoare_2118899576triple(X_c)),hAPP(fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),fun(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,hoare_2118899576triple(X_c))),combs(X_b,fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_b,com),fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hAPP(fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),fun(fun(X_b,com),fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),combs(X_b,com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hAPP(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),fun(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))))),combb(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),X_b),hoare_759811442triple(X_c)),P_1)),C0)),Q_1)),U_2)))|hBOOL(hAPP(fun(hoare_2118899576triple(X_c),bool),bool,hAPP(fun(hoare_2118899576triple(X_c),bool),fun(fun(hoare_2118899576triple(X_c),bool),bool),hoare_1301688828derivs(X_c),Ga),hAPP(fun(X_b,bool),fun(hoare_2118899576triple(X_c),bool),hAPP(fun(X_b,hoare_2118899576triple(X_c)),fun(fun(X_b,bool),fun(hoare_2118899576triple(X_c),bool)),image(X_b,hoare_2118899576triple(X_c)),hAPP(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,hoare_2118899576triple(X_c)),hAPP(fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),fun(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,hoare_2118899576triple(X_c))),combs(X_b,fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_b,com),fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hAPP(fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),fun(fun(X_b,com),fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),combs(X_b,com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hAPP(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),fun(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))))),combb(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),X_b),hoare_759811442triple(X_c)),Pa)),C0)),Qa)),U_2))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),U_2))| -hBOOL(hAPP(fun(hoare_2118899576triple(X_c),bool),bool,hAPP(fun(hoare_2118899576triple(X_c),bool),fun(fun(hoare_2118899576triple(X_c),bool),bool),hoare_1301688828derivs(X_c),Ga),hAPP(fun(hoare_2118899576triple(X_c),bool),fun(hoare_2118899576triple(X_c),bool),hAPP(hoare_2118899576triple(X_c),fun(fun(hoare_2118899576triple(X_c),bool),fun(hoare_2118899576triple(X_c),bool)),insert(hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hoare_759811442triple(X_c),hAPP(X_b,fun(X_c,fun(state,bool)),Pa,$f44(X_c,X_b,Pa,Qa,Ga,P_1,C0,Q_1,U_2))),hAPP(X_b,com,C0,$f44(X_c,X_b,Pa,Qa,Ga,P_1,C0,Q_1,U_2))),hAPP(X_b,fun(X_c,fun(state,bool)),Qa,$f44(X_c,X_b,Pa,Qa,Ga,P_1,C0,Q_1,U_2)))),bot_bot(fun(hoare_2118899576triple(X_c),bool)))))| -hBOOL(hAPP(fun(hoare_2118899576triple(X_c),bool),bool,hAPP(fun(hoare_2118899576triple(X_c),bool),fun(fun(hoare_2118899576triple(X_c),bool),bool),hoare_1301688828derivs(X_c),Ga),hAPP(fun(X_b,bool),fun(hoare_2118899576triple(X_c),bool),hAPP(fun(X_b,hoare_2118899576triple(X_c)),fun(fun(X_b,bool),fun(hoare_2118899576triple(X_c),bool)),image(X_b,hoare_2118899576triple(X_c)),hAPP(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,hoare_2118899576triple(X_c)),hAPP(fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),fun(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,hoare_2118899576triple(X_c))),combs(X_b,fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_b,com),fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hAPP(fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),fun(fun(X_b,com),fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),combs(X_b,com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hAPP(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),fun(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))))),combb(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),X_b),hoare_759811442triple(X_c)),P_1)),C0)),Q_1)),U_2)))|hBOOL(hAPP(fun(hoare_2118899576triple(X_c),bool),bool,hAPP(fun(hoare_2118899576triple(X_c),bool),fun(fun(hoare_2118899576triple(X_c),bool),bool),hoare_1301688828derivs(X_c),Ga),hAPP(fun(X_b,bool),fun(hoare_2118899576triple(X_c),bool),hAPP(fun(X_b,hoare_2118899576triple(X_c)),fun(fun(X_b,bool),fun(hoare_2118899576triple(X_c),bool)),image(X_b,hoare_2118899576triple(X_c)),hAPP(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,hoare_2118899576triple(X_c)),hAPP(fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),fun(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,hoare_2118899576triple(X_c))),combs(X_b,fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_b,com),fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hAPP(fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),fun(fun(X_b,com),fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),combs(X_b,com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hAPP(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),fun(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))))),combb(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),X_b),hoare_759811442triple(X_c)),Pa)),C0)),Qa)),U_2))).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1_1),S1_2),N1),T1))| -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2_1),S2),N2),T2))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1_1),S1_2),$f45(C2_1,S2,N2,T2,C1_1,S1_2,N1,T1)),T1)).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1_1),S1_2),N1),T1))| -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2_1),S2),N2),T2))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2_1),S2),$f45(C2_1,S2,N2,T2,C1_1,S1_2,N1,T1)),T2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))|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),A_2),$f46(X_b,A_2,A_3)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),$f46(X_b,A_2,A_3))).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C0_1),S0),N_2),S1_2))| -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1_1),S1_2),N_2),S2))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),semi,C0_1),C1_1)),S0),N_2),S2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C0_1),S0),S1_2))| -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1_1),S1_2),S2))|hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),semi,C0_1),C1_1)),S0),S2)).
% 48.27/47.95 0 [] hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1)!=hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2)|Com1_1=Com1.
% 48.27/47.95 0 [] hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1)!=hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2)|Com2_1=Com2.
% 48.27/47.95 0 [] hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1)=hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2)|Com1_1!=Com1|Com2_1!=Com2.
% 48.27/47.95 0 [] hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2)!=hAPP(pname,com,body,Pname_2).
% 48.27/47.95 0 [] hAPP(pname,com,body,Pname_2)!=hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2).
% 48.27/47.95 0 [] hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com)!=hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1).
% 48.27/47.95 0 [] hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1)!=hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com).
% 48.27/47.95 0 [] hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_3),Com2_3)!=skip.
% 48.27/47.95 0 [] skip!=hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_3),Com2_3).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),semi,C1_1),C2_1)),S),T_3))|hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1_1),S),$f47(C1_1,C2_1,S,T_3))).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),semi,C1_1),C2_1)),S),T_3))|hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C2_1),$f47(C1_1,C2_1,S,T_3)),T_3)).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),semi,C1_1),C2_1)),S),N_2),T_3))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1_1),S),N_2),$f48(C1_1,C2_1,S,N_2,T_3))).
% 48.27/47.95 0 [] -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),semi,C1_1),C2_1)),S),N_2),T_3))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2_1),$f48(C1_1,C2_1,S,N_2,T_3)),N_2),T_3)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1))|hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(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))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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))).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),bot_bot(fun(X_b,bool)))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)),Qa)))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Qa)))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)),Qa)))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)),semilattice_sup_sup(fun(X_b,bool)),F_1),Ga)))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)),semilattice_sup_sup(fun(X_b,bool)),F_1),Ga)))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),Ga)).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)),semilattice_sup_sup(fun(X_b,bool)),F_1),Ga)))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),Ga)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),Ga))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)),semilattice_sup_sup(fun(X_b,bool)),F_1),Ga))).
% 48.27/47.95 0 [] -finite_finite(X_b)|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)).
% 48.27/47.95 0 [] -finite_finite(X_b)|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)),Qa))))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)),Qa))))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Qa))).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)),Qa))))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Qa))).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(X_b),A_3)).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(X_b),A_3)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(X_b),$f49(X_b,Pa,F_1)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f50(X_b,Pa,F_1)),$f49(X_b,Pa,F_1)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,$f49(X_b,Pa,F_1)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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),$f50(X_b,Pa,F_1)),$f49(X_b,Pa,F_1))))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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),$f51(X_b,A_2)),$f52(X_b,A_2)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(X_b),$f52(X_b,A_2))).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_2))|ti(fun(X_b,bool),A_2)!=bot_bot(fun(X_b,bool)).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_2))|ti(fun(X_b,bool),A_2)!=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),A_5)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_5)).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f53(X_c,X_b,F,A_3)),A_3)).
% 48.27/47.95 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(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_1(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,$f53(X_c,X_b,F,A_3))))))).
% 48.27/47.95 0 [] ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))|ti(fun(X_b,bool),A_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f55(X_b,A_3)),$f54(X_b,A_3)).
% 48.27/47.95 0 [] ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f55(X_b,A_3)),$f54(X_b,A_3))).
% 48.27/47.95 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),B_3)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),B_3)).
% 48.27/47.95 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_1(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_1(X_b),B_2))|ti(fun(X_b,bool),B_2)=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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_1,A_3)),hAPP(fun(X_b,bool),X_b,F_1,B_2)).
% 48.27/47.95 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_1(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),hAPP(fun(X_b,bool),X_b,F_1,A_3)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),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)=hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,bool)),fun(fun(X_c,bool),fun(fun(X_b,bool),fun(X_c,bool))),hAPP(fun(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool))),fun(fun(X_b,fun(X_c,bool)),fun(fun(X_c,bool),fun(fun(X_b,bool),fun(X_c,bool)))),finite_fold_image(fun(X_c,bool),X_b),semilattice_sup_sup(fun(X_c,bool))),hAPP(fun(X_c,bool),fun(X_b,fun(X_c,bool)),hAPP(fun(X_b,fun(fun(X_c,bool),fun(X_c,bool))),fun(fun(X_c,bool),fun(X_b,fun(X_c,bool))),combc(X_b,fun(X_c,bool),fun(X_c,bool)),hAPP(fun(X_b,X_c),fun(X_b,fun(fun(X_c,bool),fun(X_c,bool))),hAPP(fun(X_c,fun(fun(X_c,bool),fun(X_c,bool))),fun(fun(X_b,X_c),fun(X_b,fun(fun(X_c,bool),fun(X_c,bool)))),combb(X_c,fun(fun(X_c,bool),fun(X_c,bool)),X_b),insert(X_c)),F)),bot_bot(fun(X_c,bool)))),bot_bot(fun(X_c,bool))),A_3).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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),$f56(X_b,Pa,F_1)),bot_bot(fun(X_b,bool)))))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),$f57(X_b,Pa,F_1)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1))|ti(fun(X_b,bool),F_1)=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f56(X_b,Pa,F_1)),bot_bot(fun(X_b,bool)))))|ti(fun(X_b,bool),$f57(X_b,Pa,F_1))!=bot_bot(fun(X_b,bool))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1))|ti(fun(X_b,bool),F_1)=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f56(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),$f58(X_b,Pa,F_1)),$f57(X_b,Pa,F_1)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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),$f56(X_b,Pa,F_1)),bot_bot(fun(X_b,bool)))))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,$f57(X_b,Pa,F_1)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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),$f56(X_b,Pa,F_1)),bot_bot(fun(X_b,bool)))))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f58(X_b,Pa,F_1)),$f57(X_b,Pa,F_1))))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),X_2)=ti(X_b,X_2).
% 48.27/47.95 0 [] hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),F),G),Z_1),bot_bot(fun(X_c,bool)))=ti(X_b,Z_1).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),hAPP(fun(X_b,bool),X_b,F_1,A_3))=hAPP(fun(X_b,bool),X_b,F_1,A_3).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1))|hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,$f60(X_b,N_3,H,F,F_1)),$f59(X_b,N_3,H,F,F_1)))!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_b,X_b,H,$f60(X_b,N_3,H,F,F_1))),hAPP(X_b,X_b,H,$f59(X_b,N_3,H,F,F_1)))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3))|ti(fun(X_b,bool),N_3)=bot_bot(fun(X_b,bool))|hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,F_1,N_3))=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_3)).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool,hAPP(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool)),big_comm_monoid_big(X_b,X_c),F),Z_1),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3))|hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,G),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_1),A_3).
% 48.27/47.95 0 [] -hBOOL(hAPP(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool,hAPP(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool)),big_comm_monoid_big(X_b,X_c),F),Z_1),F_1))|hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3))|hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,G),A_3)=ti(X_b,Z_1).
% 48.27/47.96 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_1(X_b),A_3))|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))|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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),hAPP(fun(X_b,bool),X_b,F_1,A_3)).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),X_b,the_1(X_b),hAPP(X_b,fun(X_b,bool),fe_qual(X_b),X_2))=ti(X_b,X_2).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),X_b,the_1(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).
% 48.27/47.96 0 [] -hBOOL(Pa)|ti(X_b,X_2)=hAPP(fun(X_b,bool),X_b,the_1(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_2)))),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_1)))).
% 48.27/47.96 0 [] hBOOL(Pa)|ti(X_b,Y_1)=hAPP(fun(X_b,bool),X_b,the_1(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_2)))),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_1)))).
% 48.27/47.96 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_1),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))|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)),semilattice_sup_sup(fun(X_c,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,A_3)),hAPP(fun(X_c,bool),X_b,F_1,B_2)).
% 48.27/47.96 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_1),G),F_1))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),X_2)=ti(X_b,X_2).
% 48.27/47.96 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_1),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),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))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_2)),hAPP(fun(X_c,bool),X_b,F_1,A_3))=hAPP(fun(X_c,bool),X_b,F_1,A_3).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool,hAPP(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool)),big_comm_monoid_big(X_b,X_c),F),Z_1),F_1))|hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3))|hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,G),A_3)=ti(X_b,Z_1).
% 48.27/47.96 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_2),bot_bot(fun(X_b,bool))))=ti(X_b,X_2).
% 48.27/47.96 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_1),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_2)),hAPP(fun(X_c,bool),X_b,F_1,A_3)).
% 48.27/47.96 0 [] -hBOOL(hAPP(X_b,bool,Pa,A_2))|hBOOL(hAPP(X_b,bool,Pa,$f61(X_b,Pa,A_2)))|hAPP(fun(X_b,bool),X_b,the_1(X_b),Pa)=ti(X_b,A_2).
% 48.27/47.96 0 [] -hBOOL(hAPP(X_b,bool,Pa,A_2))|ti(X_b,$f61(X_b,Pa,A_2))!=ti(X_b,A_2)|hAPP(fun(X_b,bool),X_b,the_1(X_b),Pa)=ti(X_b,A_2).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,$f63(X_b,A_3,F,F_1)),$f62(X_b,A_3,F,F_1))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f63(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),$f62(X_b,A_3,F,F_1)),bot_bot(fun(X_b,bool))))))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,F_1,A_3)),A_3)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool,hAPP(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool)),big_comm_monoid_big(X_b,X_c),F),Z_1),F_1))|ti(fun(X_c,bool),A_3)!=ti(fun(X_c,bool),B_2)|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),$f64(X_c,X_b,H,G,A_3,B_2,F,Z_1,F_1)),B_2))|hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,H),A_3)=hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,G),B_2).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool,hAPP(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool)),big_comm_monoid_big(X_b,X_c),F),Z_1),F_1))|ti(fun(X_c,bool),A_3)!=ti(fun(X_c,bool),B_2)|hAPP(X_c,X_b,H,$f64(X_c,X_b,H,G,A_3,B_2,F,Z_1,F_1))!=hAPP(X_c,X_b,G,$f64(X_c,X_b,H,G,A_3,B_2,F,Z_1,F_1))|hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,H),A_3)=hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,G),B_2).
% 48.27/47.96 0 [] -hBOOL(hAPP(X_b,bool,Pa,A_2))|hBOOL(hAPP(X_b,bool,Pa,$f65(X_b,Pa,A_2)))|hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the_1(X_b),Pa))).
% 48.27/47.96 0 [] -hBOOL(hAPP(X_b,bool,Pa,A_2))|ti(X_b,$f65(X_b,Pa,A_2))!=ti(X_b,A_2)|hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the_1(X_b),Pa))).
% 48.27/47.96 0 [] -hBOOL(hAPP(X_b,bool,Pa,X))|hBOOL(hAPP(X_b,bool,Pa,$f66(X_b,A_2,Pa,X)))| -hBOOL(hAPP(X_b,bool,Pa,A_2))|hAPP(fun(X_b,bool),X_b,the_1(X_b),Pa)=ti(X_b,A_2).
% 48.27/47.96 0 [] -hBOOL(hAPP(X_b,bool,Pa,X))|ti(X_b,$f66(X_b,A_2,Pa,X))!=ti(X_b,X)| -hBOOL(hAPP(X_b,bool,Pa,A_2))|hAPP(fun(X_b,bool),X_b,the_1(X_b),Pa)=ti(X_b,A_2).
% 48.27/47.96 0 [] -hBOOL(hAPP(X_b,bool,Pa,X))|hBOOL(hAPP(X_b,bool,Pa,$f67(X_b,Pa,X)))|hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the_1(X_b),Pa))).
% 48.27/47.96 0 [] -hBOOL(hAPP(X_b,bool,Pa,X))|ti(X_b,$f67(X_b,Pa,X))!=ti(X_b,X)|hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the_1(X_b),Pa))).
% 48.27/47.96 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)=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),$f68(X_b,X_2,A_3)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),$f68(X_b,X_2,A_3))).
% 48.27/47.96 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f69(X_b,A_3)),A_3))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool)).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(X_b),B_2))|ti(fun(X_b,bool),B_2)=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),B_2)).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|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))|hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)).
% 48.27/47.96 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_1(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_1(X_b),B_2))|ti(fun(X_b,bool),B_2)=bot_bot(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)!=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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_1,A_3)),hAPP(fun(X_b,bool),X_b,F_1,B_2)).
% 48.27/47.96 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_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)=bot_bot(fun(X_b,bool))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))),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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_1,A_3)),hAPP(fun(X_b,bool),X_b,F_1,B_2)).
% 48.27/47.96 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_1(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_2),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_2),A_3))=ti(X_b,X_2).
% 48.27/47.96 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_1(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_2),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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),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_2),bot_bot(fun(X_b,bool)))))).
% 48.27/47.96 0 [] -hBOOL(hAPP(X_b,bool,A_3,X_2))| -hBOOL(hAPP(X_b,bool,B_2,X_2))|hBOOL(hAPP(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2),X_2)).
% 48.27/47.96 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_2))|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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))).
% 48.27/47.96 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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)).
% 48.27/47.96 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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)).
% 48.27/47.96 0 [] -hBOOL(hAPP(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2),X_2))|hBOOL(hAPP(X_b,bool,A_3,X_2)).
% 48.27/47.96 0 [] -hBOOL(hAPP(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2),X_2))|hBOOL(hAPP(X_b,bool,B_2,X_2)).
% 48.27/47.96 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_2))|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_2))).
% 48.27/47.96 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_2)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)).
% 48.27/47.96 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_2)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)),semilattice_inf_inf(fun(X_b,bool)),F_1),Ga))).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),Ga))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)),semilattice_inf_inf(fun(X_b,bool)),F_1),Ga))).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2))).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),A_2),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3))=ti(X_b,A_2).
% 48.27/47.96 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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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_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),C_3)).
% 48.27/47.96 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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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_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),C_3)).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))=ti(fun(X_b,bool),A_3).
% 48.27/47.96 0 [] 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)),Qa))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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),Qa)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))))|hBOOL(hAPP(X_b,bool,Pa,X_2)).
% 48.27/47.96 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))))| -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(X_b,bool,Pa,X_2)).
% 48.27/47.96 0 [] -hBOOL(hAPP(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)),semilattice_inf_inf(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_1)),X))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),R_1),S_1))).
% 48.27/47.96 0 [] hBOOL(hAPP(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)),semilattice_inf_inf(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_1)),X))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),R_1),S_1))).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),A_3)=ti(fun(X_b,bool),A_3).
% 48.27/47.96 0 [] -semilattice_inf(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),A_1)=ti(X_a,A_1).
% 48.27/47.96 0 [] -semilattice_inf(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),X_1)=ti(X_a,X_1).
% 48.27/47.96 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_2),X)=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)),hAPP(X_b,X_c,B_2,X)).
% 48.27/47.96 0 [] -lattice(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)),semilattice_inf_inf(fun(X_b,X_c)),F),G),X)=hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),semilattice_inf_inf(X_c),hAPP(X_b,X_c,F,X)),hAPP(X_b,X_c,G,X)).
% 48.27/47.96 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_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(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_2)))).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_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(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(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_2))).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),A_3).
% 48.27/47.96 0 [] -semilattice_inf(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B),A_1).
% 48.27/47.96 0 [] -lattice(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),X_1).
% 48.27/47.96 0 [] -semilattice_inf(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),X_1).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2).
% 48.27/47.96 0 [] -semilattice_inf(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B).
% 48.27/47.96 0 [] -lattice(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y).
% 48.27/47.96 0 [] -semilattice_inf(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),C_3)).
% 48.27/47.96 0 [] -semilattice_inf(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),C))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B),C)).
% 48.27/47.96 0 [] -lattice(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Z)).
% 48.27/47.96 0 [] -semilattice_inf(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Z)).
% 48.27/47.96 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_2)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)).
% 48.27/47.96 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_2)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)).
% 48.27/47.96 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_2)))| -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_2)).
% 48.27/47.96 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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)).
% 48.27/47.96 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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)).
% 48.27/47.96 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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))| -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_2)).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),C_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),B_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)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),C_3),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)),semilattice_inf_inf(fun(X_b,bool)),C_3),B_2)).
% 48.27/47.96 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_2)),B_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),B_2).
% 48.27/47.96 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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),C_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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)),B_2),C_3)).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),C_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3)).
% 48.27/47.96 0 [] -semilattice_inf(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)),C)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B),C)).
% 48.27/47.96 0 [] -lattice(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)),Z)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)).
% 48.27/47.96 0 [] -semilattice_inf(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)),Z)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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_2)),C_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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),C_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3)).
% 48.27/47.96 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)),semilattice_inf_inf(fun(X_b,bool)),A_3),C_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),C_3)),B_2).
% 48.27/47.96 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_2),X_2)=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_2)),hAPP(X_c,X_b,B_2,X_2)).
% 48.27/47.96 0 [] -lattice(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)),semilattice_inf_inf(fun(X_c,X_b)),F),G),X_2)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,G,X_2)).
% 48.27/47.96 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_2)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)).
% 48.27/47.96 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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)).
% 48.27/47.96 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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)).
% 48.27/47.96 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_2)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)).
% 48.27/47.96 0 [] -hBOOL(hAPP(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2),X_2))|hBOOL(hAPP(X_b,bool,A_3,X_2)).
% 48.27/47.96 0 [] -hBOOL(hAPP(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2),X_2))|hBOOL(hAPP(X_b,bool,B_2,X_2)).
% 48.27/47.96 0 [] -lattice(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),X_1)=ti(X_a,X_1).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)!=bot_bot(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_2)=ti(fun(X_b,bool),A_3).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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)),B_2),A_3))=bot_bot(fun(X_b,bool)).
% 48.27/47.96 0 [] -bounded_lattice_bot(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),bot_bot(X_a)),X_1)=bot_bot(X_a).
% 48.27/47.96 0 [] -bounded_lattice_bot(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),bot_bot(X_a))=bot_bot(X_a).
% 48.27/47.96 0 [] -lattice(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y))=ti(X_a,X_1).
% 48.27/47.96 0 [] -lattice(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y))=ti(X_a,X_1).
% 48.27/47.96 0 [] -distrib_lattice(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Z)).
% 48.27/47.96 0 [] -distrib_lattice(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Z)).
% 48.27/47.96 0 [] -distrib_lattice(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)),X_1)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Z),X_1)).
% 48.27/47.96 0 [] -distrib_lattice(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)),X_1)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Z),X_1)).
% 48.27/47.96 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)).
% 48.27/47.96 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).
% 48.27/47.96 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)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2)))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2)))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_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)),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),A_3)),B_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),B_2).
% 48.27/47.96 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_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)),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),A_3)),B_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_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),B_2)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_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)),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),A_3)),B_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),B_2).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),bot_bot(fun(X_b,bool))),B_2)=bot_bot(fun(X_b,bool)).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool)))=bot_bot(fun(X_b,bool)).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)!=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),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Xa),B_2))|ti(X_b,X)!=ti(X_b,Xa).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)=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),$f71(X_b,A_3,B_2)),A_3)).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)=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),$f70(X_b,A_3,B_2)),B_2)).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)=bot_bot(fun(X_b,bool))|ti(X_b,$f71(X_b,A_3,B_2))=ti(X_b,$f70(X_b,A_3,B_2)).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),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)),B_2),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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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)),B_2),A_3)),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)),semilattice_sup_sup(fun(X_b,bool)),B_2),A_3).
% 48.27/47.96 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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),C_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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),C_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)),B_2),C_3)).
% 48.27/47.96 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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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_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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)).
% 48.27/47.96 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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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_2))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),C_3))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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),B_2)),C_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)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3)).
% 48.27/47.96 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),C_3))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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),B_2)),C_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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)),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_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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)).
% 48.27/47.96 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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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_2))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2).
% 48.27/47.96 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),C_3))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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),B_2)),C_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3).
% 48.27/47.96 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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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_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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),C_3))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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),B_2)),C_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)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3)).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),C_3)).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),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)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3))=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),C_3)).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3)),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)),semilattice_sup_sup(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)),semilattice_inf_inf(fun(X_b,bool)),B_2),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)),semilattice_inf_inf(fun(X_b,bool)),C_3),A_3)).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3)),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)),semilattice_inf_inf(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)),semilattice_sup_sup(fun(X_b,bool)),B_2),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)),semilattice_sup_sup(fun(X_b,bool)),C_3),A_3)).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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)),semilattice_sup_sup(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),C_3),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)),semilattice_inf_inf(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)),semilattice_inf_inf(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),C_3),A_3)).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2),bot_bot(fun(X_b,bool))))!=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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_2),A_3))=ti(X_b,X_2).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2),bot_bot(fun(X_b,bool))))=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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_2),bot_bot(fun(X_b,bool)))))).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),bot_bot(fun(X_b,bool))))!=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)=ti(X_b,X_2).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),bot_bot(fun(X_b,bool))))=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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_2),bot_bot(fun(X_b,bool)))))).
% 48.27/47.96 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_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)),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_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)))).
% 48.27/47.96 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_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)),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_2).
% 48.27/47.96 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).
% 48.27/47.96 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_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_2),bot_bot(fun(X_b,bool))))=ti(fun(X_b,bool),A_3).
% 48.27/47.96 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).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2))))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2))).
% 48.27/47.96 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2))))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2))).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)=bot_bot(fun(X_b,bool))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),B_2)).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(X_b),B_2))|ti(fun(X_b,bool),B_2)=bot_bot(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)!=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),B_2)).
% 48.27/47.96 0 [] -lattice(X_b)|hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(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_2),bot_bot(fun(X_b,bool))))=ti(X_b,X_2).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -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_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3))=hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3).
% 48.27/47.96 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),hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,X_b)),combs(X_c,X_b,X_b),hAPP(fun(X_c,X_b),fun(X_c,fun(X_b,X_b)),hAPP(fun(X_c,fun(X_b,fun(X_b,X_b))),fun(fun(X_c,X_b),fun(X_c,fun(X_b,X_b))),combs(X_c,X_b,fun(X_b,X_b)),hAPP(fun(X_c,bool),fun(X_c,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_c,bool),fun(X_c,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_c),if(X_b)),Pa)),F)),G)),S_1)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_inf_inf(fun(X_c,bool)),S_1),hAPP(fun(X_c,bool),fun(X_c,bool),collect(X_c),Pa)))),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),G),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_inf_inf(fun(X_c,bool)),S_1),hAPP(fun(X_c,bool),fun(X_c,bool),collect(X_c),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(bool,bool),fun(fun(X_c,bool),fun(X_c,bool)),combb(bool,bool,X_c),fNot),Pa))))).
% 48.27/47.96 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_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),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_2).
% 48.27/47.96 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_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),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_2),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_2),bot_bot(fun(X_b,bool)))))).
% 48.27/47.96 0 [] -lattice(X_b)|hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),$f73(X_b,N_3,H)),$f72(X_b,N_3,H)))!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(X_b,X_b,H,$f73(X_b,N_3,H))),hAPP(X_b,X_b,H,$f72(X_b,N_3,H)))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3))|ti(fun(X_b,bool),N_3)=bot_bot(fun(X_b,bool))|hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),N_3))=hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_3)).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),$f75(X_b,A_3)),$f74(X_b,A_3))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f75(X_b,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),$f74(X_b,A_3)),bot_bot(fun(X_b,bool))))))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)),A_3)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),$f76(X_b,Pa,A_3)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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),$f77(X_b,Pa,A_3)),$f76(X_b,Pa,A_3)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,$f76(X_b,Pa,A_3)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),$f76(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),$f77(X_b,Pa,A_3)),bot_bot(fun(X_b,bool))))))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))).
% 48.27/47.96 0 [] -lattice(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),$f80(X_a,X_1,Y,Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),$f79(X_a,X_1,Y,Z)),$f78(X_a,X_1,Y,Z)))!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),$f80(X_a,X_1,Y,Z)),$f79(X_a,X_1,Y,Z))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),$f80(X_a,X_1,Y,Z)),$f78(X_a,X_1,Y,Z)))|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Z)).
% 48.27/47.96 0 [] -lattice(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),$f83(X_a,X_1,Y,Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),$f82(X_a,X_1,Y,Z)),$f81(X_a,X_1,Y,Z)))!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),$f83(X_a,X_1,Y,Z)),$f82(X_a,X_1,Y,Z))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),$f83(X_a,X_1,Y,Z)),$f81(X_a,X_1,Y,Z)))|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Z)).
% 48.27/47.96 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_1),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))|hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_inf_inf(fun(X_c,bool)),A_3),B_2)!=bot_bot(fun(X_c,bool))|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)),semilattice_sup_sup(fun(X_c,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,A_3)),hAPP(fun(X_c,bool),X_b,F_1,B_2)).
% 48.27/47.96 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_1),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),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))|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_2)),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_2),bot_bot(fun(X_c,bool)))))).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N_2)=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat))=M.
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M)=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)!=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),M)!=zero_zero(nat)|M=N_2.
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N_2)),hAPP(nat,nat,suc,K_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)),K_2).
% 48.27/47.96 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_1),G),F_1))|hAPP(fun(X_c,bool),X_b,F_1,bot_bot(fun(X_c,bool)))=ti(X_b,Z_1).
% 48.27/47.96 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_1),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),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))|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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_2)),hAPP(fun(X_c,bool),X_b,F_1,A_3)).
% 48.27/47.96 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_1),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(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_1),A_3).
% 48.27/47.96 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_1),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,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)),semilattice_sup_sup(fun(X_c,bool)),A_3),B_2))),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)),semilattice_inf_inf(fun(X_c,bool)),A_3),B_2)))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,A_3)),hAPP(fun(X_c,bool),X_b,F_1,B_2)).
% 48.27/47.96 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_1),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_2)),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_2),bot_bot(fun(X_c,bool)))))).
% 48.27/47.96 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_1),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),$f84(X_c,X_b,B_2,A_3,F,Z_1,G,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)),semilattice_inf_inf(fun(X_c,bool)),A_3),B_2)))|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)),semilattice_sup_sup(fun(X_c,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,A_3)),hAPP(fun(X_c,bool),X_b,F_1,B_2)).
% 48.27/47.96 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_1),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))|hAPP(X_c,X_b,G,$f84(X_c,X_b,B_2,A_3,F,Z_1,G,F_1))!=ti(X_b,Z_1)|hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_sup_sup(fun(X_c,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,A_3)),hAPP(fun(X_c,bool),X_b,F_1,B_2)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_1),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),$f85(X_c,X_b,A_3,F,Z_1,G,F_1)),A_3))|hAPP(fun(X_c,bool),X_b,F_1,A_3)=ti(X_b,Z_1).
% 48.27/47.96 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_1),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3))|hAPP(X_c,X_b,G,$f85(X_c,X_b,A_3,F,Z_1,G,F_1))!=ti(X_b,Z_1)|hAPP(fun(X_c,bool),X_b,F_1,A_3)=ti(X_b,Z_1).
% 48.27/47.96 0 [] -group_add(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1)!=zero_zero(X_b)|ti(X_b,A_2)=ti(X_b,B_1).
% 48.27/47.96 0 [] -group_add(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1)=zero_zero(X_b)|ti(X_b,A_2)!=ti(X_b,B_1).
% 48.27/47.96 0 [] -ab_group_add(X_b)|ti(X_b,A_2)!=ti(X_b,B_1)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1)=zero_zero(X_b).
% 48.27/47.96 0 [] -ab_group_add(X_b)|ti(X_b,A_2)=ti(X_b,B_1)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1)!=zero_zero(X_b).
% 48.27/47.96 0 [] -group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_1)=zero_zero(X_a).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J_1)),K_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),K_2)),J_1).
% 48.27/47.96 0 [] -zero(X_b)|zero_zero(X_b)!=ti(X_b,X_2)|ti(X_b,X_2)=zero_zero(X_b).
% 48.27/47.96 0 [] -zero(X_b)|zero_zero(X_b)=ti(X_b,X_2)|ti(X_b,X_2)!=zero_zero(X_b).
% 48.27/47.96 0 [] -ab_group_add(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1)!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D)|ti(X_b,A_2)!=ti(X_b,B_1)|ti(X_b,C_1)=ti(X_b,D).
% 48.27/47.96 0 [] -ab_group_add(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1)!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D)|ti(X_b,A_2)=ti(X_b,B_1)|ti(X_b,C_1)!=ti(X_b,D).
% 48.27/47.96 0 [] -group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),zero_zero(X_a))=ti(X_a,A_1).
% 48.27/47.96 0 [] -hBOOL(hAPP(nat,bool,Pa,K_1))|hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,$f86(I_1,Pa,K_1))))|hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K_1),I_1))).
% 48.27/47.96 0 [] -hBOOL(hAPP(nat,bool,Pa,K_1))| -hBOOL(hAPP(nat,bool,Pa,$f86(I_1,Pa,K_1)))|hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K_1),I_1))).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(X_b),B_2))|ti(fun(X_b,bool),B_2)=bot_bot(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)!=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),B_2)).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)=bot_bot(fun(X_b,bool))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),B_2)).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2),bot_bot(fun(X_b,bool))))!=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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_2),A_3))=ti(X_b,X_2).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2),bot_bot(fun(X_b,bool))))=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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_2),bot_bot(fun(X_b,bool)))))).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),bot_bot(fun(X_b,bool))))!=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)=ti(X_b,X_2).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),bot_bot(fun(X_b,bool))))=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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_2),bot_bot(fun(X_b,bool)))))).
% 48.27/47.96 0 [] -lattice(X_b)|hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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_2),bot_bot(fun(X_b,bool))))=ti(X_b,X_2).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),A_2),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3))=ti(X_b,A_2).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -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_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3))=hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|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))|hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(X_b),B_2))|ti(fun(X_b,bool),B_2)=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),B_2)).
% 48.27/47.96 0 [] -lattice(X_b)|hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),$f88(X_b,N_3,H)),$f87(X_b,N_3,H)))!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(X_b,X_b,H,$f88(X_b,N_3,H))),hAPP(X_b,X_b,H,$f87(X_b,N_3,H)))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3))|ti(fun(X_b,bool),N_3)=bot_bot(fun(X_b,bool))|hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),N_3))=hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_3)).
% 48.27/47.96 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),$f90(X_b,A_3)),$f89(X_b,A_3))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f90(X_b,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),$f89(X_b,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(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)),A_3)).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,suc,N_1))=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_1),N_1)).
% 48.27/47.96 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)))))).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2),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_2),bot_bot(fun(X_b,bool)))))).
% 48.27/47.96 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_2),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_2),Z_1))=hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_2),Z_1).
% 48.27/47.96 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))).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),bot_bot(fun(X_b,bool)))=zero_zero(nat).
% 48.27/47.96 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=zero_zero(nat).
% 48.27/47.96 0 [] -semilattice_sup(X_b)|hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),semilattice_sup_sup(X_b))).
% 48.27/47.96 0 [] -semilattice_inf(X_b)|hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),semilattice_inf_inf(X_b))).
% 48.27/47.96 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).
% 48.27/47.96 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))=hAPP(nat,X_b,F2,Nat).
% 48.27/47.96 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_1(X_b),A_3)).
% 48.27/47.96 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)).
% 48.27/47.96 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_1(X_b),A_3)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),A_3))=hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),A_3))=hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),A_3))=hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))|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_2))=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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),bot_bot(fun(X_b,bool))))))=hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)!=hAPP(nat,nat,suc,K_1)|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),$f92(X_b,A_3,K_1)),$f91(X_b,A_3,K_1)).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)!=hAPP(nat,nat,suc,K_1)| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f92(X_b,A_3,K_1)),$f91(X_b,A_3,K_1))).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)!=hAPP(nat,nat,suc,K_1)|hAPP(fun(X_b,bool),nat,finite_card(X_b),$f91(X_b,A_3,K_1))=K_1.
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)!=hAPP(nat,nat,suc,K_1)|K_1!=zero_zero(nat)|ti(fun(X_b,bool),$f91(X_b,A_3,K_1))=bot_bot(fun(X_b,bool)).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=hAPP(nat,nat,suc,K_1)|ti(fun(X_b,bool),A_3)!=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_4),B_3)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_4),B_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),B_3)!=K_1|K_1=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=hAPP(nat,nat,suc,K_1)|ti(fun(X_b,bool),A_3)!=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_4),B_3)|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_4),B_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),B_3)!=K_1|ti(fun(X_b,bool),B_3)!=bot_bot(fun(X_b,bool)).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)!=hAPP(nat,nat,suc,K_1)|ti(fun(X_b,bool),A_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f94(X_b,A_3,K_1)),$f93(X_b,A_3,K_1)).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)!=hAPP(nat,nat,suc,K_1)| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f94(X_b,A_3,K_1)),$f93(X_b,A_3,K_1))).
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)!=hAPP(nat,nat,suc,K_1)|hAPP(fun(X_b,bool),nat,finite_card(X_b),$f93(X_b,A_3,K_1))=K_1.
% 48.27/47.96 0 [] hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)!=hAPP(nat,nat,suc,K_1)|K_1!=zero_zero(nat)|ti(fun(X_b,bool),$f93(X_b,A_3,K_1))=bot_bot(fun(X_b,bool)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),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)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),bot_bot(fun(X_b,bool)))))=hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),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)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2))|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_2)))=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_2))),one_one(nat)).
% 48.27/47.96 0 [] -one(X_b)|one_one(X_b)!=ti(X_b,X_2)|ti(X_b,X_2)=one_one(X_b).
% 48.27/47.96 0 [] -one(X_b)|one_one(X_b)=ti(X_b,X_2)|ti(X_b,X_2)!=one_one(X_b).
% 48.27/47.96 0 [] one_one(nat)=hAPP(nat,nat,suc,zero_zero(nat)).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N_2)),one_one(nat))=N_2.
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,N_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N_2).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f95(X_b,A_3)),A_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=zero_zero(nat).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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).
% 48.27/47.96 0 [] -zero_ne_q_one(X_a)|one_one(X_a)!=zero_zero(X_a).
% 48.27/47.96 0 [] -zero_ne_q_one(X_a)|zero_zero(X_a)!=one_one(X_a).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),bot_bot(fun(X_b,bool)))))).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2),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_2),bot_bot(fun(X_b,bool)))))).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N_2)=N_2.
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),zero_zero(nat))=M.
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)!=zero_zero(nat)|M_1=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)!=zero_zero(nat)|N_1=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)=zero_zero(nat)|M_1!=zero_zero(nat)|N_1!=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)!=M|N_2=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N_2))=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N_2)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N_2)).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),M).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X_1),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_1),Z)).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)),K_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K_2)).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_1)|M_1=N_1.
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_1)|M_1!=N_1.
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K_1)|M_1=N_1.
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K_1)|M_1!=N_1.
% 48.27/47.96 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)).
% 48.27/47.96 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_1)!=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_1)=ti(X_b,C_1).
% 48.27/47.96 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_1)=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_1)!=ti(X_b,C_1).
% 48.27/47.96 0 [] -cancel_semigroup_add(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_1),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_1)=ti(X_b,C_1).
% 48.27/47.96 0 [] -cancel_semigroup_add(X_b)|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_1),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_1)!=ti(X_b,C_1).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)),N_2)=M.
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),M)),N_2)=M.
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J_1)),K_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),K_2)).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),N_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)!=hAPP(nat,nat,suc,zero_zero(nat))|M_1=hAPP(nat,nat,suc,zero_zero(nat))|M_1=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)!=hAPP(nat,nat,suc,zero_zero(nat))|M_1=hAPP(nat,nat,suc,zero_zero(nat))|N_1=hAPP(nat,nat,suc,zero_zero(nat)).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)!=hAPP(nat,nat,suc,zero_zero(nat))|N_1=zero_zero(nat)|M_1=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)!=hAPP(nat,nat,suc,zero_zero(nat))|N_1=zero_zero(nat)|N_1=hAPP(nat,nat,suc,zero_zero(nat)).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)=hAPP(nat,nat,suc,zero_zero(nat))|M_1!=hAPP(nat,nat,suc,zero_zero(nat))|N_1!=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)=hAPP(nat,nat,suc,zero_zero(nat))|M_1!=zero_zero(nat)|N_1!=hAPP(nat,nat,suc,zero_zero(nat)).
% 48.27/47.96 0 [] hAPP(nat,nat,suc,zero_zero(nat))!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)|M_1=hAPP(nat,nat,suc,zero_zero(nat))|M_1=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,suc,zero_zero(nat))!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)|M_1=hAPP(nat,nat,suc,zero_zero(nat))|N_1=hAPP(nat,nat,suc,zero_zero(nat)).
% 48.27/47.96 0 [] hAPP(nat,nat,suc,zero_zero(nat))!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)|N_1=zero_zero(nat)|M_1=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,suc,zero_zero(nat))!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)|N_1=zero_zero(nat)|N_1=hAPP(nat,nat,suc,zero_zero(nat)).
% 48.27/47.96 0 [] hAPP(nat,nat,suc,zero_zero(nat))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)|M_1!=hAPP(nat,nat,suc,zero_zero(nat))|N_1!=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,suc,zero_zero(nat))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)|M_1!=zero_zero(nat)|N_1!=hAPP(nat,nat,suc,zero_zero(nat)).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),M))=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,suc,N_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),one_one(nat)).
% 48.27/47.96 0 [] hAPP(nat,nat,suc,N_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N_2).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))|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_b,bool),nat,finite_card(X_b),B_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))),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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))),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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))=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_b,bool),nat,finite_card(X_b),B_2)).
% 48.27/47.96 0 [] M!=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)=N_2.
% 48.27/47.96 0 [] M=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N_2)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),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)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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).
% 48.27/47.96 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)=zero_zero(nat).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)!=bot_bot(fun(X_b,bool))|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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=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_b,bool),nat,finite_card(X_b),B_2)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f96(X_b,B_2,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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))|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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=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_b,bool),nat,finite_card(X_b),B_2)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))|one_one(nat)!=zero_zero(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=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_b,bool),nat,finite_card(X_b),B_2)).
% 48.27/47.96 0 [] hAPP(com,nat,com_size,hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,com_size,Com1_2)),hAPP(com,nat,com_size,Com2_2))),hAPP(nat,nat,suc,zero_zero(nat))).
% 48.27/47.96 0 [] hAPP(com,nat,com_size,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,com_size,Com_1)),hAPP(nat,nat,suc,zero_zero(nat))).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 0 [] -semiri456707255roduct(X_b)|ti(X_b,B_1)!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_1),A_2)|ti(X_b,A_2)=zero_zero(X_b).
% 48.27/47.96 0 [] -semiri456707255roduct(X_b)|ti(X_b,B_1)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_1),A_2)|ti(X_b,A_2)!=zero_zero(X_b).
% 48.27/47.96 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).
% 48.27/47.96 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),D_1)).
% 48.27/47.96 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),D_1).
% 48.27/47.96 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)).
% 48.27/47.96 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).
% 48.27/47.96 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)).
% 48.27/47.96 0 [] hAPP(com,nat,com_size,hAPP(pname,com,body,Pname_1))=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(com,nat,com_size,skip)=zero_zero(nat).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))|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_2))=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_2)).
% 48.27/47.96 0 [] hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2))=zero_zero(nat).
% 48.27/47.96 0 [] hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))|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_2))=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(com,nat,size_size(com),hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,size_size(com),Com1_2)),hAPP(com,nat,size_size(com),Com2_2))),hAPP(nat,nat,suc,zero_zero(nat))).
% 48.27/47.96 0 [] hAPP(com,nat,size_size(com),hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,size_size(com),Com_1)),hAPP(nat,nat,suc,zero_zero(nat))).
% 48.27/47.96 0 [] -comm_monoid_mult(X_c)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)!=bot_bot(fun(X_b,bool))|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)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=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)),G),one_one(X_c)),B_2)).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),N_2)).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)),K_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_2)).
% 48.27/47.96 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),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),Z_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),W),Z_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),Y_1))|ti(X_b,W)=ti(X_b,X_2)|ti(X_b,Y_1)=ti(X_b,Z_1).
% 48.27/47.96 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),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),Z_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),W),Z_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),Y_1))|ti(X_b,W)!=ti(X_b,X_2).
% 48.27/47.96 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),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),Z_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),W),Z_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),Y_1))|ti(X_b,Y_1)!=ti(X_b,Z_1).
% 48.27/47.96 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).
% 48.27/47.96 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),M))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),M).
% 48.27/47.96 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)).
% 48.27/47.96 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)).
% 48.27/47.96 0 [] -semiri456707255roduct(X_b)|ti(X_b,A_2)=ti(X_b,B_1)|ti(X_b,C_1)=ti(X_b,D)|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_1),D))!=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)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_1),C_1)).
% 48.27/47.96 0 [] -semiri456707255roduct(X_b)|ti(X_b,A_2)!=ti(X_b,B_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_1),D))=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)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_1),C_1)).
% 48.27/47.96 0 [] -semiri456707255roduct(X_b)|ti(X_b,C_1)!=ti(X_b,D)|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_1),D))=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)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_1),C_1)).
% 48.27/47.96 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),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_1),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Z)).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 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)).
% 48.27/47.96 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).
% 48.27/47.96 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)).
% 48.27/47.96 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).
% 48.27/47.96 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))).
% 48.27/47.96 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)).
% 48.27/47.96 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)).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)!=one_one(nat)|M_1=one_one(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)!=one_one(nat)|N_1=one_one(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)=one_one(nat)|M_1!=one_one(nat)|N_1!=one_one(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),one_one(nat))=N_2.
% 48.27/47.96 0 [] one_one(nat)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)|M_1=one_one(nat).
% 48.27/47.96 0 [] one_one(nat)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)|N_1=one_one(nat).
% 48.27/47.96 0 [] one_one(nat)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)|M_1!=one_one(nat)|N_1!=one_one(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N_2)=N_2.
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),N_2)=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),zero_zero(nat))=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)!=zero_zero(nat)|M_1=zero_zero(nat)|N_1=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)=zero_zero(nat)|M_1!=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)=zero_zero(nat)|N_1!=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1)|M_1=N_1|K_1=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1)|M_1!=N_1.
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1)|K_1!=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K_1)|M_1=N_1|K_1=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K_1)|M_1!=N_1.
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K_1)|K_1!=zero_zero(nat).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_1)|M_1=N_1.
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_1)|M_1!=N_1.
% 48.27/47.96 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).
% 48.27/47.96 0 [] -ab_sem1668676832m_mult(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)=ti(X_a,X_1).
% 48.27/47.96 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).
% 48.27/47.96 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)).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)),K_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_2)).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),N_2)).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 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_1)!=zero_zero(X_b)|ti(X_b,A_2)=zero_zero(X_b)|ti(X_b,B_1)=zero_zero(X_b).
% 48.27/47.96 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_1)=zero_zero(X_b)|ti(X_b,A_2)!=zero_zero(X_b).
% 48.27/47.96 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_1)=zero_zero(X_b)|ti(X_b,B_1)!=zero_zero(X_b).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 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).
% 48.27/47.96 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))).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite_1(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_2)))|hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite_1(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_2)))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))|hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite_1(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_2))).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite_1(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_2)))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite_1(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_2)))|hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2)).
% 48.27/47.96 0 [] hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite_1(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_2)))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2)).
% 48.27/47.96 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_2),X_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_1),Y_1))!=zero_zero(X_b)|ti(X_b,X_2)=zero_zero(X_b).
% 48.27/47.96 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_2),X_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_1),Y_1))!=zero_zero(X_b)|ti(X_b,Y_1)=zero_zero(X_b).
% 48.27/47.96 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_2),X_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_1),Y_1))=zero_zero(X_b)|ti(X_b,X_2)!=zero_zero(X_b)|ti(X_b,Y_1)!=zero_zero(X_b).
% 48.27/47.96 0 [] -semiri456707255roduct(X_a)|ti(X_a,R_2)=zero_zero(X_a)|ti(X_a,A_1)!=ti(X_a,B)|ti(X_a,C)=ti(X_a,D_1)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_2),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_2),D_1)).
% 48.27/47.96 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_1),E)),D)|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_1),A_2)),E)),D).
% 48.27/47.96 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_1),E)),D)|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_1),A_2)),E)),D).
% 48.27/47.96 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_1),E)),D)|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_1)),E)),C_1)=ti(X_b,D).
% 48.27/47.96 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_1),E)),D)|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_1)),E)),C_1)!=ti(X_b,D).
% 48.27/47.96 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),M)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),M).
% 48.27/47.96 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M).
% 48.27/47.96 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),M)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)!=hAPP(nat,nat,suc,zero_zero(nat))|M_1=hAPP(nat,nat,suc,zero_zero(nat)).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)!=hAPP(nat,nat,suc,zero_zero(nat))|N_1=hAPP(nat,nat,suc,zero_zero(nat)).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)=hAPP(nat,nat,suc,zero_zero(nat))|M_1!=hAPP(nat,nat,suc,zero_zero(nat))|N_1!=hAPP(nat,nat,suc,zero_zero(nat)).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,M)),N_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2)).
% 48.27/47.96 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,suc,N_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2)).
% 48.27/47.96 0 [] M!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2)|N_2=one_one(nat)|M=zero_zero(nat).
% 48.27/47.96 0 [] -ab_semigroup_mult(X_c)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_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),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_1),A_3)).
% 48.27/47.96 0 [] hAPP(com,nat,size_size(com),hAPP(pname,com,body,Pname_1))=zero_zero(nat).
% 48.27/47.96 0 [] -comm_monoid_mult(X_c)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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)).
% 48.27/47.96 0 [] hAPP(com,nat,size_size(com),skip)=zero_zero(nat).
% 48.27/47.96 0 [] M!=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2)=zero_zero(nat).
% 48.27/47.96 0 [] M=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N_2)).
% 48.27/47.96 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))|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_2))=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_2)).
% 48.27/47.96 0 [] -comm_monoid_mult(X_c)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))|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)),G),one_one(X_c)),B_2))=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)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_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),one_one(X_c)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))).
% 48.27/47.96 0 [] -comm_monoid_mult(X_c)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),T_5))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f97(X_b,X_c,F,T_5,S_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),S_1),T_5)))|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)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),S_1),T_5))=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)),F),one_one(X_c)),S_1)),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)),T_5)).
% 48.27/47.96 0 [] -comm_monoid_mult(X_c)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),T_5))|hAPP(X_b,X_c,F,$f97(X_b,X_c,F,T_5,S_1))!=one_one(X_c)|hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),F),one_one(X_c)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),S_1),T_5))=hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),F),one_one(X_c)),S_1)),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),F),one_one(X_c)),T_5)).
% 48.27/47.96 0 [] -comm_monoid_mult(X_c)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f98(X_b,X_c,F,S_1)),S_1))|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_1)=one_one(X_c).
% 48.27/47.97 0 [] -comm_monoid_mult(X_c)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1))|hAPP(X_b,X_c,F,$f98(X_b,X_c,F,S_1))!=one_one(X_c)|hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),F),one_one(X_c)),S_1)=one_one(X_c).
% 48.27/47.97 0 [] -ab_semigroup_mult(X_c)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f99(X_b,X_c,Z_1,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_1),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_1),A_3).
% 48.27/47.97 0 [] -ab_semigroup_mult(X_c)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|hAPP(X_b,X_c,G,$f99(X_b,X_c,Z_1,G,H,A_3))!=hAPP(X_b,X_c,H,$f99(X_b,X_c,Z_1,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_1),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_1),A_3).
% 48.27/47.97 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_2)!=bot_bot(fun(sum_sum(X_b,X_c),bool))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool)).
% 48.27/47.97 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_2)!=bot_bot(fun(sum_sum(X_b,X_c),bool))|ti(fun(X_c,bool),B_2)=bot_bot(fun(X_c,bool)).
% 48.27/47.97 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_2)=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_2)!=bot_bot(fun(X_c,bool)).
% 48.27/47.97 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),M).
% 48.27/47.97 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2)),K_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_2)).
% 48.27/47.97 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U_1)),K_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_1)),U_1)),K_2).
% 48.27/47.97 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1)|K_1=zero_zero(nat)|M_1=N_1.
% 48.27/47.97 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1)|K_1!=zero_zero(nat).
% 48.27/47.97 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1)|M_1!=N_1.
% 48.27/47.97 0 [] -comm_monoid_mult(X_d)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),$f100(X_c,X_b,X_d,E,G,F,H,K_1,T_5,S_1)),T_5))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f101(X_c,X_b,X_d,E,G,F,H,K_1,T_5,S_1)),S_1))|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_1)=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_5).
% 48.27/47.97 0 [] -comm_monoid_mult(X_d)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),$f100(X_c,X_b,X_d,E,G,F,H,K_1,T_5,S_1)),T_5))| -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,H,$f101(X_c,X_b,X_d,E,G,F,H,K_1,T_5,S_1))),T_5))|hAPP(X_c,X_b,K_1,hAPP(X_b,X_c,H,$f101(X_c,X_b,X_d,E,G,F,H,K_1,T_5,S_1)))!=ti(X_b,$f101(X_c,X_b,X_d,E,G,F,H,K_1,T_5,S_1))|hAPP(X_c,X_d,G,hAPP(X_b,X_c,H,$f101(X_c,X_b,X_d,E,G,F,H,K_1,T_5,S_1)))!=hAPP(X_b,X_d,F,$f101(X_c,X_b,X_d,E,G,F,H,K_1,T_5,S_1))|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_1)=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_5).
% 48.27/47.97 0 [] -comm_monoid_mult(X_d)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1))| -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_1,$f100(X_c,X_b,X_d,E,G,F,H,K_1,T_5,S_1))),S_1))|hAPP(X_b,X_c,H,hAPP(X_c,X_b,K_1,$f100(X_c,X_b,X_d,E,G,F,H,K_1,T_5,S_1)))!=ti(X_c,$f100(X_c,X_b,X_d,E,G,F,H,K_1,T_5,S_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f101(X_c,X_b,X_d,E,G,F,H,K_1,T_5,S_1)),S_1))|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_1)=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_5).
% 48.27/47.97 0 [] -comm_monoid_mult(X_d)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1))| -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_1,$f100(X_c,X_b,X_d,E,G,F,H,K_1,T_5,S_1))),S_1))|hAPP(X_b,X_c,H,hAPP(X_c,X_b,K_1,$f100(X_c,X_b,X_d,E,G,F,H,K_1,T_5,S_1)))!=ti(X_c,$f100(X_c,X_b,X_d,E,G,F,H,K_1,T_5,S_1))| -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,H,$f101(X_c,X_b,X_d,E,G,F,H,K_1,T_5,S_1))),T_5))|hAPP(X_c,X_b,K_1,hAPP(X_b,X_c,H,$f101(X_c,X_b,X_d,E,G,F,H,K_1,T_5,S_1)))!=ti(X_b,$f101(X_c,X_b,X_d,E,G,F,H,K_1,T_5,S_1))|hAPP(X_c,X_d,G,hAPP(X_b,X_c,H,$f101(X_c,X_b,X_d,E,G,F,H,K_1,T_5,S_1)))!=hAPP(X_b,X_d,F,$f101(X_c,X_b,X_d,E,G,F,H,K_1,T_5,S_1))|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_1)=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_5).
% 48.27/47.97 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,$f105(X_c,X_b,H,G,S_1,R_1,E)),$f103(X_c,X_b,H,G,S_1,R_1,E)))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),S_1))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),$f106(X_c,X_b,H,G,S_1,R_1,E)),S_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),H),E),S_1)),hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),G),E),S_1))).
% 48.27/47.97 0 [] -comm_monoid_mult(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,E),E))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,$f105(X_c,X_b,H,G,S_1,R_1,E)),$f103(X_c,X_b,H,G,S_1,R_1,E)))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),S_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_c,X_b,H,$f106(X_c,X_b,H,G,S_1,R_1,E))),hAPP(X_c,X_b,G,$f106(X_c,X_b,H,G,S_1,R_1,E))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),H),E),S_1)),hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),G),E),S_1))).
% 48.27/47.97 0 [] -comm_monoid_mult(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,E),E))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,$f104(X_c,X_b,H,G,S_1,R_1,E)),$f102(X_c,X_b,H,G,S_1,R_1,E)))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),S_1))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),$f106(X_c,X_b,H,G,S_1,R_1,E)),S_1))|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_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)),G),E),S_1))).
% 48.27/47.97 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,$f104(X_c,X_b,H,G,S_1,R_1,E)),$f102(X_c,X_b,H,G,S_1,R_1,E)))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),S_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_c,X_b,H,$f106(X_c,X_b,H,G,S_1,R_1,E))),hAPP(X_c,X_b,G,$f106(X_c,X_b,H,G,S_1,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_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)),G),E),S_1))).
% 48.27/47.97 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),$f105(X_c,X_b,H,G,S_1,R_1,E)),$f104(X_c,X_b,H,G,S_1,R_1,E))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),$f103(X_c,X_b,H,G,S_1,R_1,E)),$f102(X_c,X_b,H,G,S_1,R_1,E))))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),S_1))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),$f106(X_c,X_b,H,G,S_1,R_1,E)),S_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),H),E),S_1)),hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),G),E),S_1))).
% 48.27/47.97 0 [] -comm_monoid_mult(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,E),E))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),$f105(X_c,X_b,H,G,S_1,R_1,E)),$f104(X_c,X_b,H,G,S_1,R_1,E))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),$f103(X_c,X_b,H,G,S_1,R_1,E)),$f102(X_c,X_b,H,G,S_1,R_1,E))))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),S_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_c,X_b,H,$f106(X_c,X_b,H,G,S_1,R_1,E))),hAPP(X_c,X_b,G,$f106(X_c,X_b,H,G,S_1,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_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)),G),E),S_1))).
% 48.27/47.97 0 [] -ab_semigroup_mult(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(X_b),B_2))|ti(fun(X_b,bool),B_2)=bot_bot(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)!=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),B_2)).
% 48.27/47.97 0 [] hAPP(com,nat,size_size(com),hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,size_size(com),Com1_1)),hAPP(com,nat,size_size(com),Com2_1))),hAPP(nat,nat,suc,zero_zero(nat))).
% 48.27/47.97 0 [] hAPP(com,nat,com_size,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,com_size,Com1_1)),hAPP(com,nat,com_size,Com2_1))),hAPP(nat,nat,suc,zero_zero(nat))).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))).
% 48.27/47.97 0 [] -preorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),X_1)).
% 48.27/47.97 0 [] hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(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_1)))).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C1),C2)),S_2),N_1),T_4))|hBOOL(hAPP(state,bool,B_1,S_2))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2),S_2),N_1),T_4)).
% 48.27/47.97 0 [] -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C1),C2)),S_2),N_1),T_4))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1),S_2),N_1),T_4))| -hBOOL(hAPP(state,bool,B_1,S_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C1),C2)),S_2),N_1),T_4))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1),S_2),N_1),T_4))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2),S_2),N_1),T_4)).
% 48.27/47.97 0 [] -hBOOL(hAPP(state,bool,B_1,S_2))| -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C0),S_2),N_1),S1))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C0),C1)),S_2),N_1),S1)).
% 48.27/47.97 0 [] hBOOL(hAPP(state,bool,B_1,S_2))| -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1),S_2),N_1),S1))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C0),C1)),S_2),N_1),S1)).
% 48.27/47.97 0 [] hBOOL(hAPP(state,bool,B_1,S_2))| -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1),S_2),S1))|hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C0),C1)),S_2),S1)).
% 48.27/47.97 0 [] -hBOOL(hAPP(state,bool,B_1,S_2))| -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C0),S_2),S1))|hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C0),C1)),S_2),S1)).
% 48.27/47.97 0 [] -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C1),C2)),S_2),T_4))|hBOOL(hAPP(state,bool,B_1,S_2))|hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C2),S_2),T_4)).
% 48.27/47.97 0 [] -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C1),C2)),S_2),T_4))|hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1),S_2),T_4))| -hBOOL(hAPP(state,bool,B_1,S_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C1),C2)),S_2),T_4))|hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1),S_2),T_4))|hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C2),S_2),T_4)).
% 48.27/47.97 0 [] hAPP(pname,com,body,Pname)!=hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1).
% 48.27/47.97 0 [] hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1)!=hAPP(pname,com,body,Pname).
% 48.27/47.97 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1)).
% 48.27/47.97 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))).
% 48.27/47.97 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))| -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_1)).
% 48.27/47.97 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))|ti(X_a,X_1)=ti(X_a,Y).
% 48.27/47.97 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),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_1),Z)).
% 48.27/47.97 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))|ti(X_a,X_1)=ti(X_a,Y).
% 48.27/47.97 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)).
% 48.27/47.97 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)).
% 48.27/47.97 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)).
% 48.27/47.97 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)).
% 48.27/47.97 0 [] -order(X_b)| -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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),Y_1))|ti(X_b,X_2)=ti(X_b,Y_1).
% 48.27/47.97 0 [] -order(X_b)| -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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),Y_1))|ti(X_b,X_2)!=ti(X_b,Y_1).
% 48.27/47.97 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))).
% 48.27/47.97 0 [] -preorder(X_a)|X_1!=Y|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y)).
% 48.27/47.97 0 [] -order(X_b)|ti(X_b,X_2)!=ti(X_b,Y_1)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),Y_1)).
% 48.27/47.97 0 [] -order(X_b)|ti(X_b,X_2)!=ti(X_b,Y_1)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_1),X_2)).
% 48.27/47.97 0 [] -order(X_b)|ti(X_b,X_2)=ti(X_b,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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_1),X_2)).
% 48.27/47.97 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1)).
% 48.27/47.97 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)),hAPP(X_b,X_c,G,X))).
% 48.27/47.97 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,$f107(X_b,X_c,F,G))),hAPP(X_b,X_c,G,$f107(X_b,X_c,F,G)))).
% 48.27/47.97 0 [] hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1)!=hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun),Com1),Com2)|Fun_1=Fun.
% 48.27/47.97 0 [] hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1)!=hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun),Com1),Com2)|Com1_1=Com1.
% 48.27/47.97 0 [] hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1)!=hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun),Com1),Com2)|Com2_1=Com2.
% 48.27/47.97 0 [] hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1)=hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun),Com1),Com2)|Fun_1!=Fun|Com1_1!=Com1|Com2_1!=Com2.
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M))|M=N_2.
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),K_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),K_2)).
% 48.27/47.97 0 [] M!=N_2|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2)).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M)).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),N_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M)),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,suc,N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))|M=hAPP(nat,nat,suc,N_2).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,suc,N_2))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_1)),hAPP(nat,nat,suc,M_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M_1)).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_1)),hAPP(nat,nat,suc,M_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),M_1)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,suc,N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))|M_1=hAPP(nat,nat,suc,N_1).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,suc,N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1)).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),hAPP(nat,nat,suc,N_1)))|M_1!=hAPP(nat,nat,suc,N_1).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_1)),M_1)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_1)),M_1)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_2)),N_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),zero_zero(nat)))|N_1=zero_zero(nat).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),zero_zero(nat)))|N_1!=zero_zero(nat).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N_2)).
% 48.27/47.97 0 [] -lattice(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),semilattice_inf_inf(X_a),X_1),Y)),X_1)).
% 48.27/47.97 0 [] -semilattice_inf(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),semilattice_inf_inf(X_a),X_1),Y)),X_1)).
% 48.27/47.97 0 [] -lattice(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),semilattice_inf_inf(X_a),X_1),Y)),Y)).
% 48.27/47.97 0 [] -semilattice_inf(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),semilattice_inf_inf(X_a),X_1),Y)),Y)).
% 48.27/47.97 0 [] -semilattice_inf(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),Y_1))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X_2),Y_1)=ti(X_b,X_2).
% 48.27/47.97 0 [] -semilattice_inf(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),Y_1))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X_2),Y_1)!=ti(X_b,X_2).
% 48.27/47.97 0 [] -semilattice_inf(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),Y_1),Z_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),Y_1)).
% 48.27/47.97 0 [] -semilattice_inf(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),Y_1),Z_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),Z_1)).
% 48.27/47.97 0 [] -semilattice_inf(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),Y_1),Z_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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),Z_1)).
% 48.27/47.97 0 [] -semilattice_inf(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),X_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)),X_1)).
% 48.27/47.97 0 [] -semilattice_inf(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),X_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)),X_1)).
% 48.27/47.97 0 [] -semilattice_inf(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)=ti(X_a,X_1).
% 48.27/47.97 0 [] -semilattice_inf(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)=ti(X_a,Y).
% 48.27/47.97 0 [] -semilattice_inf(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B))).
% 48.27/47.97 0 [] -semilattice_inf(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Z))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))).
% 48.27/47.97 0 [] -semilattice_inf(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),C))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),D_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),C),D_1))).
% 48.27/47.97 0 [] -semilattice_inf(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),A_1)).
% 48.27/47.97 0 [] -semilattice_inf(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),B)).
% 48.27/47.97 0 [] -lattice(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y))).
% 48.27/47.97 0 [] -semilattice_sup(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y))).
% 48.27/47.97 0 [] -lattice(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y))).
% 48.27/47.97 0 [] -semilattice_sup(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y))).
% 48.27/47.97 0 [] -semilattice_sup(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),Y_1))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),Y_1)=ti(X_b,Y_1).
% 48.27/47.97 0 [] -semilattice_sup(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),Y_1))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),Y_1)!=ti(X_b,Y_1).
% 48.27/47.97 0 [] -semilattice_sup(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),semilattice_sup_sup(X_b),X_2),Y_1)),Z_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),Z_1)).
% 48.27/47.97 0 [] -semilattice_sup(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),semilattice_sup_sup(X_b),X_2),Y_1)),Z_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_1),Z_1)).
% 48.27/47.97 0 [] -semilattice_sup(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),semilattice_sup_sup(X_b),X_2),Y_1)),Z_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),Z_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_1),Z_1)).
% 48.27/47.97 0 [] -semilattice_sup(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B))).
% 48.27/47.97 0 [] -semilattice_sup(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B))).
% 48.27/47.97 0 [] -semilattice_sup(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)=ti(X_a,Y).
% 48.27/47.97 0 [] -semilattice_sup(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)=ti(X_a,X_1).
% 48.27/47.97 0 [] -semilattice_sup(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),X_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),X_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B)),X_1)).
% 48.27/47.97 0 [] -semilattice_sup(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Z),X_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)),X_1)).
% 48.27/47.97 0 [] -semilattice_sup(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),C))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),D_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),C),D_1))).
% 48.27/47.97 0 [] -semilattice_sup(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),semilattice_sup_sup(X_a),A_1),B)),X_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),X_1)).
% 48.27/47.97 0 [] -semilattice_sup(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),semilattice_sup_sup(X_a),A_1),B)),X_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),X_1)).
% 48.27/47.97 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_1)!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C_1),D)).
% 48.27/47.97 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_1)!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C_1),D)).
% 48.27/47.97 0 [] -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C),S),N_2),T_3))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M))|hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C),S),M),T_3)).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)),M)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),L)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),L))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),N_2))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),I))=I.
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K_1)|M_1=N_1.
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K_1)|M_1!=N_1.
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),M))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),N_2))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),K_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1)).
% 48.27/47.97 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)).
% 48.27/47.97 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)).
% 48.27/47.97 0 [] -ordere779506340up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))).
% 48.27/47.97 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))).
% 48.27/47.97 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))).
% 48.27/47.97 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_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_1)).
% 48.27/47.97 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_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_1)).
% 48.27/47.97 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_1),C_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_1)).
% 48.27/47.97 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_1),C_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),B_1)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),N_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),N_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),L))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),L))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),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),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),K_2))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J_1))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),M))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1)).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))|N_1=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),$f108(M_1,N_1)).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))|N_1!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),M))).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2))).
% 48.27/47.97 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)),N_1)))=hAPP(nat,nat,suc,N_1).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M_1)),N_1))|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_1)),N_1)).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M_1)),N_1))| -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_1)),N_1)).
% 48.27/47.97 0 [] -semilattice_inf(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),semilattice_inf_inf(X_b)),A_3)))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),X)).
% 48.27/47.97 0 [] -semilattice_inf(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),semilattice_inf_inf(X_b)),A_3)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f109(X_b,X_2,A_3)),A_3)).
% 48.27/47.97 0 [] -semilattice_inf(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),semilattice_inf_inf(X_b)),A_3)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),$f109(X_b,X_2,A_3))).
% 48.27/47.97 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).
% 48.27/47.97 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).
% 48.27/47.97 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).
% 48.27/47.97 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)).
% 48.27/47.97 0 [] -semilattice_inf(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),semilattice_inf_inf(X_b)),A_3)),A_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),L))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),L))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),I)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),J_1))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),K_2))).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M)))).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M))).
% 48.27/47.97 0 [] hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1)!=hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com).
% 48.27/47.97 0 [] hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com)!=hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1).
% 48.27/47.97 0 [] hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun),Com1),Com2)!=hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1).
% 48.27/47.97 0 [] hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1)!=hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun),Com1),Com2).
% 48.27/47.97 0 [] hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun),Com1),Com2)!=skip.
% 48.27/47.97 0 [] skip!=hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun),Com1),Com2).
% 48.27/47.97 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)).
% 48.27/47.97 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)).
% 48.27/47.97 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))).
% 48.27/47.97 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))).
% 48.27/47.97 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))).
% 48.27/47.97 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_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),Y_1))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),X_2),Y_1)!=zero_zero(X_b)|ti(X_b,X_2)=zero_zero(X_b).
% 48.27/47.97 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_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),Y_1))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),X_2),Y_1)!=zero_zero(X_b)|ti(X_b,Y_1)=zero_zero(X_b).
% 48.27/47.97 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_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),Y_1))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),X_2),Y_1)=zero_zero(X_b)|ti(X_b,X_2)!=zero_zero(X_b)|ti(X_b,Y_1)!=zero_zero(X_b).
% 48.27/47.97 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))).
% 48.27/47.97 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))).
% 48.27/47.97 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))).
% 48.27/47.97 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))).
% 48.27/47.97 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))).
% 48.27/47.97 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))).
% 48.27/47.97 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))).
% 48.27/47.97 0 [] -ordered_semiring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1))).
% 48.27/47.97 0 [] -ordered_semiring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1))).
% 48.27/47.97 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))).
% 48.27/47.97 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))).
% 48.27/47.97 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))).
% 48.27/47.97 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))).
% 48.27/47.97 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))).
% 48.27/47.97 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))).
% 48.27/47.97 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))).
% 48.27/47.97 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))).
% 48.27/47.97 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))).
% 48.27/47.97 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))).
% 48.27/47.97 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_1)),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))).
% 48.27/47.97 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_1)),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_1)).
% 48.27/47.97 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_1)),zero_zero(X_b)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),B_1),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))).
% 48.27/47.97 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_1)),zero_zero(X_b)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),B_1),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_1)).
% 48.27/47.97 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_1)),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_1),zero_zero(X_b))).
% 48.27/47.97 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_1)),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_1)).
% 48.27/47.97 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_1)))|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))).
% 48.27/47.97 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_1)))|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_1),zero_zero(X_b))).
% 48.27/47.97 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_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),B_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),A_2),zero_zero(X_b))).
% 48.27/47.97 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_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),zero_zero(X_b)),B_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),B_1),zero_zero(X_b))).
% 48.27/47.97 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_1)))| -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_1)).
% 48.27/47.97 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_1)))| -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_1),zero_zero(X_b))).
% 48.27/47.97 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))).
% 48.27/47.97 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_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),minus_minus(X_b),A_2),B_1)),zero_zero(X_b))).
% 48.27/47.97 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_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),minus_minus(X_b),A_2),B_1)),zero_zero(X_b))).
% 48.27/47.97 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))).
% 48.27/47.97 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))).
% 48.27/47.97 0 [] -lattice(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),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Z))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)))).
% 48.27/47.97 0 [] -lattice(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),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Z)))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)=zero_zero(nat).
% 48.27/47.97 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)!=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1)).
% 48.27/47.97 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N_2)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1)).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),J_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_2)),J_1).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)),I_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1))).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)),I_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),M)),K_2))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2))=M.
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),J_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_1)),K_2).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),J_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_2),M))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)),N_2)=M.
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)!=K_1|J_2=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),I_1).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)=K_1|J_2!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),I_1).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),J_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_1)),K_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),J_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2)),I)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),I)),K_2).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),J_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),I)),K_2)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2)),I).
% 48.27/47.97 0 [] hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),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,A_2).
% 48.27/47.97 0 [] G!=hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F)|hAPP(fun(X_b,bool),X_b,G,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,A_2).
% 48.27/47.97 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_1(X_b),A_3))|hAPP(fun(X_b,bool),X_b,F_1,A_3)=hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_3).
% 48.27/47.97 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_2),X_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_1),Y_1))),zero_zero(X_b)))|ti(X_b,X_2)=zero_zero(X_b).
% 48.27/47.97 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_2),X_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_1),Y_1))),zero_zero(X_b)))|ti(X_b,Y_1)=zero_zero(X_b).
% 48.27/47.97 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_2),X_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_1),Y_1))),zero_zero(X_b)))|ti(X_b,X_2)!=zero_zero(X_b)|ti(X_b,Y_1)!=zero_zero(X_b).
% 48.27/47.97 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_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y)))).
% 48.27/47.97 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))| -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_1),Y)),X_1)).
% 48.27/47.97 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))| -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_1)),X_1)).
% 48.27/47.97 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_1),E)),D)))|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_1)),E)),C_1)),D)).
% 48.27/47.97 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_1),E)),D)))| -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_1)),E)),C_1)),D)).
% 48.27/47.97 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_1),E)),D)))|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_1),A_2)),E)),D))).
% 48.27/47.97 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_1),E)),D)))| -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_1),A_2)),E)),D))).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_2),A_3)))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1)).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1)).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),J_1))|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_1),K_2))),M)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,J_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),M)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_2),J_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2)))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)),hAPP(nat,nat,suc,J_1)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U)),M_1)),N_1)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U)),M_1)),N_1)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_1),I))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U_1)),N_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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J_1)),U_1)),M)),N_2).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_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),I_1),J_2)),U)),M_1)=N_1.
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),I_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_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),I_1),J_2)),U)),M_1)!=N_1.
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_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),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N_1))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_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),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N_1))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U_1)),N_2))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I)),U_1)),N_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N_1).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),J_2))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N_1).
% 48.27/47.97 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)=hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),semilattice_sup_sup(X_b)),A_3).
% 48.27/47.97 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)=hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),semilattice_inf_inf(X_b)),A_3).
% 48.27/47.97 0 [] -linord1278240602ring_1(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),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_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2))),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_2)))).
% 48.27/47.97 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3))).
% 48.27/47.97 0 [] -ab_semigroup_mult(X_b)|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))|hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3)).
% 48.27/47.97 0 [] -ab_sem1668676832m_mult(X_b)|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(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_2),A_3))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3)).
% 48.27/47.97 0 [] -ab_sem1668676832m_mult(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(X_b),B_2))|ti(fun(X_b,bool),B_2)=bot_bot(fun(X_b,bool))|hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),B_2)).
% 48.27/47.97 0 [] -ab_sem1668676832m_mult(X_b)|hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),$f111(X_b,N_3,H)),$f110(X_b,N_3,H)))!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,H,$f111(X_b,N_3,H))),hAPP(X_b,X_b,H,$f110(X_b,N_3,H)))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3))|ti(fun(X_b,bool),N_3)=bot_bot(fun(X_b,bool))|hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),N_3))=hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),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_3)).
% 48.27/47.97 0 [] -ab_semigroup_mult(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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),times_times(X_b),$f113(X_b,A_3)),$f112(X_b,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),$f113(X_b,A_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f112(X_b,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(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3)),A_3)).
% 48.27/47.97 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),big_semilattice_big(X_b),F),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|hAPP(fun(X_b,bool),X_b,F_1,A_3)=hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_3).
% 48.27/47.97 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)).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|hBOOL(hAPP(fun(fun(X_b,bool),bool),bool,finite_finite_1(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)))).
% 48.27/47.97 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_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(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_e_q(fun(X_c,bool)),$f114(X_b,X_c,B_2,F,A_3)),A_3)).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))|ti(fun(X_b,bool),B_2)=hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),$f114(X_b,X_c,B_2,F,A_3)).
% 48.27/47.97 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_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(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_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),AA).
% 48.27/47.97 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_2))|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_2))).
% 48.27/47.97 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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),A_3)).
% 48.27/47.97 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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),B_2)).
% 48.27/47.97 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_2))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)=ti(fun(X_b,bool),A_3).
% 48.27/47.97 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_2),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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)=ti(fun(X_b,bool),B_2).
% 48.27/47.97 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_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)),C_3),B_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)),C_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))).
% 48.27/47.97 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_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_2),D_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),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),C_3),D_2))).
% 48.27/47.97 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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))).
% 48.27/47.97 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_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))).
% 48.27/47.97 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_2))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)=ti(fun(X_b,bool),B_2).
% 48.27/47.97 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_2))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)!=ti(fun(X_b,bool),B_2).
% 48.27/47.97 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_2))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)=ti(fun(X_b,bool),B_2).
% 48.27/47.97 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_2),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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)=ti(fun(X_b,bool),A_3).
% 48.27/47.97 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_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_2),C_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)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),C_3)).
% 48.27/47.97 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_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_2),D_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),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),C_3),D_2))).
% 48.27/47.97 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_2))|hBOOL(hAPP(fun(fun(X_b,bool),bool),bool,hAPP(fun(fun(X_b,bool),bool),fun(fun(fun(X_b,bool),bool),bool),ord_less_e_q(fun(fun(X_b,bool),bool)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),powp(X_b),A_3)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),powp(X_b),B_2))).
% 48.27/47.97 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_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_2))).
% 48.27/47.97 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_2),A_3)),B_2))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)).
% 48.27/47.97 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_2),A_3)),B_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),B_2)).
% 48.27/47.97 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_2),A_3)),B_2))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_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),B_2)).
% 48.27/47.97 0 [] 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(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_2),B_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),B_2)).
% 48.27/47.97 0 [] 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(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_2),B_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),B_2)).
% 48.27/47.97 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_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),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_1),B_2))).
% 48.27/47.97 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_3),D_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),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),C_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),D_2))).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),G_1),Ts))| -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),ord_less_e_q(fun(hoare_2118899576triple(X_b),bool)),G_1),Ga))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts)).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts_1))| -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),ord_less_e_q(fun(hoare_2118899576triple(X_b),bool)),Ts),Ts_1))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts)).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),ord_less_e_q(fun(hoare_2118899576triple(X_b),bool)),Ts),Ga))|hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts)).
% 48.27/47.97 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_2)),A_3)).
% 48.27/47.97 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_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)),D_2),B_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),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_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)),C_3),D_2))).
% 48.27/47.97 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_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_2),C_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)),B_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)),C_3),A_3))=ti(fun(X_b,bool),A_3).
% 48.27/47.97 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)).
% 48.27/47.97 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)).
% 48.27/47.97 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_2))| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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),B_2))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)).
% 48.27/47.97 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_2),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_2),bot_bot(fun(X_b,bool))).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_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),A_3)))|hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2)).
% 48.27/47.97 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_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)),semilattice_inf_inf(fun(X_c,bool)),A_3),B_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(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_2)))).
% 48.27/47.97 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),C_3)!=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_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_3),A_3)).
% 48.27/47.97 0 [] hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(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)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),C_3)=hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_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_3),A_3)).
% 48.27/47.97 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_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),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_2)))).
% 48.27/47.97 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_2)),C_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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3))).
% 48.27/47.97 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_2)),C_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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3))).
% 48.27/47.97 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_2))|hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),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)),B_2),A_3))=ti(fun(X_b,bool),B_2).
% 48.27/47.97 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_1),G),F_1))| -hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(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_2),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_2)),hAPP(fun(X_c,bool),X_b,F_1,A_3))=hAPP(fun(X_c,bool),X_b,F_1,A_3).
% 48.27/47.97 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_2),B_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(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_2),bot_bot(fun(X_b,bool))))),B_2)).
% 48.27/47.97 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_2),B_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(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_2)).
% 48.27/47.97 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_2),B_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(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_2)).
% 48.27/47.97 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_2),B_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),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_2),bot_bot(fun(X_b,bool))))),B_2))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)).
% 48.27/47.97 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_2),B_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),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_2),bot_bot(fun(X_b,bool))))),B_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),B_2)).
% 48.27/47.97 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_2),bot_bot(fun(X_b,bool))))),B_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(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_2),B_2))).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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),B_2))|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_2))).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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),B_2))| -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_2)),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_2).
% 48.27/47.97 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_1(X_b),A_3))|ti(fun(X_b,bool),B_2)=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_2),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_2)),hAPP(fun(X_b,bool),X_b,F_1,A_3))=hAPP(fun(X_b,bool),X_b,F_1,A_3).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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_2),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_2))=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_2)).
% 48.27/47.97 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|ti(fun(X_b,bool),B_2)=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_2),A_3))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),B_2)),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3))=hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3).
% 48.27/47.97 0 [] -lattice(X_b)| -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|ti(fun(X_b,bool),B_2)=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_2),A_3))|hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),B_2)),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3))=hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3).
% 48.27/47.97 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,$f115(X_b,N_1,N_4,F))),hAPP(nat,X_b,F,hAPP(nat,nat,suc,$f115(X_b,N_1,N_4,F)))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),N_4))|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,N_4))).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_1(X_b),$f116(X_b,Pa,A_3,F_1)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),F_1),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f117(X_b,Pa,A_3,F_1)),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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),$f117(X_b,Pa,A_3,F_1)),$f116(X_b,Pa,A_3,F_1)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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,$f116(X_b,Pa,A_3,F_1)))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),F_1),A_3))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))| -hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),$f117(X_b,Pa,A_3,F_1)),$f116(X_b,Pa,A_3,F_1))))|hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)).
% 48.27/47.97 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_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_2),A_3))|ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_2).
% 48.27/47.97 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_2))| -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_2)).
% 48.27/47.97 0 [] ti(fun(X_b,bool),A_3)!=ti(fun(X_b,bool),B_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),B_2)).
% 48.27/47.97 0 [] ti(fun(X_b,bool),A_3)!=ti(fun(X_b,bool),B_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_2),A_3)).
% 48.27/47.97 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_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_2),C_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),C_3)).
% 48.27/47.97 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_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_2)).
% 48.27/47.97 0 [] -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(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_2))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)).
% 48.27/47.97 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),Qa))| -hBOOL(hAPP(X_b,bool,Pa,X_2))|hBOOL(hAPP(X_b,bool,Qa,X_2)).
% 48.27/47.97 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_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_2)).
% 48.27/47.97 0 [] ti(fun(X_b,bool),A_3)!=ti(fun(X_b,bool),B_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_2),A_3)).
% 48.27/47.97 0 [] ti(fun(X_b,bool),A_3)!=ti(fun(X_b,bool),B_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),B_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(X_b,bool,Pa,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)),Pa),Qa))|hBOOL(hAPP(X_b,bool,Qa,X_2)).
% 48.27/47.97 0 [] ti(fun(X_b,bool),A_3)!=ti(fun(X_b,bool),B_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),B_2)).
% 48.27/47.97 0 [] ti(fun(X_b,bool),A_3)!=ti(fun(X_b,bool),B_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_2),A_3)).
% 48.27/47.97 0 [] ti(fun(X_b,bool),A_3)=ti(fun(X_b,bool),B_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),B_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_2),A_3)).
% 48.27/47.97 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)).
% 48.27/47.97 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_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)),R_1),S_1)).
% 48.27/47.97 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_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)),R_1),S_1)).
% 48.27/47.97 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f118(X_b,B_2,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_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f118(X_b,B_2,A_3)),B_2))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_e_q(fun(X_c,bool)),$f119(X_c,X_b,F,A_3,B_2)),A_3)).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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_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,finite_finite_1(X_c),$f119(X_c,X_b,F,A_3,B_2))).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),B_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))|ti(fun(X_b,bool),B_2)=hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),$f119(X_c,X_b,F,A_3,B_2)).
% 48.27/47.97 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_2))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f120(X_b,Qa,Pa,A_3,B_2)),A_3))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Qa)))).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),A_3),B_2))|hBOOL(hAPP(X_b,bool,Pa,$f120(X_b,Qa,Pa,A_3,B_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),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Qa)))).
% 48.27/47.97 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_2))| -hBOOL(hAPP(X_b,bool,Qa,$f120(X_b,Qa,Pa,A_3,B_2)))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_e_q(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Qa)))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_2)),M_4))|M_4=hAPP(nat,nat,suc,$f121(N_2,M_4)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_1)),M_3))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N_1),$f122(Pa,N_1,M_3)))|hBOOL(hAPP(nat,bool,Pa,M_3)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_1)),M_3))| -hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,$f122(Pa,N_1,M_3))))|hBOOL(hAPP(nat,bool,Pa,M_3)).
% 48.27/47.97 0 [] hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f123(X_c,X_b,F,B_2,A_3)),A_3))|hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_e_q(fun(X_c,bool)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)),B_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,$f123(X_c,X_b,F,B_2,A_3))),B_2))|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_2)).
% 48.27/47.97 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,$f124(X_b,X_c,F,G))),hAPP(X_b,X_c,G,$f124(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)).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3))| -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X),N_3))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X),$f125(N_3))).
% 48.27/47.97 0 [] hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3))|hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),$f126(N_3,M_2)),N_3)).
% 48.27/47.97 0 [] hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f126(N_3,M_2)),M_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f127(U,F)),hAPP(nat,nat,F,$f127(U,F))))|hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(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)))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_1),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_1),Z))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))).
% 48.27/47.97 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_1),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_1),A_3)=ti(X_b,B_1).
% 48.27/47.97 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_1),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_1),A_3)=hAPP(fun(X_b,bool),X_b,the_1(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_1),bot_bot(fun(X_b,bool)))))).
% 48.27/47.97 0 [] hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_3)=hAPP(fun(X_b,bool),X_b,the_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_3)).
% 48.27/47.97 0 [] -hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_3),X_2))|ti(fun(X_b,bool),A_3)!=bot_bot(fun(X_b,bool)).
% 48.27/47.97 0 [] -hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),bot_bot(fun(X_b,bool))),X_2)).
% 48.27/47.97 0 [] -hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),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))|ti(X_b,A_2)=ti(X_b,B_1).
% 48.27/47.97 0 [] hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),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))|ti(X_b,A_2)!=ti(X_b,B_1).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))|ti(fun(X_b,bool),A_3)=bot_bot(fun(X_b,bool))|hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_3),$f128(X_b,F,A_3))).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))| -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(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_2),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),zero_zero(nat))).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,N_2))).
% 48.27/47.97 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N_2))).
% 48.27/47.97 0 [] hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(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_1)))).
% 48.27/47.97 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_2))).
% 48.27/47.97 0 [] hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(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))))).
% 48.27/47.97 0 [] -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3))| -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X),N_3))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),$f129(N_3))).
% 48.27/47.97 0 [] hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3))|hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),$f130(N_3,M_2)),N_3)).
% 48.27/47.98 0 [] hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f130(N_3,M_2)),M_2)).
% 48.27/47.98 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))| -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_1)).
% 48.27/47.98 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),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_1),Z)).
% 48.27/47.98 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1))| -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_1)).
% 48.27/47.98 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),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_1),Z)).
% 48.27/47.98 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)).
% 48.27/47.98 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)).
% 48.27/47.98 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))|ti(X_a,X_1)=ti(X_a,Y).
% 48.27/47.98 0 [] -linorder(X_b)| -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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1))|ti(X_b,X_2)=ti(X_b,Y_1).
% 48.27/47.98 0 [] -linorder(X_b)| -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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1))|ti(X_b,X_2)!=ti(X_b,Y_1).
% 48.27/47.98 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y)).
% 48.27/47.98 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)).
% 48.27/47.98 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)).
% 48.27/47.98 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)).
% 48.27/47.98 0 [] -linorder(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),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))|ti(X_b,X_2)=ti(X_b,Y_1).
% 48.27/47.98 0 [] -linorder(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),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))|ti(X_b,X_2)!=ti(X_b,Y_1).
% 48.27/47.98 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)).
% 48.27/47.98 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X_1)).
% 48.27/47.98 0 [] -order(X_b)| -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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1))|ti(X_b,X_2)=ti(X_b,Y_1).
% 48.27/47.98 0 [] -order(X_b)|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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1)).
% 48.27/47.98 0 [] -order(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_2),Y_1))|ti(X_b,X_2)!=ti(X_b,Y_1).
% 48.27/47.98 0 [] -preorder(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),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)).
% 48.27/47.98 0 [] -preorder(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),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)).
% 48.27/47.98 0 [] -preorder(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_1),X_2)).
% 48.27/47.98 0 [] -order(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),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)).
% 48.27/47.98 0 [] -order(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1))|ti(X_b,X_2)!=ti(X_b,Y_1).
% 48.27/47.98 0 [] -order(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),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))|ti(X_b,X_2)=ti(X_b,Y_1).
% 48.27/47.98 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1)).
% 48.27/47.98 0 [] -linorder(X_b)|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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2)).
% 48.27/47.98 0 [] -linorder(X_b)| -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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2)).
% 48.27/47.98 0 [] -linorder(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),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)).
% 48.27/47.98 0 [] -linorder(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),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)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2)).
% 48.27/47.98 0 [] M!=N_2|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))|M=N_2|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))|M_1=N_1.
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))|M_1!=N_1.
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))|M_1!=N_1.
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))|M_1=N_1.
% 48.27/47.98 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)),N_1)))|hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)).
% 48.27/47.98 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C),D_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))).
% 48.27/47.98 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M)),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M_1)))|N_1=M_1.
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M_1)))|N_1!=M_1.
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M)),N_2)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N_2))).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M_1)),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,M_1)),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N_1)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_1)),M_1)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,N_1)),M_1)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 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))).
% 48.27/47.98 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))).
% 48.27/47.98 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)).
% 48.27/47.98 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)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_1)),I)).
% 48.27/47.98 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_1),I)),I)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),M))).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J_1))).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),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),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),K_2))).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),L))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),L))).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),L))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),L)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),N_2)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_1)),K_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K_2)).
% 48.27/47.98 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_1),C_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1)).
% 48.27/47.98 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_1),C_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1)).
% 48.27/47.98 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_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1)).
% 48.27/47.98 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_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1)).
% 48.27/47.98 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))).
% 48.27/47.98 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))).
% 48.27/47.98 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))).
% 48.27/47.98 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)).
% 48.27/47.98 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)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M))).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),K_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),N_2)),K_2)).
% 48.27/47.98 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_1)!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),D)).
% 48.27/47.98 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_1)!=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),D)).
% 48.27/47.98 0 [] -semilattice_sup(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B))).
% 48.27/47.98 0 [] -semilattice_sup(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B))).
% 48.27/47.98 0 [] -semilattice_inf(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),X_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)),X_1)).
% 48.27/47.98 0 [] -semilattice_inf(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),X_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)),X_1)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),zero_zero(nat))).
% 48.27/47.98 0 [] N_1=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)).
% 48.27/47.98 0 [] N_1!=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),zero_zero(nat))).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))|N_2!=zero_zero(nat).
% 48.27/47.98 0 [] N_2=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M_1))).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M_1))).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))|M_1=N_1.
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1)))|M_1!=N_1.
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M_1)))|N_1=M_1.
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M_1)))|N_1!=M_1.
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M)))|M=N_2.
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N_2))).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))|hAPP(nat,nat,suc,M)=N_2|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N_2)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),K_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I)),K_2)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))|M=N_2.
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),N_2)).
% 48.27/47.98 0 [] M_1=N_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1)).
% 48.27/47.98 0 [] M_1!=N_1| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 0 [] M_1!=N_1| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1)).
% 48.27/47.98 0 [] X_1=Y|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X_1)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),N_2)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M))|M!=N_2.
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3))|S!=T_3.
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))|M_1=N_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N_1),M_1)).
% 48.27/47.98 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),X_1)).
% 48.27/47.98 0 [] -linorder(X_b)|ti(X_b,X_2)=ti(X_b,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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2)).
% 48.27/47.98 0 [] -linorder(X_b)|ti(X_b,X_2)!=ti(X_b,Y_1)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1)).
% 48.27/47.98 0 [] -linorder(X_b)|ti(X_b,X_2)!=ti(X_b,Y_1)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2)).
% 48.27/47.98 0 [] -linorder(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2))|ti(X_b,X_2)=ti(X_b,Y_1).
% 48.27/47.98 0 [] -linorder(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2)).
% 48.27/47.98 0 [] -linorder(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1))|ti(X_b,X_2)!=ti(X_b,Y_1).
% 48.27/47.98 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))|ti(X_a,X_1)=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1)).
% 48.27/47.98 0 [] -linorder(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1))|ti(X_b,X_2)=ti(X_b,Y_1).
% 48.27/47.98 0 [] -linorder(X_b)|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1))|ti(X_b,X_2)!=ti(X_b,Y_1).
% 48.27/47.98 0 [] -linorder(X_a)|ti(X_a,X_1)=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1)).
% 48.27/47.98 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))|ti(X_a,X_1)!=ti(X_a,Y).
% 48.27/47.98 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1)).
% 48.27/47.98 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1)).
% 48.27/47.98 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))|ti(X_a,X_1)!=ti(X_a,Y).
% 48.27/47.98 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))|ti(X_a,Y)!=ti(X_a,X_1).
% 48.27/47.98 0 [] -preorder(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),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(Pa).
% 48.27/47.98 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)).
% 48.27/47.98 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)).
% 48.27/47.98 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)).
% 48.27/47.98 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)).
% 48.27/47.98 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)).
% 48.27/47.98 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)).
% 48.27/47.98 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),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_1),Z)).
% 48.27/47.98 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1))| -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_1)).
% 48.27/47.98 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1)).
% 48.27/47.98 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))|ti(X_a,X_1)=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1)).
% 48.27/47.98 0 [] -linordered_idom(X_a)|ti(X_a,X_1)=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_2)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_2)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2))=M.
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)),hAPP(nat,nat,suc,M))).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),K_2))).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),I)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),J_1))).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1)|M_1=N_1.
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1)|M_1!=N_1.
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)),M)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),M)))).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),I)))).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))|N_1=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),$f131(M_1,N_1))).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))|N_1!=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|N_1=hAPP(nat,nat,suc,$f132(N_1)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))|N_1!=hAPP(nat,nat,suc,M_2).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat))))|N_1=zero_zero(nat).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat))))|N_1!=zero_zero(nat).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1)))|M_1=zero_zero(nat)|M_1=hAPP(nat,nat,suc,$f133(M_1,N_1)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1)))|M_1=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f133(M_1,N_1)),N_1)).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1)))|M_1!=zero_zero(nat).
% 48.27/47.98 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1)))|M_1!=hAPP(nat,nat,suc,J)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),N_1)).
% 48.27/47.98 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),N_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M),N_2))).
% 48.27/47.98 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)))).
% 48.27/47.98 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))).
% 48.27/47.98 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))).
% 48.27/47.98 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_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),minus_minus(X_b),A_2),B_1)),zero_zero(X_b))).
% 48.27/47.98 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_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),minus_minus(X_b),A_2),B_1)),zero_zero(X_b))).
% 48.27/47.98 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))).
% 48.27/47.98 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))).
% 48.27/47.98 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))).
% 48.27/47.98 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))).
% 48.27/47.98 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))).
% 48.27/47.98 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))).
% 48.27/47.98 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))).
% 48.27/47.98 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_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_1),A_2)).
% 48.27/47.98 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_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_1),A_2)).
% 48.27/47.98 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)).
% 48.27/47.98 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)).
% 48.27/47.98 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))).
% 48.27/47.98 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))).
% 48.27/47.98 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))).
% 48.27/47.98 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_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1)).
% 48.27/47.98 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_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1)).
% 48.27/47.98 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_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))).
% 48.27/47.98 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_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_1),A_2)).
% 48.27/47.98 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_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))).
% 48.27/47.98 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_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_1),A_2)).
% 48.27/47.98 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_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_1)).
% 48.27/47.98 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_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_1),A_2)).
% 48.27/47.98 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_1),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))).
% 48.27/47.98 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_1),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_1),A_2)).
% 48.27/47.98 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_1),C_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))).
% 48.27/47.98 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_1),C_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_1),A_2)).
% 48.27/47.98 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_1),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_1)).
% 48.27/47.98 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_1),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_1),A_2)).
% 48.27/47.98 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))).
% 48.27/47.98 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))).
% 48.27/47.98 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))).
% 48.27/47.98 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)).
% 48.27/47.98 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)).
% 48.27/47.98 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))).
% 48.27/47.98 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))).
% 48.27/47.98 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))).
% 48.27/47.98 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))).
% 48.27/47.98 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))).
% 48.27/47.98 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)),N_1)))=N_1.
% 48.27/47.98 0 [] hAPP(nat,fun(nat,bool),ord_less(nat),X)=hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,suc,X)).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Z))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))).
% 48.27/47.98 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),X_1),Y)).
% 48.27/47.98 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))).
% 48.27/47.98 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))).
% 48.27/47.98 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))).
% 48.27/47.98 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))).
% 48.27/47.98 0 [] bounded_lattice(bool).
% 48.27/47.98 0 [] -bounded_lattice(T_1)|bounded_lattice(fun(T_2,T_1)).
% 48.27/47.98 0 [] -bounded_lattice(T_1)|bounded_lattice_bot(fun(T_2,T_1)).
% 48.27/47.98 0 [] -lattice(T_1)|semilattice_sup(fun(T_2,T_1)).
% 48.27/47.98 0 [] -lattice(T_1)|semilattice_inf(fun(T_2,T_1)).
% 48.27/47.98 0 [] -distrib_lattice(T_1)|distrib_lattice(fun(T_2,T_1)).
% 48.27/47.98 0 [] -preorder(T_1)|preorder(fun(T_2,T_1)).
% 48.27/47.98 0 [] -finite_finite(T_1)| -finite_finite(T_2)|finite_finite(fun(T_2,T_1)).
% 48.27/47.98 0 [] -lattice(T_1)|lattice(fun(T_2,T_1)).
% 48.27/47.98 0 [] -order(T_1)|order(fun(T_2,T_1)).
% 48.27/47.98 0 [] -ord(T_1)|ord(fun(T_2,T_1)).
% 48.27/47.98 0 [] -bot(T_1)|bot(fun(T_2,T_1)).
% 48.27/47.98 0 [] -minus(T_1)|minus(fun(T_2,T_1)).
% 48.27/47.98 0 [] semiri456707255roduct(nat).
% 48.27/47.98 0 [] ordere223160158up_add(nat).
% 48.27/47.98 0 [] ordere236663937imp_le(nat).
% 48.27/47.98 0 [] linord893533164strict(nat).
% 48.27/47.98 0 [] linord20386208strict(nat).
% 48.27/47.98 0 [] ordere779506340up_add(nat).
% 48.27/47.98 0 [] ordere216010020id_add(nat).
% 48.27/47.98 0 [] cancel146912293up_add(nat).
% 48.27/47.98 0 [] ordere453448008miring(nat).
% 48.27/47.98 0 [] ordere1490568538miring(nat).
% 48.27/47.98 0 [] cancel_semigroup_add(nat).
% 48.27/47.98 0 [] linordered_semidom(nat).
% 48.27/47.98 0 [] semilattice_sup(nat).
% 48.27/47.98 0 [] semilattice_inf(nat).
% 48.27/47.98 0 [] distrib_lattice(nat).
% 48.27/47.98 0 [] ab_semigroup_mult(nat).
% 48.27/47.98 0 [] comm_monoid_mult(nat).
% 48.27/47.98 0 [] ab_semigroup_add(nat).
% 48.27/47.98 0 [] ordered_semiring(nat).
% 48.27/47.98 0 [] no_zero_divisors(nat).
% 48.27/47.98 0 [] comm_monoid_add(nat).
% 48.27/47.98 0 [] comm_semiring_1(nat).
% 48.27/47.98 0 [] comm_semiring(nat).
% 48.27/47.98 0 [] zero_ne_q_one(nat).
% 48.27/47.98 0 [] preorder(nat).
% 48.27/47.98 0 [] linorder(nat).
% 48.27/47.98 0 [] monoid_mult(nat).
% 48.27/47.98 0 [] monoid_add(nat).
% 48.27/47.98 0 [] lattice(nat).
% 48.27/47.98 0 [] mult_zero(nat).
% 48.27/47.98 0 [] order(nat).
% 48.27/47.98 0 [] semiring(nat).
% 48.27/47.98 0 [] ord(nat).
% 48.27/47.98 0 [] bot(nat).
% 48.27/47.98 0 [] minus(nat).
% 48.27/47.98 0 [] zero(nat).
% 48.27/47.98 0 [] one(nat).
% 48.27/47.98 0 [] bounded_lattice_bot(bool).
% 48.27/47.98 0 [] semilattice_sup(bool).
% 48.27/47.98 0 [] semilattice_inf(bool).
% 48.27/47.98 0 [] distrib_lattice(bool).
% 48.27/47.98 0 [] preorder(bool).
% 48.27/47.98 0 [] finite_finite(bool).
% 48.27/47.98 0 [] lattice(bool).
% 48.27/47.98 0 [] order(bool).
% 48.27/47.98 0 [] ord(bool).
% 48.27/47.98 0 [] bot(bool).
% 48.27/47.98 0 [] minus(bool).
% 48.27/47.98 0 [] -finite_finite(T_1)| -finite_finite(T_2)|finite_finite(sum_sum(T_2,T_1)).
% 48.27/47.98 0 [] ti(T,ti(T,A))=ti(T,A).
% 48.27/47.98 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_1),Y)=ti(X_a,X_1).
% 48.27/47.98 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_1),Y)=ti(X_a,Y).
% 48.27/47.98 0 [] ti(bool,P)=fTrue|ti(bool,P)=fFalse.
% 48.27/47.98 0 [] -hBOOL(hAPP(bool,bool,fNot,P))| -hBOOL(P).
% 48.27/47.98 0 [] hBOOL(P)|hBOOL(hAPP(bool,bool,fNot,P)).
% 48.27/47.98 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)).
% 48.27/47.98 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).
% 48.27/47.98 0 [] hAPP(X_a,X_a,combi(X_a),P)=ti(X_a,P).
% 48.27/47.98 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).
% 48.27/47.98 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)).
% 48.27/47.98 0 [] -hBOOL(P)| -hBOOL(Q)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)).
% 48.27/47.98 0 [] -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))|hBOOL(P).
% 48.27/47.98 0 [] -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))|hBOOL(Q).
% 48.27/47.98 0 [] -hBOOL(P)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)).
% 48.27/47.98 0 [] -hBOOL(Q)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)).
% 48.27/47.98 0 [] -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q))|hBOOL(P)|hBOOL(Q).
% 48.27/47.98 0 [] -hBOOL(fFalse).
% 48.27/47.98 0 [] ti(bool,P)=fTrue|ti(bool,P)=fFalse.
% 48.27/47.98 0 [] -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fe_qual(X_a),X_1),Y))|ti(X_a,X_1)=ti(X_a,Y).
% 48.27/47.98 0 [] ti(X_a,X_1)!=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fe_qual(X_a),X_1),Y)).
% 48.27/47.98 0 [] hBOOL(P)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)).
% 48.27/47.98 0 [] -hBOOL(Q)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)).
% 48.27/47.98 0 [] -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q))| -hBOOL(P)|hBOOL(Q).
% 48.27/47.98 0 [] hBOOL(hAPP(fun(hoare_2118899576triple(x_a),bool),bool,hAPP(hoare_2118899576triple(x_a),fun(fun(hoare_2118899576triple(x_a),bool),bool),member(hoare_2118899576triple(x_a)),$f134(N)),hAPP(fun(hoare_2118899576triple(x_a),bool),fun(hoare_2118899576triple(x_a),bool),hAPP(fun(hoare_2118899576triple(x_a),bool),fun(fun(hoare_2118899576triple(x_a),bool),fun(hoare_2118899576triple(x_a),bool)),semilattice_sup_sup(fun(hoare_2118899576triple(x_a),bool)),g),hAPP(fun(pname,bool),fun(hoare_2118899576triple(x_a),bool),hAPP(fun(pname,hoare_2118899576triple(x_a)),fun(fun(pname,bool),fun(hoare_2118899576triple(x_a),bool)),image(pname,hoare_2118899576triple(x_a)),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_2118899576triple(x_a)),hAPP(fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_2118899576triple(x_a))),combs(pname,fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)),hAPP(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hAPP(fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),fun(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),combs(pname,com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),hAPP(fun(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))))),combb(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),pname),hoare_759811442triple(x_a)),p)),body)),q)),procs))))| -hBOOL(hAPP(fun(hoare_2118899576triple(x_a),bool),bool,hAPP(hoare_2118899576triple(x_a),fun(fun(hoare_2118899576triple(x_a),bool),bool),member(hoare_2118899576triple(x_a)),X),hAPP(fun(pname,bool),fun(hoare_2118899576triple(x_a),bool),hAPP(fun(pname,hoare_2118899576triple(x_a)),fun(fun(pname,bool),fun(hoare_2118899576triple(x_a),bool)),image(pname,hoare_2118899576triple(x_a)),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_2118899576triple(x_a)),hAPP(fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_2118899576triple(x_a))),combs(pname,fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)),hAPP(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hAPP(fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),fun(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),combs(pname,com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),hAPP(fun(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))))),combb(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),pname),hoare_759811442triple(x_a)),p)),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body_1))),q)),procs)))|hBOOL(hAPP(hoare_2118899576triple(x_a),bool,hAPP(nat,fun(hoare_2118899576triple(x_a),bool),hoare_1942962616_valid(x_a),N),X)).
% 48.27/47.98 0 [] -hBOOL(hAPP(hoare_2118899576triple(x_a),bool,hAPP(nat,fun(hoare_2118899576triple(x_a),bool),hoare_1942962616_valid(x_a),N),$f134(N)))| -hBOOL(hAPP(fun(hoare_2118899576triple(x_a),bool),bool,hAPP(hoare_2118899576triple(x_a),fun(fun(hoare_2118899576triple(x_a),bool),bool),member(hoare_2118899576triple(x_a)),X),hAPP(fun(pname,bool),fun(hoare_2118899576triple(x_a),bool),hAPP(fun(pname,hoare_2118899576triple(x_a)),fun(fun(pname,bool),fun(hoare_2118899576triple(x_a),bool)),image(pname,hoare_2118899576triple(x_a)),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_2118899576triple(x_a)),hAPP(fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_2118899576triple(x_a))),combs(pname,fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)),hAPP(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hAPP(fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),fun(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),combs(pname,com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),hAPP(fun(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))))),combb(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),pname),hoare_759811442triple(x_a)),p)),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body_1))),q)),procs)))|hBOOL(hAPP(hoare_2118899576triple(x_a),bool,hAPP(nat,fun(hoare_2118899576triple(x_a),bool),hoare_1942962616_valid(x_a),N),X)).
% 48.27/47.98 0 [] -hBOOL(hAPP(fun(hoare_2118899576triple(x_a),bool),bool,hAPP(hoare_2118899576triple(x_a),fun(fun(hoare_2118899576triple(x_a),bool),bool),member(hoare_2118899576triple(x_a)),X),g))|hBOOL(hAPP(hoare_2118899576triple(x_a),bool,hAPP(nat,fun(hoare_2118899576triple(x_a),bool),hoare_1942962616_valid(x_a),n),X)).
% 48.27/47.98 0 [] hBOOL(hAPP(fun(hoare_2118899576triple(x_a),bool),bool,hAPP(hoare_2118899576triple(x_a),fun(fun(hoare_2118899576triple(x_a),bool),bool),member(hoare_2118899576triple(x_a)),$c1),hAPP(fun(pname,bool),fun(hoare_2118899576triple(x_a),bool),hAPP(fun(pname,hoare_2118899576triple(x_a)),fun(fun(pname,bool),fun(hoare_2118899576triple(x_a),bool)),image(pname,hoare_2118899576triple(x_a)),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_2118899576triple(x_a)),hAPP(fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_2118899576triple(x_a))),combs(pname,fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)),hAPP(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hAPP(fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),fun(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),combs(pname,com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),hAPP(fun(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))))),combb(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),pname),hoare_759811442triple(x_a)),p)),body)),q)),procs))).
% 48.27/47.98 0 [] -hBOOL(hAPP(hoare_2118899576triple(x_a),bool,hAPP(nat,fun(hoare_2118899576triple(x_a),bool),hoare_1942962616_valid(x_a),n),$c1)).
% 48.27/47.98 end_of_list.
% 48.27/47.98
% 48.27/47.98 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 48.27/47.98
% 48.27/47.98 This ia a non-Horn set with equality. The strategy will be
% 48.27/47.98 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 48.27/47.98 deletion, with positive clauses in sos and nonpositive
% 48.27/47.98 clauses in usable.
% 48.27/47.98
% 48.27/47.98 dependent: set(knuth_bendix).
% 48.27/47.98 dependent: set(anl_eq).
% 48.27/47.98 dependent: set(para_from).
% 48.27/47.98 dependent: set(para_into).
% 48.27/47.98 dependent: clear(para_from_right).
% 48.27/47.98 dependent: clear(para_into_right).
% 48.27/47.98 dependent: set(para_from_vars).
% 48.27/47.98 dependent: set(eq_units_both_ways).
% 48.27/47.98 dependent: set(dynamic_demod_all).
% 48.27/47.98 dependent: set(dynamic_demod).
% 48.27/47.98 dependent: set(order_eq).
% 48.27/47.98 dependent: set(back_demod).
% 48.27/47.98 dependent: set(lrpo).
% 48.27/47.98 dependent: set(hyper_res).
% 48.27/47.98 dependent: set(unit_deletion).
% 48.27/47.98 dependent: set(factor).
% 48.27/47.98
% 48.27/47.98 ------------> process usable:
% 48.27/47.98 ** KEPT (pick-wt=13): 1 [] -lattice(A)|ti(fun(fun(A,bool),A),big_lattice_Inf_fin(A))=big_lattice_Inf_fin(A).
% 48.27/47.98 ** KEPT (pick-wt=13): 2 [] -lattice(A)|ti(fun(fun(A,bool),A),big_lattice_Sup_fin(A))=big_lattice_Sup_fin(A).
% 48.27/47.98 ** KEPT (pick-wt=13): 3 [] -minus(A)|ti(fun(A,fun(A,A)),minus_minus(A))=minus_minus(A).
% 48.27/47.98 ** KEPT (pick-wt=9): 4 [] -one(A)|ti(A,one_one(A))=one_one(A).
% 48.27/47.98 ** KEPT (pick-wt=13): 5 [] -monoid_add(A)|ti(fun(A,fun(A,A)),plus_plus(A))=plus_plus(A).
% 48.27/47.98 ** KEPT (pick-wt=13): 6 [] -cancel_semigroup_add(A)|ti(fun(A,fun(A,A)),plus_plus(A))=plus_plus(A).
% 48.27/47.98 ** KEPT (pick-wt=13): 7 [] -ab_semigroup_add(A)|ti(fun(A,fun(A,A)),plus_plus(A))=plus_plus(A).
% 48.27/47.98 ** KEPT (pick-wt=13): 8 [] -monoid_mult(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A).
% 48.27/47.98 ** KEPT (pick-wt=13): 9 [] -no_zero_divisors(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A).
% 48.27/47.98 ** KEPT (pick-wt=13): 10 [] -mult_zero(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A).
% 48.27/47.98 ** KEPT (pick-wt=13): 11 [] -ab_semigroup_mult(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A).
% 48.27/47.98 ** KEPT (pick-wt=13): 12 [] -semiring(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A).
% 48.27/47.98 ** KEPT (pick-wt=9): 13 [] -zero(A)|ti(A,zero_zero(A))=zero_zero(A).
% 48.27/47.98 ** KEPT (pick-wt=13): 14 [] -semilattice_inf(A)|ti(fun(A,fun(A,A)),semilattice_inf_inf(A))=semilattice_inf_inf(A).
% 48.27/47.98 ** KEPT (pick-wt=13): 15 [] -semilattice_sup(A)|ti(fun(A,fun(A,A)),semilattice_sup_sup(A))=semilattice_sup_sup(A).
% 48.27/47.98 ** KEPT (pick-wt=9): 16 [] -bot(A)|ti(A,bot_bot(A))=bot_bot(A).
% 48.27/47.98 ** KEPT (pick-wt=13): 17 [] -ord(A)|ti(fun(A,fun(A,bool)),ord_less(A))=ord_less(A).
% 48.27/47.98 ** KEPT (pick-wt=13): 18 [] -ord(A)|ti(fun(A,fun(A,bool)),ord_less_e_q(A))=ord_less_e_q(A).
% 48.27/47.98 ** KEPT (pick-wt=6): 19 [] -hBOOL(ti(bool,A))|hBOOL(A).
% 48.27/47.98 ** KEPT (pick-wt=6): 20 [] hBOOL(ti(bool,A))| -hBOOL(A).
% 48.27/47.98 ** KEPT (pick-wt=82): 21 [] hAPP(fun(A,fun(state,bool)),hoare_2118899576triple(A),hAPP(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)),hAPP(fun(A,fun(state,bool)),fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),hoare_759811442triple(A),B),C),D)!=hAPP(fun(A,fun(state,bool)),hoare_2118899576triple(A),hAPP(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)),hAPP(fun(A,fun(state,bool)),fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),hoare_759811442triple(A),E),F),G)|B=E.
% 48.27/47.98 ** KEPT (pick-wt=82): 22 [] hAPP(fun(A,fun(state,bool)),hoare_2118899576triple(A),hAPP(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)),hAPP(fun(A,fun(state,bool)),fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),hoare_759811442triple(A),B),C),D)!=hAPP(fun(A,fun(state,bool)),hoare_2118899576triple(A),hAPP(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)),hAPP(fun(A,fun(state,bool)),fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),hoare_759811442triple(A),E),F),G)|C=F.
% 48.27/47.98 ** KEPT (pick-wt=82): 23 [] hAPP(fun(A,fun(state,bool)),hoare_2118899576triple(A),hAPP(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)),hAPP(fun(A,fun(state,bool)),fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),hoare_759811442triple(A),B),C),D)!=hAPP(fun(A,fun(state,bool)),hoare_2118899576triple(A),hAPP(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)),hAPP(fun(A,fun(state,bool)),fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),hoare_759811442triple(A),E),F),G)|D=G.
% 48.27/47.98 ** KEPT (pick-wt=88): 24 [] hAPP(fun(A,fun(state,bool)),hoare_2118899576triple(A),hAPP(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)),hAPP(fun(A,fun(state,bool)),fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),hoare_759811442triple(A),B),C),D)=hAPP(fun(A,fun(state,bool)),hoare_2118899576triple(A),hAPP(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)),hAPP(fun(A,fun(state,bool)),fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),hoare_759811442triple(A),E),F),G)|B!=E|C!=F|D!=G.
% 48.27/47.98 ** KEPT (pick-wt=83): 25 [] -hBOOL(hAPP(fun(hoare_2118899576triple(A),bool),bool,hAPP(fun(hoare_2118899576triple(A),bool),fun(fun(hoare_2118899576triple(A),bool),bool),hoare_902341502valids(A),B),C))|hBOOL(hAPP(fun(hoare_2118899576triple(A),bool),bool,hAPP(hoare_2118899576triple(A),fun(fun(hoare_2118899576triple(A),bool),bool),member(hoare_2118899576triple(A)),$f1(A,B,C,D)),B))| -hBOOL(hAPP(fun(hoare_2118899576triple(A),bool),bool,hAPP(hoare_2118899576triple(A),fun(fun(hoare_2118899576triple(A),bool),bool),member(hoare_2118899576triple(A)),E),C))|hBOOL(hAPP(hoare_2118899576triple(A),bool,hAPP(nat,fun(hoare_2118899576triple(A),bool),hoare_1942962616_valid(A),D),E)).
% 48.27/47.98 ** KEPT (pick-wt=77): 26 [] -hBOOL(hAPP(fun(hoare_2118899576triple(A),bool),bool,hAPP(fun(hoare_2118899576triple(A),bool),fun(fun(hoare_2118899576triple(A),bool),bool),hoare_902341502valids(A),B),C))| -hBOOL(hAPP(hoare_2118899576triple(A),bool,hAPP(nat,fun(hoare_2118899576triple(A),bool),hoare_1942962616_valid(A),D),$f1(A,B,C,D)))| -hBOOL(hAPP(fun(hoare_2118899576triple(A),bool),bool,hAPP(hoare_2118899576triple(A),fun(fun(hoare_2118899576triple(A),bool),bool),member(hoare_2118899576triple(A)),E),C))|hBOOL(hAPP(hoare_2118899576triple(A),bool,hAPP(nat,fun(hoare_2118899576triple(A),bool),hoare_1942962616_valid(A),D),E)).
% 48.27/47.98 ** KEPT (pick-wt=61): 27 [] hBOOL(hAPP(fun(hoare_2118899576triple(A),bool),bool,hAPP(fun(hoare_2118899576triple(A),bool),fun(fun(hoare_2118899576triple(A),bool),bool),hoare_902341502valids(A),B),C))| -hBOOL(hAPP(fun(hoare_2118899576triple(A),bool),bool,hAPP(hoare_2118899576triple(A),fun(fun(hoare_2118899576triple(A),bool),bool),member(hoare_2118899576triple(A)),D),B))|hBOOL(hAPP(hoare_2118899576triple(A),bool,hAPP(nat,fun(hoare_2118899576triple(A),bool),hoare_1942962616_valid(A),$f3(A,B,C)),D)).
% 48.27/47.98 ** KEPT (pick-wt=43): 28 [] hBOOL(hAPP(fun(hoare_2118899576triple(A),bool),bool,hAPP(fun(hoare_2118899576triple(A),bool),fun(fun(hoare_2118899576triple(A),bool),bool),hoare_902341502valids(A),B),C))| -hBOOL(hAPP(hoare_2118899576triple(A),bool,hAPP(nat,fun(hoare_2118899576triple(A),bool),hoare_1942962616_valid(A),$f3(A,B,C)),$f2(A,B,C))).
% 48.27/47.99 ** KEPT (pick-wt=701): 29 [] -hBOOL(hAPP(fun(hoare_2118899576triple(A),bool),bool,hAPP(fun(hoare_2118899576triple(A),bool),fun(fun(hoare_2118899576triple(A),bool),bool),hoare_1301688828derivs(A),hAPP(fun(hoare_2118899576triple(A),bool),fun(hoare_2118899576triple(A),bool),hAPP(fun(hoare_2118899576triple(A),bool),fun(fun(hoare_2118899576triple(A),bool),fun(hoare_2118899576triple(A),bool)),semilattice_sup_sup(fun(hoare_2118899576triple(A),bool)),B),hAPP(fun(pname,bool),fun(hoare_2118899576triple(A),bool),hAPP(fun(pname,hoare_2118899576triple(A)),fun(fun(pname,bool),fun(hoare_2118899576triple(A),bool)),image(pname,hoare_2118899576triple(A)),hAPP(fun(pname,fun(A,fun(state,bool))),fun(pname,hoare_2118899576triple(A)),hAPP(fun(pname,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),fun(fun(pname,fun(A,fun(state,bool))),fun(pname,hoare_2118899576triple(A))),combs(pname,fun(A,fun(state,bool)),hoare_2118899576triple(A)),hAPP(fun(pname,com),fun(pname,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),hAPP(fun(pname,fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)))),fun(fun(pname,com),fun(pname,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)))),combs(pname,com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),hAPP(fun(pname,fun(A,fun(state,bool))),fun(pname,fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)))),hAPP(fun(fun(A,fun(state,bool)),fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)))),fun(fun(pname,fun(A,fun(state,bool))),fun(pname,fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))))),combb(fun(A,fun(state,bool)),fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),pname),hoare_759811442triple(A)),C)),body)),D)),E))),hAPP(fun(pname,bool),fun(hoare_2118899576triple(A),bool),hAPP(fun(pname,hoare_2118899576triple(A)),fun(fun(pname,bool),fun(hoare_2118899576triple(A),bool)),image(pname,hoare_2118899576triple(A)),hAPP(fun(pname,fun(A,fun(state,bool))),fun(pname,hoare_2118899576triple(A)),hAPP(fun(pname,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),fun(fun(pname,fun(A,fun(state,bool))),fun(pname,hoare_2118899576triple(A))),combs(pname,fun(A,fun(state,bool)),hoare_2118899576triple(A)),hAPP(fun(pname,com),fun(pname,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),hAPP(fun(pname,fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)))),fun(fun(pname,com),fun(pname,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)))),combs(pname,com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),hAPP(fun(pname,fun(A,fun(state,bool))),fun(pname,fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)))),hAPP(fun(fun(A,fun(state,bool)),fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)))),fun(fun(pname,fun(A,fun(state,bool))),fun(pname,fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))))),combb(fun(A,fun(state,bool)),fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),pname),hoare_759811442triple(A)),C)),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body_1))),D)),E)))|hBOOL(hAPP(fun(hoare_2118899576triple(A),bool),bool,hAPP(fun(hoare_2118899576triple(A),bool),fun(fun(hoare_2118899576triple(A),bool),bool),hoare_1301688828derivs(A),B),hAPP(fun(pname,bool),fun(hoare_2118899576triple(A),bool),hAPP(fun(pname,hoare_2118899576triple(A)),fun(fun(pname,bool),fun(hoare_2118899576triple(A),bool)),image(pname,hoare_2118899576triple(A)),hAPP(fun(pname,fun(A,fun(state,bool))),fun(pname,hoare_2118899576triple(A)),hAPP(fun(pname,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),fun(fun(pname,fun(A,fun(state,bool))),fun(pname,hoare_2118899576triple(A))),combs(pname,fun(A,fun(state,bool)),hoare_2118899576triple(A)),hAPP(fun(pname,com),fun(pname,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),hAPP(fun(pname,fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)))),fun(fun(pname,com),fun(pname,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)))),combs(pname,com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),hAPP(fun(pname,fun(A,fun(state,bool))),fun(pname,fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)))),hAPP(fun(fun(A,fun(state,bool)),fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)))),fun(fun(pname,fun(A,fun(state,bool))),fun(pname,fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))))),combb(fun(A,fun(state,bool)),fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),pname),hoare_759811442triple(A)),C)),body)),D)),E))).
% 48.27/47.99 ** KEPT (pick-wt=74): 30 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),C),D)))|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)).
% 48.27/47.99 ** KEPT (pick-wt=41): 31 [] -hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),B),C),D))|hBOOL(hAPP(A,bool,B,D))|hBOOL(hAPP(A,bool,C,D)).
% 48.27/47.99 ** KEPT (pick-wt=35): 32 [] -hBOOL(hAPP(A,bool,B,C))|hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),D),B),C)).
% 48.27/47.99 ** KEPT (pick-wt=35): 33 [] -hBOOL(hAPP(A,bool,B,C))|hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),B),D),C)).
% 48.27/47.99 ** KEPT (pick-wt=57): 34 [] -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(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),D),C))).
% 48.27/47.99 ** KEPT (pick-wt=57): 35 [] -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(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),C),D))).
% 48.27/47.99 ** KEPT (pick-wt=65): 36 [] 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))).
% 48.27/47.99 ** KEPT (pick-wt=51): 37 [] -lattice(A)|hAPP(B,A,hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D),E)=hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),hAPP(B,A,C,E)),hAPP(B,A,D,E)).
% 48.27/47.99 Following clause subsumed by 37 during input processing: 0 [] -lattice(A)|hAPP(B,A,hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D),E)=hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),hAPP(B,A,C,E)),hAPP(B,A,D,E)).
% 48.27/47.99 ** KEPT (pick-wt=66): 38 [] -hBOOL(hAPP(fun(hoare_2118899576triple(A),bool),bool,hAPP(fun(hoare_2118899576triple(A),bool),fun(fun(hoare_2118899576triple(A),bool),bool),hoare_1301688828derivs(A),B),C))| -hBOOL(hAPP(fun(hoare_2118899576triple(A),bool),bool,hAPP(fun(hoare_2118899576triple(A),bool),fun(fun(hoare_2118899576triple(A),bool),bool),hoare_1301688828derivs(A),D),B))|hBOOL(hAPP(fun(hoare_2118899576triple(A),bool),bool,hAPP(fun(hoare_2118899576triple(A),bool),fun(fun(hoare_2118899576triple(A),bool),bool),hoare_1301688828derivs(A),D),C)).
% 48.27/47.99 ** KEPT (pick-wt=49): 39 [] -semilattice_sup(A)|hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),D)).
% 48.27/47.99 ** KEPT (pick-wt=49): 40 [] -lattice(A)|hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),D)).
% 48.27/47.99 Following clause subsumed by 39 during input processing: 0 [] -semilattice_sup(A)|hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),D)).
% 48.27/47.99 ** KEPT (pick-wt=49): 41 [] -semilattice_sup(A)|hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),D))=hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),D)).
% 48.27/47.99 ** KEPT (pick-wt=49): 42 [] -lattice(A)|hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),D))=hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),D)).
% 48.27/47.99 Following clause subsumed by 41 during input processing: 0 [] -semilattice_sup(A)|hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),D))=hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),D)).
% 48.27/47.99 ** KEPT (pick-wt=38): 43 [] -semilattice_sup(A)|hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C))=hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C).
% 48.27/47.99 ** KEPT (pick-wt=38): 44 [] -lattice(A)|hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C))=hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C).
% 48.27/47.99 Following clause subsumed by 43 during input processing: 0 [] -semilattice_sup(A)|hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C))=hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C).
% 48.27/47.99 ** KEPT (pick-wt=27): 45 [] -semilattice_sup(A)|hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)=hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),B).
% 48.27/47.99 ** KEPT (pick-wt=27): 46 [] -lattice(A)|hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)=hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),B).
% 48.27/47.99 Following clause subsumed by 45 during input processing: 0 [] -semilattice_sup(A)|hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)=hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),B).
% 48.27/47.99 ** KEPT (pick-wt=18): 47 [] -semilattice_sup(A)|hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),B)=ti(A,B).
% 48.27/47.99 Following clause subsumed by 47 during input processing: 0 [] -semilattice_sup(A)|hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),B)=ti(A,B).
% 48.27/47.99 Following clause subsumed by 36 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))).
% 48.27/47.99 ** KEPT (pick-wt=60): 48 [] -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))).
% 48.27/47.99 ** KEPT (pick-wt=61): 49 [] -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),$f4(A,C,B,D,E)),E)).
% 48.27/47.99 ** KEPT (pick-wt=53): 50 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(C,bool),fun(A,bool),hAPP(fun(C,A),fun(fun(C,bool),fun(A,bool)),image(C,A),D),E)))|ti(A,B)=hAPP(C,A,D,$f4(A,C,B,D,E)).
% 48.27/47.99 Following clause subsumed by 36 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).
% 48.27/47.99 Following clause subsumed by 34 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(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),D),C))).
% 48.27/47.99 Following clause subsumed by 35 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(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),C),D))).
% 48.27/47.99 Following clause subsumed by 32 during input processing: 0 [] -hBOOL(hAPP(A,bool,B,C))|hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),D),B),C)).
% 48.27/47.99 Following clause subsumed by 33 during input processing: 0 [] -hBOOL(hAPP(A,bool,B,C))|hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),B),D),C)).
% 48.27/47.99 ** KEPT (pick-wt=67): 51 [] hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),$f5(A,B,C,D)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),C),D)))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),E),C))|hBOOL(hAPP(A,bool,B,E)).
% 48.27/47.99 ** KEPT (pick-wt=67): 52 [] hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),$f5(A,B,C,D)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),C),D)))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),E),D))|hBOOL(hAPP(A,bool,B,E)).
% 48.27/47.99 ** KEPT (pick-wt=33): 53 [] -hBOOL(hAPP(A,bool,B,$f5(A,B,C,D)))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),E),C))|hBOOL(hAPP(A,bool,B,E)).
% 48.27/47.99 ** KEPT (pick-wt=33): 54 [] -hBOOL(hAPP(A,bool,B,$f5(A,B,C,D)))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),E),D))|hBOOL(hAPP(A,bool,B,E)).
% 48.27/47.99 ** KEPT (pick-wt=88): 55 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),C),D)))|hBOOL(hAPP(A,bool,E,B))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),$f6(A,E,C,D)),C))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),$f7(A,E,C,D)),D)).
% 48.27/47.99 ** KEPT (pick-wt=77): 56 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),C),D)))|hBOOL(hAPP(A,bool,E,B))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),$f6(A,E,C,D)),C))| -hBOOL(hAPP(A,bool,E,$f7(A,E,C,D))).
% 48.27/47.99 ** KEPT (pick-wt=77): 57 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),C),D)))|hBOOL(hAPP(A,bool,E,B))| -hBOOL(hAPP(A,bool,E,$f6(A,E,C,D)))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),$f7(A,E,C,D)),D)).
% 48.27/47.99 ** KEPT (pick-wt=66): 58 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),C),D)))|hBOOL(hAPP(A,bool,E,B))| -hBOOL(hAPP(A,bool,E,$f6(A,E,C,D)))| -hBOOL(hAPP(A,bool,E,$f7(A,E,C,D))).
% 48.27/47.99 ** KEPT (pick-wt=88): 59 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),C),D)))| -hBOOL(hAPP(A,bool,E,B))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),$f8(A,E,C,D)),C))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),$f9(A,E,C,D)),D)).
% 48.27/47.99 ** KEPT (pick-wt=77): 60 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),C),D)))| -hBOOL(hAPP(A,bool,E,B))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),$f8(A,E,C,D)),C))|hBOOL(hAPP(A,bool,E,$f9(A,E,C,D))).
% 48.27/47.99 ** KEPT (pick-wt=77):
% 48.27/47.99 Search stopped in tp_alloc by max_mem option.
% 48.27/47.99 61 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),C),D)))| -hBOOL(hAPP(A,bool,E,B))|hBOOL(hAPP(A,bool,E,$f8(A,E,C,D)))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),$f9(A,E,C,D)),D)).
% 48.27/47.99 ** KEPT (pick-wt=66): 62 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),C),D)))| -hBOOL(hAPP(A,bool,E,B))|hBOOL(hAPP(A,bool,E,$f8(A,E,C,D)))|hBOOL(hAPP(A,bool,E,$f9(A,E,C,D))).
% 48.27/47.99 ** KEPT (pick-wt=67): 63 [] hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),$f10(A,B,C,D)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),C),D)))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),E),C))| -hBOOL(hAPP(A,bool,B,E)).
% 48.27/47.99 ** KEPT (pick-wt=67): 64 [] hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),$f10(A,B,C,D)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),C),D)))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),E),D))| -hBOOL(hAPP(A,bool,B,E)).
% 48.27/47.99 ** KEPT (pick-wt=33): 65 [] hBOOL(hAPP(A,bool,B,$f10(A,B,C,D)))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),E),C))| -hBOOL(hAPP(A,bool,B,E)).
% 48.27/47.99 ** KEPT (pick-wt=33): 66 [] hBOOL(hAPP(A,bool,B,$f10(A,B,C,D)))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),E),D))| -hBOOL(hAPP(A,bool,B,E)).
% 48.27/47.99 Following clause subsumed by 30 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(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),C),D)))|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)).
% 48.27/47.99 Following clause subsumed by 35 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(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),C),D)))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C)).
% 48.27/47.99 Following clause subsumed by 34 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(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),C),D)))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),D)).
% 48.27/47.99
% 48.27/47.99 Search stopped in tp_alloc by max_mem option.
% 48.27/47.99
% 48.27/47.99 ============ end of search ============
% 48.27/47.99
% 48.27/47.99 -------------- statistics -------------
% 48.27/47.99 clauses given 0
% 48.27/47.99 clauses generated 0
% 48.27/47.99 clauses kept 66
% 48.27/47.99 clauses forward subsumed 15
% 48.27/47.99 clauses back subsumed 0
% 48.27/47.99 Kbytes malloced 11718
% 48.27/47.99
% 48.27/47.99 ----------- times (seconds) -----------
% 48.27/47.99 user CPU time 0.30 (0 hr, 0 min, 0 sec)
% 48.27/47.99 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 48.27/47.99 wall-clock time 48 (0 hr, 0 min, 48 sec)
% 48.27/47.99
% 48.27/47.99 Process 24454 finished Wed Jul 27 03:09:29 2022
% 48.27/47.99 Otter interrupted
% 48.27/47.99 PROOF NOT FOUND
%------------------------------------------------------------------------------