TSTP Solution File: SWW474+7 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW474+7 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 : 600s
% DateTime : Thu Jul 21 01:17:11 EDT 2022
% Result : Unknown 62.49s 62.75s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.09 % Problem : SWW474+7 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.10 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Sun Jun 5 12:05:03 EDT 2022
% 0.10/0.29 % CPUTime :
% 1.99/2.29 ============================== Prover9 ===============================
% 1.99/2.29 Prover9 (32) version 2009-11A, November 2009.
% 1.99/2.29 Process 7628 was started by sandbox2 on n032.cluster.edu,
% 1.99/2.29 Sun Jun 5 12:05:05 2022
% 1.99/2.29 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7475_n032.cluster.edu".
% 1.99/2.29 ============================== end of head ===========================
% 1.99/2.29
% 1.99/2.29 ============================== INPUT =================================
% 1.99/2.29
% 1.99/2.29 % Reading from file /tmp/Prover9_7475_n032.cluster.edu
% 1.99/2.29
% 1.99/2.29 set(prolog_style_variables).
% 1.99/2.29 set(auto2).
% 1.99/2.29 % set(auto2) -> set(auto).
% 1.99/2.29 % set(auto) -> set(auto_inference).
% 1.99/2.29 % set(auto) -> set(auto_setup).
% 1.99/2.29 % set(auto_setup) -> set(predicate_elim).
% 1.99/2.29 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.99/2.29 % set(auto) -> set(auto_limits).
% 1.99/2.29 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.99/2.29 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.99/2.29 % set(auto) -> set(auto_denials).
% 1.99/2.29 % set(auto) -> set(auto_process).
% 1.99/2.29 % set(auto2) -> assign(new_constants, 1).
% 1.99/2.29 % set(auto2) -> assign(fold_denial_max, 3).
% 1.99/2.29 % set(auto2) -> assign(max_weight, "200.000").
% 1.99/2.29 % set(auto2) -> assign(max_hours, 1).
% 1.99/2.29 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.99/2.29 % set(auto2) -> assign(max_seconds, 0).
% 1.99/2.29 % set(auto2) -> assign(max_minutes, 5).
% 1.99/2.29 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.99/2.29 % set(auto2) -> set(sort_initial_sos).
% 1.99/2.29 % set(auto2) -> assign(sos_limit, -1).
% 1.99/2.29 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.99/2.29 % set(auto2) -> assign(max_megs, 400).
% 1.99/2.29 % set(auto2) -> assign(stats, some).
% 1.99/2.29 % set(auto2) -> clear(echo_input).
% 1.99/2.29 % set(auto2) -> set(quiet).
% 1.99/2.29 % set(auto2) -> clear(print_initial_clauses).
% 1.99/2.29 % set(auto2) -> clear(print_given).
% 1.99/2.29 assign(lrs_ticks,-1).
% 1.99/2.29 assign(sos_limit,10000).
% 1.99/2.29 assign(order,kbo).
% 1.99/2.29 set(lex_order_vars).
% 1.99/2.29 clear(print_given).
% 1.99/2.29
% 1.99/2.29 % formulas(sos). % not echoed (1169 formulas)
% 1.99/2.29
% 1.99/2.29 ============================== end of input ==========================
% 1.99/2.29
% 1.99/2.29 % From the command line: assign(max_seconds, 300).
% 1.99/2.29
% 1.99/2.29 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.99/2.29
% 1.99/2.29 % Formulas that are not ordinary clauses:
% 1.99/2.29 1 (all X_a all X_b ti(fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool))),big_comm_monoid_big(X_a,X_b)) = big_comm_monoid_big(X_a,X_b)) # label(tsy_c_Big__Operators_Ocomm__monoid__big_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 2 (all X_a (linorder(X_a) -> ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a)),big_Inf_fin(X_a)) = big_Inf_fin(X_a))) # label(tsy_c_Big__Operators_Olattice_OInf__fin_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 3 (all X_a (lattice(X_a) -> ti(fun(fun(X_a,bool),X_a),big_lattice_Inf_fin(X_a)) = big_lattice_Inf_fin(X_a))) # label(tsy_c_Big__Operators_Olattice__class_OInf__fin_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 4 (all X_a (lattice(X_a) -> ti(fun(fun(X_a,bool),X_a),big_lattice_Sup_fin(X_a)) = big_lattice_Sup_fin(X_a))) # label(tsy_c_Big__Operators_Olattice__class_OSup__fin_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 5 (all X_a (linorder(X_a) -> ti(fun(fun(X_a,bool),X_a),big_linorder_Max(X_a)) = big_linorder_Max(X_a))) # label(tsy_c_Big__Operators_Olinorder__class_OMax_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 6 (all X_a (linorder(X_a) -> ti(fun(fun(X_a,bool),X_a),big_linorder_Min(X_a)) = big_linorder_Min(X_a))) # label(tsy_c_Big__Operators_Olinorder__class_OMin_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 7 (all X_a ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool)),big_semilattice_big(X_a)) = big_semilattice_big(X_a)) # label(tsy_c_Big__Operators_Osemilattice__big_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 8 (all X_b all X_c all 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)) # label(tsy_c_COMBB_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 9 (all X_a all X_b all 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)) # label(tsy_c_COMBC_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 10 (all X_a ti(fun(X_a,X_a),combi(X_a)) = combi(X_a)) # label(tsy_c_COMBI_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 11 (all X_a all X_b ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b)) = combk(X_a,X_b)) # label(tsy_c_COMBK_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 12 (all X_a all X_b all 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)) # label(tsy_c_COMBS_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 13 (all X_a (comple44059174attice(X_a) -> ti(fun(fun(X_a,bool),X_a),complete_Inf_Inf(X_a)) = complete_Inf_Inf(X_a))) # label(tsy_c_Complete__Lattice_OInf__class_OInf_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 14 (all X_a (comple44059174attice(X_a) -> ti(fun(fun(X_a,bool),X_a),complete_Sup_Sup(X_a)) = complete_Sup_Sup(X_a))) # label(tsy_c_Complete__Lattice_OSup__class_OSup_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 15 (all X_a all X_b ti(fun(fun(X_a,fun(X_b,X_b)),bool),finite100568337ommute(X_a,X_b)) = finite100568337ommute(X_a,X_b)) # label(tsy_c_Finite__Set_Ocomp__fun__commute_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 16 (all X_a all X_b ti(fun(fun(X_a,fun(X_b,X_b)),bool),finite_comp_fun_idem(X_a,X_b)) = finite_comp_fun_idem(X_a,X_b)) # label(tsy_c_Finite__Set_Ocomp__fun__idem_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 17 (all X_a ti(fun(fun(X_a,bool),bool),finite_finite(X_a)) = finite_finite(X_a)) # label(tsy_c_Finite__Set_Ofinite_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 18 (all X_b all X_a ti(fun(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,bool),X_a))),finite_fold(X_b,X_a)) = finite_fold(X_b,X_a)) # label(tsy_c_Finite__Set_Ofold_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 19 (all X_a ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a)),finite_fold1(X_a)) = finite_fold1(X_a)) # label(tsy_c_Finite__Set_Ofold1_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 20 (all X_a ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool))),finite_fold1Set(X_a)) = finite_fold1Set(X_a)) # label(tsy_c_Finite__Set_Ofold1Set_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 21 (all X_a all X_b ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a)))),finite_fold_image(X_a,X_b)) = finite_fold_image(X_a,X_b)) # label(tsy_c_Finite__Set_Ofold__image_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 22 (all X_a all X_b ti(fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)))),finite1357897459simple(X_a,X_b)) = finite1357897459simple(X_a,X_b)) # label(tsy_c_Finite__Set_Ofolding__image__simple_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 23 (all X_a all X_b ti(fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)))),finite908156982e_idem(X_a,X_b)) = finite908156982e_idem(X_a,X_b)) # label(tsy_c_Finite__Set_Ofolding__image__simple__idem_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 24 (all X_a ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool)),finite_folding_one(X_a)) = finite_folding_one(X_a)) # label(tsy_c_Finite__Set_Ofolding__one_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 25 (all X_a ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool)),finite2073411215e_idem(X_a)) = finite2073411215e_idem(X_a)) # label(tsy_c_Finite__Set_Ofolding__one__idem_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 26 (all X_a all X_b ti(fun(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b)))),fun_upd(X_a,X_b)) = fun_upd(X_a,X_b)) # label(tsy_c_Fun_Ofun__upd_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 27 (all X_a all X_b ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),bool)),inj_on(X_a,X_b)) = inj_on(X_a,X_b)) # label(tsy_c_Fun_Oinj__on_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 28 (all X_a all X_b ti(fun(fun(X_a,X_b),fun(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)))),override_on(X_a,X_b)) = override_on(X_a,X_b)) # label(tsy_c_Fun_Ooverride__on_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 29 (all X_a all X_b ti(fun(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a))),the_inv_into(X_a,X_b)) = the_inv_into(X_a,X_b)) # label(tsy_c_Fun_Othe__inv__into_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 30 (all X_a (minus(X_a) -> ti(fun(X_a,fun(X_a,X_a)),minus_minus(X_a)) = minus_minus(X_a))) # label(tsy_c_Groups_Ominus__class_Ominus_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 31 (all X_a (uminus(X_a) -> ti(fun(X_a,X_a),uminus_uminus(X_a)) = uminus_uminus(X_a))) # label(tsy_c_Groups_Ouminus__class_Ouminus_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 32 (all X_a ti(fun(fun(X_a,bool),X_a),the_1(X_a)) = the_1(X_a)) # label(tsy_c_HOL_OThe_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 33 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 34 (all X_a ti(fun(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool)),hoare_1301688828derivs(X_a)) = hoare_1301688828derivs(X_a)) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Ohoare__derivs_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 35 (all X_a ti(fun(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool)),hoare_902341502valids(X_a)) = hoare_902341502valids(X_a)) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Ohoare__valids_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 36 (all X_a ti(fun(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)))),hoare_759811442triple(X_a)) = hoare_759811442triple(X_a)) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Otriple_Otriple_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 37 (all X_b all X_a ti(fun(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a))),fun(hoare_2118899576triple(X_b),X_a)),hoare_225284258e_case(X_b,X_a)) = hoare_225284258e_case(X_b,X_a)) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Otriple_Otriple__case_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 38 (all X_b all X_a ti(fun(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a))),fun(hoare_2118899576triple(X_b),X_a)),hoare_1759541758le_rec(X_b,X_a)) = hoare_1759541758le_rec(X_b,X_a)) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Otriple_Otriple__rec_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 39 (all X_a ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a)) = if(X_a)) # label(tsy_c_If_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 40 (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))) # label(tsy_c_Lattices_Osemilattice__inf__class_Oinf_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 41 (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))) # label(tsy_c_Lattices_Osemilattice__sup__class_Osup_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 42 (all X_b all X_a ti(fun(fun(X_b,option(X_a)),fun(X_b,bool)),dom(X_b,X_a)) = dom(X_b,X_a)) # label(tsy_c_Map_Odom_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 43 (all X_b all X_a ti(fun(fun(X_b,option(X_a)),fun(X_a,bool)),ran(X_b,X_a)) = ran(X_b,X_a)) # label(tsy_c_Map_Oran_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 44 (all X_a all X_b ti(fun(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b)))),restrict_map(X_a,X_b)) = restrict_map(X_a,X_b)) # label(tsy_c_Map_Orestrict__map_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 45 (all X_a all X_b ti(fun(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool)))),fold_graph(X_a,X_b)) = fold_graph(X_a,X_b)) # label(tsy_c_Nitpick_Ofold__graph_H_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 46 (all X_b ti(fun(option(X_b),bool),is_none(X_b)) = is_none(X_b)) # label(tsy_c_Option_Ois__none_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 47 (all X_b ti(option(X_b),none(X_b)) = none(X_b)) # label(tsy_c_Option_Ooption_ONone_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 48 (all X_a ti(fun(X_a,option(X_a)),some(X_a)) = some(X_a)) # label(tsy_c_Option_Ooption_OSome_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 49 (all X_a all X_b ti(fun(X_a,fun(fun(X_b,X_a),fun(option(X_b),X_a))),option_rec(X_a,X_b)) = option_rec(X_a,X_b)) # label(tsy_c_Option_Ooption_Ooption__rec_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 50 (all X_a ti(fun(option(X_a),fun(X_a,bool)),set(X_a)) = set(X_a)) # label(tsy_c_Option_Oset_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 51 (all X_a ti(fun(option(X_a),X_a),the(X_a)) = the(X_a)) # label(tsy_c_Option_Othe_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 52 (all X_a (bot(X_a) -> ti(X_a,bot_bot(X_a)) = bot_bot(X_a))) # label(tsy_c_Orderings_Obot__class_Obot_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 53 (all X_a (ord(X_a) -> ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a))),max(X_a)) = max(X_a))) # label(tsy_c_Orderings_Oord_Omax_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 54 (all X_a (ord(X_a) -> ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a))),min(X_a)) = min(X_a))) # label(tsy_c_Orderings_Oord_Omin_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 55 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,bool)),ord_less_eq(X_a)) = ord_less_eq(X_a))) # label(tsy_c_Orderings_Oord__class_Oless__eq_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 56 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,X_a)),ord_max(X_a)) = ord_max(X_a))) # label(tsy_c_Orderings_Oord__class_Omax_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 57 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,X_a)),ord_min(X_a)) = ord_min(X_a))) # label(tsy_c_Orderings_Oord__class_Omin_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 58 (all X_a (top(X_a) -> ti(X_a,top_top(X_a)) = top_top(X_a))) # label(tsy_c_Orderings_Otop__class_Otop_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 59 (all X_a ti(fun(X_a,fun(fun(X_a,bool),X_a)),partial_flat_lub(X_a)) = partial_flat_lub(X_a)) # label(tsy_c_Partial__Function_Oflat__lub_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 60 (all X_a ti(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),powp(X_a)) = powp(X_a)) # label(tsy_c_Predicate_OPowp_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 61 (all X_a ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a)) = collect(X_a)) # label(tsy_c_Set_OCollect_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 62 (all X_a ti(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),pow(X_a)) = pow(X_a)) # label(tsy_c_Set_OPow_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 63 (all X_a all X_b ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool))),image(X_a,X_b)) = image(X_a,X_b)) # label(tsy_c_Set_Oimage_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 64 (all X_a ti(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),insert(X_a)) = insert(X_a)) # label(tsy_c_Set_Oinsert_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 65 (all X_a ti(fun(fun(X_a,bool),X_a),the_elem(X_a)) = the_elem(X_a)) # label(tsy_c_Set_Othe__elem_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 66 (all X_a all X_b ti(fun(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool))),vimage(X_a,X_b)) = vimage(X_a,X_b)) # label(tsy_c_Set_Ovimage_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 67 (all X_a ti(fun(fun(X_a,bool),bool),fAll(X_a)) = fAll(X_a)) # label(tsy_c_fAll_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 68 (all X_a ti(fun(fun(X_a,bool),bool),fEx(X_a)) = fEx(X_a)) # label(tsy_c_fEx_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 69 (all X_a ti(fun(X_a,fun(X_a,bool)),fequal(X_a)) = fequal(X_a)) # label(tsy_c_fequal_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 70 (all X_a all X_c all B_1_1 all 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)) # label(tsy_c_hAPP_arg1) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 71 (all X_a all X_c all B_1_1 all 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)) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 72 (all X_c all X_a all B_1_1 all 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)) # label(tsy_c_hAPP_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 73 (all B_1_1 (hBOOL(ti(bool,B_1_1)) <-> hBOOL(B_1_1))) # label(tsy_c_hBOOL_arg1) # label(hypothesis) # label(non_clause). [assumption].
% 1.99/2.29 74 (all X_a ti(fun(X_a,fun(fun(X_a,bool),bool)),member(X_a)) = member(X_a)) # label(tsy_c_member_res) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 75 (all X_a all G_2 hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),bot_bot(fun(hoare_2118899576triple(X_a),bool))))) # label(fact_0_empty) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 76 (all X_a all Ts all G_2 (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),ord_less_eq(fun(hoare_2118899576triple(X_a),bool)),Ts),G_2)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),Ts)))) # label(fact_1_asm) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 77 (all X_a all Ts all G_2 all Ts_1 (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),Ts_1)) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),ord_less_eq(fun(hoare_2118899576triple(X_a),bool)),Ts),Ts_1)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),Ts))))) # label(fact_2_weaken) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 78 (all X_a all G_2 all G_3 all Ts (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_3),Ts)) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),ord_less_eq(fun(hoare_2118899576triple(X_a),bool)),G_3),G_2)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),Ts))))) # label(fact_3_thin) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 79 (all X_a all G_2 all G_3 all Ts (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_3),Ts)) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),G_3)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),Ts))))) # label(fact_4_cut) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 80 (all X_a all Ts all G_2 all T_3 (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),T_3),bot_bot(fun(hoare_2118899576triple(X_a),bool))))) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),Ts)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),T_3),Ts)))))) # label(fact_5_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 81 (all X_a all G_2 all T_3 all Ts (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),T_3),Ts))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),T_3),bot_bot(fun(hoare_2118899576triple(X_a),bool))))) & hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),Ts)))) # label(fact_6_derivs__insertD) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 82 (all Pn_1 all G_2 (hBOOL(hAPP(fun(hoare_2118899576triple(state),bool),bool,hAPP(fun(hoare_2118899576triple(state),bool),fun(fun(hoare_2118899576triple(state),bool),bool),hoare_1301688828derivs(state),hAPP(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool),hAPP(hoare_2118899576triple(state),fun(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool)),insert(hoare_2118899576triple(state)),hAPP(com,hoare_2118899576triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,Pn_1))),G_2)),hAPP(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool),hAPP(hoare_2118899576triple(state),fun(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool)),insert(hoare_2118899576triple(state)),hAPP(com,hoare_2118899576triple(state),hoare_Mirabelle_MGT,hAPP(option(com),com,the(com),hAPP(pname,option(com),body,Pn_1)))),bot_bot(fun(hoare_2118899576triple(state),bool))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(state),bool),bool,hAPP(fun(hoare_2118899576triple(state),bool),fun(fun(hoare_2118899576triple(state),bool),bool),hoare_1301688828derivs(state),G_2),hAPP(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool),hAPP(hoare_2118899576triple(state),fun(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool)),insert(hoare_2118899576triple(state)),hAPP(com,hoare_2118899576triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,Pn_1))),bot_bot(fun(hoare_2118899576triple(state),bool))))))) # label(fact_7_MGT__BodyN) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 83 (all X_a all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),combc(fun(X_a,bool),fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool))),A_1)))))) # label(fact_8_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 84 (all X_b all X_a all H all Fa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),H),Fa))))) # label(fact_9_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 85 (all X_a all A_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),bot_bot(fun(X_a,bool))),A_1))) # label(fact_10_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 86 (all X_a all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1))))) # label(fact_11_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 87 (all X_a hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),bot_bot(fun(X_a,bool))))) # label(fact_12_finite_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 88 (all X_a all Q_2 all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) | hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_2))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),P_1)),Q_2)))))) # label(fact_13_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 89 (all X_b all X_a all C all A_1 ((ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),C)),A_1) = bot_bot(fun(X_b,bool))) & (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),C)),A_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),C),bot_bot(fun(X_b,bool)))))) # label(fact_14_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 90 (all X_b all X_a all C all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),C)),A_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),C),bot_bot(fun(X_b,bool))))) # label(fact_15_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 91 (all X_b all X_a all F all X_2 all Y_2 (hAPP(X_b,option(X_a),F,X_2) = hAPP(X_a,option(X_a),some(X_a),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_2),hAPP(fun(X_b,option(X_a)),fun(X_b,bool),dom(X_b,X_a),F)) = hAPP(fun(X_b,option(X_a)),fun(X_b,bool),dom(X_b,X_a),F))) # label(fact_16_insert__dom) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 92 (all X_b all X_a all B_1 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1))))) # label(fact_17_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 93 (all X_a all A_1 all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))) -> ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)) | ti(fun(X_a,bool),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))) # label(fact_18_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 94 (all C (hBOOL(hoare_511481251gleton) -> (hBOOL(wT_bodies) -> (hBOOL(hAPP(com,bool,wt,C)) -> hBOOL(hAPP(fun(hoare_2118899576triple(state),bool),bool,hAPP(fun(hoare_2118899576triple(state),bool),fun(fun(hoare_2118899576triple(state),bool),bool),hoare_1301688828derivs(state),bot_bot(fun(hoare_2118899576triple(state),bool))),hAPP(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool),hAPP(hoare_2118899576triple(state),fun(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool)),insert(hoare_2118899576triple(state)),hAPP(com,hoare_2118899576triple(state),hoare_Mirabelle_MGT,C)),bot_bot(fun(hoare_2118899576triple(state),bool))))))))) # label(fact_19_MGF) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 95 (all X_a all A_2 -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),bot_bot(fun(X_a,bool))))) # label(fact_20_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 96 (all X_a all B all A_2 all B_1 ((-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),B_1)) -> ti(X_a,A_2) = ti(X_a,B)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),B_1))))) # label(fact_21_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 97 (all X_a all A_2 all B all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),A_1))) -> (ti(X_a,A_2) != ti(X_a,B) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1))))) # label(fact_22_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 98 (all X_a all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_1)) -> ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B_1)))) # label(fact_23_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 99 (all X_a all C all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),B_1))))) # label(fact_24_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 100 (all X_a all X_b all A_1 all B all F all X_2 (ti(X_a,B) = hAPP(X_b,X_a,F,X_2) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))))) # label(fact_25_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 101 (all X_a all A_2 all A_1 (ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1)))) # label(fact_26_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 102 (all X_a all P_1 (hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1) = bot_bot(fun(X_a,bool)) <-> (all X_1 -hBOOL(hAPP(X_a,bool,P_1,X_1))))) # label(fact_27_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 103 (all X_a all C -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),bot_bot(fun(X_a,bool))))) # label(fact_28_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 104 (all X_a all P_1 (bot_bot(fun(X_a,bool)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1) <-> (all X_1 -hBOOL(hAPP(X_a,bool,P_1,X_1))))) # label(fact_29_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 105 (all X_a all A_1 ((exists X_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))) <-> ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)))) # label(fact_30_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.99/2.29 106 (all X_a all A_1 ((all X_1 -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))) <-> ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)))) # label(fact_31_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.29 107 (all X_a bot_bot(fun(X_a,bool)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(bool,fun(X_a,bool),combk(bool,X_a),fFalse))) # label(fact_32_empty__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.29 108 (all X_a (finite_finite_1(X_a) -> (all A_1 hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1))))) # label(fact_33_finite__code) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.29 109 (all X_a (finite_finite_1(X_a) -> (all A_1 hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1))))) # label(fact_34_finite) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.29 110 (all X_a all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1) = ti(fun(X_a,bool),A_1))) # label(fact_35_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.29 111 (all X_a all B all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),B_1))))) # label(fact_36_insertI2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.29 112 (all X_a all B_1 all X_2 all A_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),B_1) <-> ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B_1))))) # label(fact_37_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.29 113 (all X_a all Y_2 all A_1 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_2),A_1),X_2)) <-> ti(X_a,Y_2) = ti(X_a,X_2) | hBOOL(hAPP(X_a,bool,A_1,X_2)))) # label(fact_38_insert__code) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.29 114 (all X_a all A_2 all B all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),A_1))) <-> ti(X_a,A_2) = ti(X_a,B) | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1)))) # label(fact_39_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.29 115 (all X_a all X_2 all Y_2 all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_2),A_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1))) # label(fact_40_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.29 116 (all X_a all X_2 all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) # label(fact_41_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.29 117 (all X_a all A_2 all P_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fimplies),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2)))),P_1))) # label(fact_42_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 118 (all X_a all A_2 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),B_1) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_1)))) # label(fact_43_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 119 (all X_a all A_2 all B_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),B_1)))) # label(fact_44_insertI1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 120 (all X_a all A_1 all B_1 (ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B_1) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_1))))) # label(fact_45_equalityE) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 121 (all X_a all C_2 all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C_2))))) # label(fact_46_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 122 (all X_a all X_2 all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B_1))))) # label(fact_47_set__mp) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 123 (all X_a all B_1 all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B_1))))) # label(fact_48_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 124 (all X_a all X_2 all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B_1))))) # label(fact_49_in__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 125 (all X_a all A_1 all B_1 (ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B_1) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_1)))) # label(fact_50_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 126 (all X_a all A_1 all B_1 (ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B_1) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)))) # label(fact_51_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 127 (all X_a all A_1 all B_1 (ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B_1) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_1)))) # label(fact_52_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 128 (all X_a all A_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),A_1))) # label(fact_53_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 129 (all X_b all X_a all B all F all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (ti(X_b,B) = hAPP(X_a,X_b,F,X_2) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))))) # label(fact_54_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 130 (all X_b all X_a all F all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))))) # label(fact_55_imageI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 131 (all X_a all X_b all Z_2 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z_2),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) <-> (exists X_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) & ti(X_a,Z_2) = hAPP(X_b,X_a,F,X_1))))) # label(fact_56_image__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 132 (all X_a all P_1 all Q_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),P_1)),Q_2)))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_2))))) # label(fact_57_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 133 (all X_a all X_1 all Xa hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),Xa) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),Xa)))) # label(fact_58_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 134 (all X_a all Y_3 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),combi(X_a)),Y_3) = ti(fun(X_a,bool),Y_3)) # label(fact_59_image__ident) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 135 (all X_b all X_a all X_c all F all G all A_1 hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),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),G),A_1)) = hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),hAPP(fun(X_c,X_b),fun(X_c,X_a),hAPP(fun(X_b,X_a),fun(fun(X_c,X_b),fun(X_c,X_a)),combb(X_b,X_a,X_c),F),G)),A_1)) # label(fact_60_image__image) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 136 (all X_a all A_2 all B (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),bot_bot(fun(X_a,bool))) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),bot_bot(fun(X_a,bool))) -> ti(X_a,A_2) = ti(X_a,B))) # label(fact_61_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 137 (all X_a all B all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),bot_bot(fun(X_a,bool))))) -> ti(X_a,B) = ti(X_a,A_2))) # label(fact_62_singletonE) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 138 (all X_a all A_2 all B all C all D_1 (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),bot_bot(fun(X_a,bool)))) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),D_1),bot_bot(fun(X_a,bool)))) <-> ti(X_a,A_2) = ti(X_a,C) & ti(X_a,B) = ti(X_a,D_1) | ti(X_a,A_2) = ti(X_a,D_1) & ti(X_a,B) = ti(X_a,C))) # label(fact_63_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 139 (all X_a all B all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),bot_bot(fun(X_a,bool))))) <-> ti(X_a,B) = ti(X_a,A_2))) # label(fact_64_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 140 (all X_a all A_2 all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1) != bot_bot(fun(X_a,bool))) # label(fact_65_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 141 (all X_a all A_2 all A_1 bot_bot(fun(X_a,bool)) != hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1)) # label(fact_66_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 142 (all X_a all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)))) # label(fact_67_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 143 (all X_a all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),bot_bot(fun(X_a,bool)))) <-> ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)))) # label(fact_68_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 144 (all X_b all X_a all F all A_1 (hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1) = bot_bot(fun(X_a,bool)) <-> ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,bool)))) # label(fact_69_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 145 (all X_b all X_a all F hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),bot_bot(fun(X_b,bool))) = bot_bot(fun(X_a,bool))) # label(fact_70_image__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 146 (all X_a all X_b all F all A_1 (bot_bot(fun(X_a,bool)) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1) <-> ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,bool)))) # label(fact_71_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 147 (all X_a all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1))))) # label(fact_72_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 148 (all X_a all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1))))) # label(fact_73_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 149 (all X_a all A_2 all C_2 all D_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),C_2),D_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),C_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),D_2))))) # label(fact_74_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 150 (all X_a all X_b all F all G ((all X_1 hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,G,X_1)) -> ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G))) # label(fact_75_ext) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 151 (all X_a all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) <-> hBOOL(hAPP(X_a,bool,A_1,X_2)))) # label(fact_76_mem__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 152 (all X_a all P_1 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1) = ti(fun(X_a,bool),P_1)) # label(fact_77_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 153 (all X_a all B all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),B_1))))) # label(fact_78_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 154 (all X_a all B_1 all X_2 all A_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),B_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1))))) # label(fact_79_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 155 (all X_a all X_2 all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)),B_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B_1)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)))) # label(fact_80_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 156 (all X_a all B_1 all A_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),B_1)))) # label(fact_81_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 157 (all X_b all X_a all F all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)) = hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) # label(fact_82_insert__image) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 158 (all X_b all X_a all F all A_2 all B_1 hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),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),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),hAPP(X_b,X_a,F,A_2)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),B_1))) # label(fact_83_image__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 159 (all X_b all X_a all F all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B_1))))) # label(fact_84_image__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 160 (all X_a all X_b all B_1 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) <-> (exists AA (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),AA),A_1)) & ti(fun(X_a,bool),B_1) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),AA))))) # label(fact_85_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 161 (all X_b all X_a all M_1 all A_2 all B (hAPP(X_b,option(X_a),M_1,A_2) = hAPP(X_a,option(X_a),some(X_a),B) -> 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,option(X_a)),fun(X_b,bool),dom(X_b,X_a),M_1))))) # label(fact_86_domI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 162 (all X_a all P_1 all A_2 ((hBOOL(hAPP(X_a,bool,P_1,A_2)) -> hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),P_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),bot_bot(fun(X_a,bool)))) & (-hBOOL(hAPP(X_a,bool,P_1,A_2)) -> hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),P_1)) = bot_bot(fun(X_a,bool))))) # label(fact_87_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 163 (all X_a all P_1 all A_2 ((hBOOL(hAPP(X_a,bool,P_1,A_2)) -> hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_2))),P_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),bot_bot(fun(X_a,bool)))) & (-hBOOL(hAPP(X_a,bool,P_1,A_2)) -> hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_2))),P_1)) = bot_bot(fun(X_a,bool))))) # label(fact_88_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 164 (all X_a all A_2 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),bot_bot(fun(X_a,bool)))) # label(fact_89_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 165 (all X_a all A_2 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_2)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),bot_bot(fun(X_a,bool)))) # label(fact_90_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 166 (all C all G_2 (hBOOL(hoare_511481251gleton) -> ((all X_1 (hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X_1),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body))) -> hBOOL(hAPP(fun(hoare_2118899576triple(state),bool),bool,hAPP(fun(hoare_2118899576triple(state),bool),fun(fun(hoare_2118899576triple(state),bool),bool),hoare_1301688828derivs(state),G_2),hAPP(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool),hAPP(hoare_2118899576triple(state),fun(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool)),insert(hoare_2118899576triple(state)),hAPP(com,hoare_2118899576triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,X_1))),bot_bot(fun(hoare_2118899576triple(state),bool))))))) -> (hBOOL(hAPP(com,bool,wt,C)) -> hBOOL(hAPP(fun(hoare_2118899576triple(state),bool),bool,hAPP(fun(hoare_2118899576triple(state),bool),fun(fun(hoare_2118899576triple(state),bool),bool),hoare_1301688828derivs(state),G_2),hAPP(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool),hAPP(hoare_2118899576triple(state),fun(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool)),insert(hoare_2118899576triple(state)),hAPP(com,hoare_2118899576triple(state),hoare_Mirabelle_MGT,C)),bot_bot(fun(hoare_2118899576triple(state),bool))))))))) # label(fact_91_MGF__lemma1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 167 (all Pn all B_2 (hBOOL(wT_bodies) -> (hAPP(pname,option(com),body,Pn) = hAPP(com,option(com),some(com),B_2) -> hBOOL(hAPP(com,bool,wt,B_2))))) # label(fact_92_WT__bodiesD) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 168 (all X_a all X_b all B all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) -> -(all X_1 (ti(X_a,B) = hAPP(X_b,X_a,F,X_1) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)))))) # label(fact_93_imageE) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 169 (all X_a all P_1 all A_1 all Fa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),Fa),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,P_1,bot_bot(fun(X_a,bool)))) -> ((all A_4 all F_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),F_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_4),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_4),F_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,P_1,F_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,P_1,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_4),F_2)))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,P_1,Fa))))))) # label(fact_94_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 170 (all P (hBOOL(hAPP(com,bool,wt,hAPP(pname,com,body_1,P))) -> -(all Y_1 hAPP(pname,option(com),body,P) != hAPP(com,option(com),some(com),Y_1)))) # label(fact_95_WTs__elim__cases_I7_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 171 (all X_a all B_1 all A_1 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_1)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)))) # label(fact_96_subsetI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 172 (all X_b all X_a all F all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) -> (exists C_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),C_3),A_1)) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),C_3)) & ti(fun(X_a,bool),B_1) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),C_3)))))) # label(fact_97_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 173 (all X_a all P_1 all Fa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,P_1,bot_bot(fun(X_a,bool)))) -> ((all X_1 all F_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),F_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),F_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,P_1,F_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,P_1,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),F_2))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,P_1,Fa)))))) # label(fact_99_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 174 (all X_a all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_2)) <-> ti(fun(X_a,bool),A_2) = bot_bot(fun(X_a,bool)) | (exists A_5 exists A_4 (ti(fun(X_a,bool),A_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_4),A_5) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_5)))))) # label(fact_100_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 175 (all X_b all X_a all F all A_1 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) -> (exists X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) & -hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),hAPP(X_b,fun(X_a,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,bool))),combb(X_b,fun(X_b,bool),X_a),fequal(X_b)),F)),hAPP(X_a,X_b,F,X_1))))))))))) # label(fact_101_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 176 (all Pname_2 all Pname_1 (hAPP(pname,com,body_1,Pname_2) = hAPP(pname,com,body_1,Pname_1) <-> ti(pname,Pname_2) = ti(pname,Pname_1))) # label(fact_102_com_Osimps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 177 (all G_2 all Procs (hBOOL(hAPP(fun(hoare_2118899576triple(state),bool),bool,hAPP(fun(hoare_2118899576triple(state),bool),fun(fun(hoare_2118899576triple(state),bool),bool),hoare_1301688828derivs(state),hAPP(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool),hAPP(fun(hoare_2118899576triple(state),bool),fun(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool)),semilattice_sup_sup(fun(hoare_2118899576triple(state),bool)),G_2),hAPP(fun(pname,bool),fun(hoare_2118899576triple(state),bool),hAPP(fun(pname,hoare_2118899576triple(state)),fun(fun(pname,bool),fun(hoare_2118899576triple(state),bool)),image(pname,hoare_2118899576triple(state)),hAPP(fun(pname,com),fun(pname,hoare_2118899576triple(state)),hAPP(fun(com,hoare_2118899576triple(state)),fun(fun(pname,com),fun(pname,hoare_2118899576triple(state))),combb(com,hoare_2118899576triple(state),pname),hoare_Mirabelle_MGT),body_1)),Procs))),hAPP(fun(pname,bool),fun(hoare_2118899576triple(state),bool),hAPP(fun(pname,hoare_2118899576triple(state)),fun(fun(pname,bool),fun(hoare_2118899576triple(state),bool)),image(pname,hoare_2118899576triple(state)),hAPP(fun(pname,com),fun(pname,hoare_2118899576triple(state)),hAPP(fun(com,hoare_2118899576triple(state)),fun(fun(pname,com),fun(pname,hoare_2118899576triple(state))),combb(com,hoare_2118899576triple(state),pname),hoare_Mirabelle_MGT),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))),Procs))) -> (hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),Procs)) -> hBOOL(hAPP(fun(hoare_2118899576triple(state),bool),bool,hAPP(fun(hoare_2118899576triple(state),bool),fun(fun(hoare_2118899576triple(state),bool),bool),hoare_1301688828derivs(state),G_2),hAPP(fun(pname,bool),fun(hoare_2118899576triple(state),bool),hAPP(fun(pname,hoare_2118899576triple(state)),fun(fun(pname,bool),fun(hoare_2118899576triple(state),bool)),image(pname,hoare_2118899576triple(state)),hAPP(fun(pname,com),fun(pname,hoare_2118899576triple(state)),hAPP(fun(com,hoare_2118899576triple(state)),fun(fun(pname,com),fun(pname,hoare_2118899576triple(state))),combb(com,hoare_2118899576triple(state),pname),hoare_Mirabelle_MGT),body_1)),Procs)))))) # label(fact_103_MGT__Body) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 178 (all X_a all X_b all A_2 all M_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),M_1))) -> (exists B_4 hAPP(X_a,option(X_b),M_1,A_2) = hAPP(X_b,option(X_b),some(X_b),B_4)))) # label(fact_104_domD) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 179 (all X_a all X_2 hAPP(fun(X_a,bool),X_a,the_elem(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = ti(X_a,X_2)) # label(fact_105_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 180 (all X_b all X_a all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),B_1)))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),B_1)))) # label(fact_106_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 181 (all X_a (preorder(X_a) -> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),X))))) # label(fact_107_order__refl) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 182 (all X_a all A_1 (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) <-> (exists X_1 exists B_3 (ti(fun(X_a,bool),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),B_3) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_3)))))) # label(fact_108_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 183 (all X_a all X hAPP(option(X_a),X_a,the(X_a),hAPP(X_a,option(X_a),some(X_a),X)) = ti(X_a,X)) # label(fact_109_the_Osimps) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 184 (all X_a all G_2 all P_1 all Pn_1 all Q_2 (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),P_1),hAPP(option(com),com,the(com),hAPP(pname,option(com),body,Pn_1))),Q_2)),bot_bot(fun(hoare_2118899576triple(X_a),bool))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),P_1),hAPP(pname,com,body_1,Pn_1)),Q_2)),bot_bot(fun(hoare_2118899576triple(X_a),bool))))))) # label(fact_110_weak__Body) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 185 (all X_a all P_1 all Pn_1 all Q_2 all G_2 (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),P_1),hAPP(pname,com,body_1,Pn_1)),Q_2)),G_2)),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),P_1),hAPP(option(com),com,the(com),hAPP(pname,option(com),body,Pn_1))),Q_2)),bot_bot(fun(hoare_2118899576triple(X_a),bool))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),P_1),hAPP(pname,com,body_1,Pn_1)),Q_2)),bot_bot(fun(hoare_2118899576triple(X_a),bool))))))) # label(fact_111_BodyN) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 186 hBOOL(hoare_511481251gleton) <-> (exists S_1 exists T_5 S_1 != T_5) # label(fact_112_state__not__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 187 (all X_a all A_1 all C all B_1 ((-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1))))) # label(fact_113_UnCI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 188 (all X_a all C all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1))) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),B_1))))) # label(fact_114_UnE) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 189 (all X_a all Fun1_1 all Com_1 all Fun2_1 all Fun1_2 all Com_2 all Fun2_2 (hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),Fun1_1),Com_1),Fun2_1) = hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),Fun1_2),Com_2),Fun2_2) <-> Fun1_1 = Fun1_2 & Com_1 = Com_2 & Fun2_1 = Fun2_2)) # label(fact_115_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 190 (all X_a all A_1 all C all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1))))) # label(fact_116_UnI2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 191 (all X_a all B_1 all C all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1))))) # label(fact_117_UnI1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 192 (all X_a all P_1 all A_1 all B_1 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1))) -> hBOOL(hAPP(X_a,bool,P_1,X_1)))) <-> (all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(X_a,bool,P_1,X_1)))) & (all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_1)) -> hBOOL(hAPP(X_a,bool,P_1,X_1)))))) # label(fact_118_ball__Un) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 193 (all X_a all P_1 all A_1 all B_1 ((exists X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1))) & hBOOL(hAPP(X_a,bool,P_1,X_1)))) <-> (exists X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) & hBOOL(hAPP(X_a,bool,P_1,X_1)))) | (exists X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_1)) & hBOOL(hAPP(X_a,bool,P_1,X_1)))))) # label(fact_119_bex__Un) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 194 (all X_a all A_1 all B_1 all C_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)),C_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B_1),C_2))) # label(fact_120_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 195 (all X_a all C all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1)) | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),B_1)))) # label(fact_121_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 196 (all X_a all A_1 all B_1 all C_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B_1),C_2)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),C_2))) # label(fact_122_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 197 (all X_a all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)) # label(fact_123_Un__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 198 (all X_a all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B_1),A_1)) # label(fact_124_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 199 (all X_a all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_1)))) # label(fact_125_Un__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 200 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),A_1) = ti(fun(X_a,bool),A_1)) # label(fact_126_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 201 (all X_a all P_1 all Q_2 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),P_1)),Q_2)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_2))) # label(fact_127_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 202 (all X_a all A_1 all B_1 (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1) = bot_bot(fun(X_a,bool)) <-> ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)) & ti(fun(X_a,bool),B_1) = bot_bot(fun(X_a,bool)))) # label(fact_128_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 203 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),bot_bot(fun(X_a,bool))) = ti(fun(X_a,bool),A_1)) # label(fact_129_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 204 (all X_a all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),bot_bot(fun(X_a,bool))),B_1) = ti(fun(X_a,bool),B_1)) # label(fact_130_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 205 (all X_a all G_2 all Fa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),G_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),Fa),G_2)))))) # label(fact_131_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 206 (all X_a all Fa all G_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),Fa),G_2))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa)) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),G_2)))) # label(fact_132_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 207 (all X_a all A_2 all B_1 all C_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),B_1)),C_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B_1),C_2))) # label(fact_133_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 208 (all X_a all A_1 all A_2 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1))) # label(fact_134_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 209 (all X_a all B_1 all D_2 all A_1 all C_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),D_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),C_2),D_2)))))) # label(fact_135_Un__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 210 (all X_a all B_1 all A_1 all C_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)),C_2))))) # label(fact_136_Un__least) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 211 (all X_a all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1) = ti(fun(X_a,bool),A_1))) # label(fact_137_Un__absorb2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 212 (all X_a all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1) = ti(fun(X_a,bool),B_1))) # label(fact_138_Un__absorb1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 213 (all X_a all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) <-> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1) = ti(fun(X_a,bool),B_1))) # label(fact_139_subset__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 214 (all X_a all B_1 all A_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)))) # label(fact_140_Un__upper2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 215 (all X_a all A_1 all B_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)))) # label(fact_141_Un__upper1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 216 (all X_b all X_a all F all A_1 all B_1 hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),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_1),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),B_1))) # label(fact_142_image__Un) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 217 (all X_a all A_2 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),B_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),B_1)) # label(fact_143_insert__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 218 (all X_a all A_2 all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),bot_bot(fun(X_a,bool)))),A_1)) # label(fact_144_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 219 (all X_a all G_2 all P_1 all Q_2 all Procs (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),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_2),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_1)),body_1)),Q_2)),Procs))),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_1)),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))),Q_2)),Procs))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),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_1)),body_1)),Q_2)),Procs))))) # label(fact_145_hoare__derivs_OBody) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.30 220 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_146_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 221 (all X_a (order(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X))))))) # label(fact_147_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 222 (all X_a (order(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> ti(X_a,X) = ti(X_a,Y)))))) # label(fact_148_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 223 (all X_a (preorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z))))))) # label(fact_149_order__trans) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 224 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> ti(X_a,X) = ti(X_a,Y)))))) # label(fact_150_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 225 (all X_a (order(X_a) -> (all C_1 all B_2 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),A_3)) -> (ti(X_a,B_2) = ti(X_a,C_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_3))))))) # label(fact_151_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 226 (all X_a (ord(X_a) -> (all C_1 all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_2)) -> (ti(X_a,B_2) = ti(X_a,C_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),C_1))))))) # label(fact_152_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 227 (all X_a (order(X_a) -> (all C_1 all A_3 all B_2 (ti(X_a,A_3) = ti(X_a,B_2) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_3))))))) # label(fact_153_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 228 (all X_a (ord(X_a) -> (all C_1 all A_3 all B_2 (ti(X_a,A_3) = ti(X_a,B_2) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),C_1))))))) # label(fact_154_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 229 (all X_a (order(X_a) -> (all Y_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) <-> ti(X_a,X_2) = ti(X_a,Y_2)))))) # label(fact_155_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 230 (all X_a (preorder(X_a) -> (all X all Y (X = Y -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_156_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 231 (all X_a (order(X_a) -> (all X_2 all Y_2 (ti(X_a,X_2) = ti(X_a,Y_2) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_2)))))) # label(fact_157_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 232 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_158_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 233 (all X_a all A_2 all A_9 (hAPP(X_a,option(X_a),some(X_a),A_2) = hAPP(X_a,option(X_a),some(X_a),A_9) <-> ti(X_a,A_2) = ti(X_a,A_9))) # label(fact_159_option_Oinject) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 234 (all X_a all G_2 all P_1 all C all Q_2 all C_2 ((hBOOL(C_2) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),P_1),C),Q_2)),bot_bot(fun(hoare_2118899576triple(X_a),bool)))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),hAPP(bool,fun(X_a,fun(state,bool)),hAPP(fun(X_a,fun(bool,fun(state,bool))),fun(bool,fun(X_a,fun(state,bool))),combc(X_a,bool,fun(state,bool)),hAPP(fun(X_a,fun(state,fun(bool,bool))),fun(X_a,fun(bool,fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(bool,fun(state,bool))),fun(fun(X_a,fun(state,fun(bool,bool))),fun(X_a,fun(bool,fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X_a),combc(state,bool,bool)),hAPP(fun(X_a,fun(state,bool)),fun(X_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X_a,fun(state,bool)),fun(X_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),P_1))),C_2)),C),Q_2)),bot_bot(fun(hoare_2118899576triple(X_a),bool))))))) # label(fact_160_constant) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 235 (all X_a all Pn_1 all G_2 all P_1 all Q_2 all Procs (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),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_2),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_1)),body_1)),Q_2)),Procs))),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_1)),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))),Q_2)),Procs))) -> (hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),Pn_1),Procs)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),hAPP(pname,fun(X_a,fun(state,bool)),P_1,Pn_1)),hAPP(pname,com,body_1,Pn_1)),hAPP(pname,fun(X_a,fun(state,bool)),Q_2,Pn_1))),bot_bot(fun(hoare_2118899576triple(X_a),bool)))))))) # label(fact_161_Body1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 236 (all X_a (bot(X_a) -> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),bot_bot(X_a))) -> ti(X_a,A_3) = bot_bot(X_a))))) # label(fact_162_le__bot) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 237 (all X_a (bot(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),bot_bot(X_a))) <-> ti(X_a,A_2) = bot_bot(X_a))))) # label(fact_163_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 238 (all X_a (bot(X_a) -> (all A_3 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),bot_bot(X_a)),A_3))))) # label(fact_164_bot__least) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 239 (all X_a all X_b (ord(X_b) -> (all X_2 all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))))))) # label(fact_165_le__funE) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 240 (all X_a all X_b (ord(X_b) -> (all X_2 all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))))))) # label(fact_166_le__funD) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 241 (all X_a all X_b (ord(X_b) -> (all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) <-> (all X_1 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1)))))))) # label(fact_167_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 242 (all X_b all X_a (bot(X_a) -> (all X_2 hAPP(X_b,X_a,bot_bot(fun(X_b,X_a)),X_2) = bot_bot(X_a)))) # label(fact_168_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 243 (all X_a all X_b (bot(X_b) -> (all X_1 hAPP(X_a,X_b,bot_bot(fun(X_a,X_b)),X_1) = bot_bot(X_b)))) # label(fact_169_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 244 (all X_b all X_a all P_1 all Q_2 all G_2 all P_3 all C0_1 all Q_4 all U_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),U_2)) -> ((all P_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),G_2),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(X_a,fun(X_b,fun(state,bool)),P_3,P_4)),hAPP(X_a,com,C0_1,P_4)),hAPP(X_a,fun(X_b,fun(state,bool)),Q_4,P_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),G_2),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(X_a,fun(X_b,fun(state,bool)),P_1,P_4)),hAPP(X_a,com,C0_1,P_4)),hAPP(X_a,fun(X_b,fun(state,bool)),Q_2,P_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),G_2),hAPP(fun(X_a,bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(X_a,hoare_2118899576triple(X_b)),fun(fun(X_a,bool),fun(hoare_2118899576triple(X_b),bool)),image(X_a,hoare_2118899576triple(X_b)),hAPP(fun(X_a,fun(X_b,fun(state,bool))),fun(X_a,hoare_2118899576triple(X_b)),hAPP(fun(X_a,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),fun(fun(X_a,fun(X_b,fun(state,bool))),fun(X_a,hoare_2118899576triple(X_b))),combs(X_a,fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_a,com),fun(X_a,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(X_a,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(X_a,com),fun(X_a,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),combs(X_a,com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(X_a,fun(X_b,fun(state,bool))),fun(X_a,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(X_a,fun(X_b,fun(state,bool))),fun(X_a,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))),X_a),hoare_759811442triple(X_b)),P_3)),C0_1)),Q_4)),U_2))) -> 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_2),hAPP(fun(X_a,bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(X_a,hoare_2118899576triple(X_b)),fun(fun(X_a,bool),fun(hoare_2118899576triple(X_b),bool)),image(X_a,hoare_2118899576triple(X_b)),hAPP(fun(X_a,fun(X_b,fun(state,bool))),fun(X_a,hoare_2118899576triple(X_b)),hAPP(fun(X_a,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),fun(fun(X_a,fun(X_b,fun(state,bool))),fun(X_a,hoare_2118899576triple(X_b))),combs(X_a,fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_a,com),fun(X_a,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(X_a,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(X_a,com),fun(X_a,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),combs(X_a,com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(X_a,fun(X_b,fun(state,bool))),fun(X_a,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(X_a,fun(X_b,fun(state,bool))),fun(X_a,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))),X_a),hoare_759811442triple(X_b)),P_1)),C0_1)),Q_2)),U_2))))))) # label(fact_170_finite__pointwise) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 245 (all X_a all G_2 all C all Q_2 all P_1 ((all Z_3 all S_1 (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),P_1,Z_3),S_1)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),hAPP(fun(state,bool),fun(X_a,fun(state,bool)),combk(fun(state,bool),X_a),hAPP(state,fun(state,bool),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),S_1))),C),hAPP(fun(state,bool),fun(X_a,fun(state,bool)),combk(fun(state,bool),X_a),hAPP(X_a,fun(state,bool),Q_2,Z_3)))),bot_bot(fun(hoare_2118899576triple(X_a),bool))))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),P_1),C),Q_2)),bot_bot(fun(hoare_2118899576triple(X_a),bool))))))) # label(fact_171_escape) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 246 (all X_a all G_2 all P_1 all Q_2 all Procs (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_902341502valids(X_a),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_2),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_1)),body_1)),Q_2)),Procs))),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_1)),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))),Q_2)),Procs))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_902341502valids(X_a),G_2),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_1)),body_1)),Q_2)),Procs))))) # label(fact_172_Body__sound__lemma) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 247 (all X_a all P_1 all G_2 all P_3 all C all Q_2 (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),P_3),C),Q_2)),bot_bot(fun(hoare_2118899576triple(X_a),bool))))) -> ((all Z_3 all S_1 (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),P_1,Z_3),S_1)) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),P_3,Z_3),S_1)))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),P_1),C),Q_2)),bot_bot(fun(hoare_2118899576triple(X_a),bool)))))))) # label(fact_173_conseq1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 248 (all X_a all Q_2 all G_2 all P_1 all C all Q_4 (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),P_1),C),Q_4)),bot_bot(fun(hoare_2118899576triple(X_a),bool))))) -> ((all Z_3 all S_1 (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Q_4,Z_3),S_1)) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Q_2,Z_3),S_1)))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),P_1),C),Q_2)),bot_bot(fun(hoare_2118899576triple(X_a),bool)))))))) # label(fact_174_conseq2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 249 (all P_1 all Q_2 all C (hBOOL(hAPP(fun(hoare_2118899576triple(state),bool),bool,hAPP(fun(hoare_2118899576triple(state),bool),fun(fun(hoare_2118899576triple(state),bool),bool),hoare_1301688828derivs(state),bot_bot(fun(hoare_2118899576triple(state),bool))),hAPP(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool),hAPP(hoare_2118899576triple(state),fun(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool)),insert(hoare_2118899576triple(state)),hAPP(com,hoare_2118899576triple(state),hoare_Mirabelle_MGT,C)),bot_bot(fun(hoare_2118899576triple(state),bool))))) -> (hBOOL(hAPP(fun(hoare_2118899576triple(state),bool),bool,hAPP(fun(hoare_2118899576triple(state),bool),fun(fun(hoare_2118899576triple(state),bool),bool),hoare_902341502valids(state),bot_bot(fun(hoare_2118899576triple(state),bool))),hAPP(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool),hAPP(hoare_2118899576triple(state),fun(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool)),insert(hoare_2118899576triple(state)),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),P_1),C),Q_2)),bot_bot(fun(hoare_2118899576triple(state),bool))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(state),bool),bool,hAPP(fun(hoare_2118899576triple(state),bool),fun(fun(hoare_2118899576triple(state),bool),bool),hoare_1301688828derivs(state),bot_bot(fun(hoare_2118899576triple(state),bool))),hAPP(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool),hAPP(hoare_2118899576triple(state),fun(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool)),insert(hoare_2118899576triple(state)),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),P_1),C),Q_2)),bot_bot(fun(hoare_2118899576triple(state),bool)))))))) # label(fact_175_MGF__complete) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 250 (all X_a all A_1 all B_1 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1),X_2)) -> (-hBOOL(hAPP(X_a,bool,A_1,X_2)) -> hBOOL(hAPP(X_a,bool,B_1,X_2))))) # label(fact_176_sup1E) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 251 (all X_a all A_1 all B_1 all X_2 ((-hBOOL(hAPP(X_a,bool,B_1,X_2)) -> hBOOL(hAPP(X_a,bool,A_1,X_2))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1),X_2)))) # label(fact_177_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 252 (all X_a all Q_2 all P_1 all G_2 all P_3 all C all Q_4 (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),P_3),C),Q_4)),bot_bot(fun(hoare_2118899576triple(X_a),bool))))) -> ((all Z_3 all S_1 (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),P_1,Z_3),S_1)) -> (all S_2 ((all Z_4 (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),P_3,Z_4),S_1)) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Q_4,Z_4),S_2)))) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Q_2,Z_3),S_2)))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),P_1),C),Q_2)),bot_bot(fun(hoare_2118899576triple(X_a),bool)))))))) # label(fact_178_conseq12) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 253 (all X_a all G_2 all Ts (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),Ts)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_902341502valids(X_a),G_2),Ts)))) # label(fact_179_hoare__sound) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 254 (all X_a all X_1 (hBOOL(hAPP(X_a,bool,bot_bot(fun(X_a,bool)),X_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),bot_bot(fun(X_a,bool)))))) # label(fact_180_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 255 (all X_a all Q_2 all P_1 all X_2 (hBOOL(hAPP(X_a,bool,P_1,X_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),P_1),Q_2)) -> hBOOL(hAPP(X_a,bool,Q_2,X_2))))) # label(fact_181_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 256 (all X_a all X_2 all P_1 all Q_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),P_1),Q_2)) -> (hBOOL(hAPP(X_a,bool,P_1,X_2)) -> hBOOL(hAPP(X_a,bool,Q_2,X_2))))) # label(fact_182_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 257 (all X_a all A_1 all B_1 all X_2 (hBOOL(hAPP(X_a,bool,B_1,X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1),X_2)))) # label(fact_183_sup1I2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 258 (all X_a all B_1 all A_1 all X_2 (hBOOL(hAPP(X_a,bool,A_1,X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1),X_2)))) # label(fact_184_sup1I1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 259 (all X_a all R_1 all S (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),R_1),S)))) # label(fact_185_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 260 (all X_a all R_1 all S all X_1 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)),X_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),R_1),S))))) # label(fact_186_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 261 (all X_a all X_b (ord(X_b) -> (all F all G ((all X_1 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1)))) -> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)))))) # label(fact_187_le__funI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 262 (all X_b all X_a all F1 all Fun1_1 all Com_1 all Fun2_1 hAPP(hoare_2118899576triple(X_b),X_a,hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a))),fun(hoare_2118899576triple(X_b),X_a),hoare_225284258e_case(X_b,X_a),F1),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_1),Fun2_1)) = hAPP(fun(X_b,fun(state,bool)),X_a,hAPP(com,fun(fun(X_b,fun(state,bool)),X_a),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a)),F1,Fun1_1),Com_1),Fun2_1)) # label(fact_188_triple_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 263 (all X_b all X_a all F1 all Fun1_1 all Com_1 all Fun2_1 hAPP(hoare_2118899576triple(X_b),X_a,hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a))),fun(hoare_2118899576triple(X_b),X_a),hoare_1759541758le_rec(X_b,X_a),F1),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_1),Fun2_1)) = hAPP(fun(X_b,fun(state,bool)),X_a,hAPP(com,fun(fun(X_b,fun(state,bool)),X_a),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a)),F1,Fun1_1),Com_1),Fun2_1)) # label(fact_189_triple_Orecs) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 264 (all X_a all X_2 hAPP(option(X_a),fun(X_a,bool),set(X_a),hAPP(X_a,option(X_a),some(X_a),X_2)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) # label(fact_190_Option_Oset_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 265 (all X_b all X_a (lattice(X_a) -> (all F all G all X_2 hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),semilattice_sup_sup(fun(X_b,X_a)),F),G),X_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,G,X_2))))) # label(fact_191_sup__apply) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 266 (all X_a all X_b (lattice(X_b) -> (all F all G all X_1 hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),semilattice_sup_sup(fun(X_a,X_b)),F),G),X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))) # label(fact_192_sup__fun__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 267 hBOOL(hoare_511481251gleton) -> (all T_5 -(all S_1 S_1 = T_5)) # label(fact_193_single__stateE) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 268 (all X_a (bounded_lattice_bot(X_a) -> (all X_2 all Y_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2),Y_2) = bot_bot(X_a) <-> ti(X_a,X_2) = bot_bot(X_a) & ti(X_a,Y_2) = bot_bot(X_a))))) # label(fact_194_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 269 (all X_a all X_2 all Xo (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(option(X_a),fun(X_a,bool),set(X_a),Xo))) <-> ti(option(X_a),Xo) = hAPP(X_a,option(X_a),some(X_a),X_2))) # label(fact_195_elem__set) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 270 (all X_a (semilattice_sup(X_a) -> (all A_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),A_3) = ti(X_a,A_3)))) # label(fact_196_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 271 (all X_a (semilattice_sup(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),X) = ti(X_a,X)))) # label(fact_197_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 272 (all X_a (semilattice_sup(X_a) -> (all A_3 all B_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),B_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_2),A_3)))) # label(fact_198_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 273 (all X_a (lattice(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X)))) # label(fact_199_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 274 (all X_a (semilattice_sup(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X)))) # label(fact_200_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 275 (all X_a (semilattice_sup(X_a) -> (all A_3 all B_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),B_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),B_2)))) # label(fact_201_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 276 (all X_a (lattice(X_a) -> (all X all Y 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_sup_sup(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)))) # label(fact_202_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 277 (all X_a (semilattice_sup(X_a) -> (all X all Y 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_sup_sup(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)))) # label(fact_203_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 278 (all X_a (semilattice_sup(X_a) -> (all B_2 all A_3 all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_2),C_1))))) # label(fact_204_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 279 (all X_a (lattice(X_a) -> (all X all Y all Z 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_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),Z))))) # label(fact_205_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 280 (all X_a (semilattice_sup(X_a) -> (all X all Y all Z 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_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),Z))))) # label(fact_206_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 281 (all X_a (semilattice_sup(X_a) -> (all A_3 all B_2 all C_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_sup_sup(X_a),A_3),B_2)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_2),C_1))))) # label(fact_207_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 282 (all X_a (lattice(X_a) -> (all X all Y all 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),Y)),Z) = 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_sup_sup(X_a),Y),Z))))) # label(fact_208_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 283 (all X_a (semilattice_sup(X_a) -> (all X all Y all 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),Y)),Z) = 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_sup_sup(X_a),Y),Z))))) # label(fact_209_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 284 (all X_a (lattice(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)))))) # label(fact_210_inf__sup__ord_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 285 (all X_a (semilattice_sup(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)))))) # label(fact_211_sup__ge1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 286 (all X_a (lattice(X_a) -> (all Y all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)))))) # label(fact_212_inf__sup__ord_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 287 (all X_a (semilattice_sup(X_a) -> (all Y all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)))))) # label(fact_213_sup__ge2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 288 (all X_a (semilattice_sup(X_a) -> (all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2),Y_2) = ti(X_a,Y_2))))) # label(fact_214_le__iff__sup) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 289 (all X_a (semilattice_sup(X_a) -> (all X_2 all Y_2 all Z_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2),Y_2)),Z_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),Z_2)))))) # label(fact_215_le__sup__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 290 (all X_a (semilattice_sup(X_a) -> (all B_2 all X all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),B_2))))))) # label(fact_216_le__supI1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 291 (all X_a (semilattice_sup(X_a) -> (all A_3 all X all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),B_2))))))) # label(fact_217_le__supI2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 292 (all X_a (semilattice_sup(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y) = ti(X_a,Y))))) # label(fact_218_sup__absorb2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 293 (all X_a (semilattice_sup(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y) = ti(X_a,X))))) # label(fact_219_sup__absorb1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 294 (all X_a (semilattice_sup(X_a) -> (all B_2 all A_3 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),B_2)),X))))))) # label(fact_220_le__supI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 295 (all X_a (semilattice_sup(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)),X))))))) # label(fact_221_sup__least) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 296 (all X_a (semilattice_sup(X_a) -> (all B_2 all D all A_3 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),B_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),C_1),D)))))))) # label(fact_222_sup__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 297 (all X_a (semilattice_sup(X_a) -> (all A_3 all B_2 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),B_2)),X)) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),X)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),X))))))) # label(fact_223_le__supE) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 298 (all X_a (bounded_lattice_bot(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),bot_bot(X_a)),X) = ti(X_a,X)))) # label(fact_224_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 299 (all X_a (bounded_lattice_bot(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),bot_bot(X_a)) = ti(X_a,X)))) # label(fact_225_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 300 (all X_a all X_2 all P_1 all A_1 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(option(X_a),fun(X_a,bool),set(X_a),A_1))) -> hBOOL(hAPP(X_a,bool,P_1,X_1)))) -> (ti(option(X_a),A_1) = hAPP(X_a,option(X_a),some(X_a),X_2) -> hBOOL(hAPP(X_a,bool,P_1,X_2))))) # label(fact_226_ospec) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 301 (all X_a all B_1 all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_a,bool),X_a,Fa,A_1)),hAPP(fun(X_a,bool),X_a,Fa,B_1)))))))) # label(fact_227_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 302 (all X_a all B_1 all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_a,bool),X_a,Fa,B_1)),hAPP(fun(X_a,bool),X_a,Fa,A_1)) = hAPP(fun(X_a,bool),X_a,Fa,A_1)))))) # label(fact_228_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 303 (all X_a all G_2 all P_1 hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),P_1),skip),P_1)),bot_bot(fun(hoare_2118899576triple(X_a),bool)))))) # label(fact_229_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 304 (all X_a all X_2 all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),hAPP(fun(X_a,bool),X_a,Fa,A_1)))))) # label(fact_230_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 305 (all X_a all P_1 all Fa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa)) -> (ti(fun(X_a,bool),Fa) != bot_bot(fun(X_a,bool)) -> ((all X_1 hBOOL(hAPP(fun(X_a,bool),bool,P_1,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),bot_bot(fun(X_a,bool)))))) -> ((all X_1 all F_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),F_2)) -> (ti(fun(X_a,bool),F_2) != bot_bot(fun(X_a,bool)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),F_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,P_1,F_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,P_1,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),F_2)))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,P_1,Fa))))))) # label(fact_231_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 306 (all X_a all G_2 all P_1 all B all C hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),hAPP(fun(state,bool),fun(X_a,fun(state,bool)),hAPP(fun(X_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(X_a,fun(state,bool))),combc(X_a,fun(state,bool),fun(state,bool)),hAPP(fun(X_a,fun(state,fun(bool,bool))),fun(X_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(X_a,fun(state,fun(bool,bool))),fun(X_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),X_a),combs(state,bool,bool)),hAPP(fun(X_a,fun(state,bool)),fun(X_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X_a,fun(state,bool)),fun(X_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),P_1))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),B))),hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B),C)),P_1)),bot_bot(fun(hoare_2118899576triple(X_a),bool)))))) # label(fact_232_LoopF) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 307 (all X_a all D_1 all R_1 all G_2 all P_1 all C all Q_2 (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),P_1),C),Q_2)),bot_bot(fun(hoare_2118899576triple(X_a),bool))))) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),Q_2),D_1),R_1)),bot_bot(fun(hoare_2118899576triple(X_a),bool))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),P_1),hAPP(com,com,hAPP(com,fun(com,com),semi,C),D_1)),R_1)),bot_bot(fun(hoare_2118899576triple(X_a),bool)))))))) # label(fact_233_Comp) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 308 (all B all C (hBOOL(hAPP(com,bool,wt,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B),C))) -> hBOOL(hAPP(com,bool,wt,C)))) # label(fact_234_WTs__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 309 (all C1 all C2 (hBOOL(hAPP(com,bool,wt,hAPP(com,com,hAPP(com,fun(com,com),semi,C1),C2))) -> -(hBOOL(hAPP(com,bool,wt,C1)) -> -hBOOL(hAPP(com,bool,wt,C2))))) # label(fact_235_WTs__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 310 (all X_a all X_2 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F),Fa)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),X_2) = ti(X_a,X_2))) # label(fact_236_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 311 (all Com1_3 all Com2_3 skip != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_3),Com2_3)) # label(fact_237_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 312 (all Fun_1 all Com_2 skip != hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_2)) # label(fact_238_com_Osimps_I16_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 313 (all Com1_3 all Com2_3 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_3),Com2_3) != skip) # label(fact_239_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 314 (all Fun_1 all Com_2 hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_2) != skip) # label(fact_240_com_Osimps_I17_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 315 (all Com1_2 all Com2_2 all Fun_1 all Com_2 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2) != hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_2)) # label(fact_241_com_Osimps_I46_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 316 (all Fun_1 all Com_2 all Com1_2 all Com2_2 hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_2) != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2)) # label(fact_242_com_Osimps_I47_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 317 (all Com1_2 all Com2_2 all Com1_1 all Com2_1 (hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2) = hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1) <-> Com1_2 = Com1_1 & Com2_2 = Com2_1)) # label(fact_243_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 318 (all Fun all Com_1 all Fun_1 all Com_2 (hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com_1) = hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_2) <-> Fun = Fun_1 & Com_1 = Com_2)) # label(fact_244_com_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 319 (all Pname_1 all Fun all Com_1 hAPP(pname,com,body_1,Pname_1) != hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com_1)) # label(fact_245_com_Osimps_I59_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 320 (all Fun all Com_1 all Pname_1 hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com_1) != hAPP(pname,com,body_1,Pname_1)) # label(fact_246_com_Osimps_I58_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 321 (all B all C (hBOOL(hAPP(com,bool,wt,C)) -> hBOOL(hAPP(com,bool,wt,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B),C))))) # label(fact_247_While) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 322 (all Pname all Com1 all Com2 hAPP(pname,com,body_1,Pname) != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2)) # label(fact_248_com_Osimps_I49_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 323 (all Com1 all Com2 all Pname hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2) != hAPP(pname,com,body_1,Pname)) # label(fact_249_com_Osimps_I48_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 324 (all C1 all C0 (hBOOL(hAPP(com,bool,wt,C0)) -> (hBOOL(hAPP(com,bool,wt,C1)) -> hBOOL(hAPP(com,bool,wt,hAPP(com,com,hAPP(com,fun(com,com),semi,C0),C1)))))) # label(fact_250_WT_OSemi) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 325 (all Pname skip != hAPP(pname,com,body_1,Pname)) # label(fact_251_com_Osimps_I18_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 326 (all Pname hAPP(pname,com,body_1,Pname) != skip) # label(fact_252_com_Osimps_I19_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 327 (all X_a all X_2 all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),hAPP(fun(X_a,bool),X_a,Fa,A_1)) = hAPP(fun(X_a,bool),X_a,Fa,A_1))))) # label(fact_254_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.31 328 (all X_a all N all H all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F),Fa)) -> ((all X_1 all Y_1 hAPP(X_a,X_a,H,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_1),Y_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_a,X_a,H,X_1)),hAPP(X_a,X_a,H,Y_1))) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),N)) -> (ti(fun(X_a,bool),N) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,H,hAPP(fun(X_a,bool),X_a,Fa,N)) = hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),H),N))))))) # label(fact_255_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 329 (all X_a all X_4 hAPP(fun(X_a,bool),X_a,the_elem(X_a),X_4) = hAPP(fun(X_a,bool),X_a,the_1(X_a),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,fun(X_a,bool)),fun(X_a,bool)),combb(fun(X_a,bool),bool,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),fequal(fun(X_a,bool)),X_4)),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(X_a,fun(X_a,bool))),combc(X_a,fun(X_a,bool),fun(X_a,bool)),insert(X_a)),bot_bot(fun(X_a,bool)))))) # label(fact_256_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 330 (all X_a all X_2 all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),hAPP(fun(X_a,bool),X_a,Fa,A_1))))))) # label(fact_257_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 331 (all X_a all Y_2 -(all Fun1 all Com all Fun2 Y_2 != hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),Fun1),Com),Fun2))) # label(fact_258_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 332 (all X_b all X_a all B_1 all A_1 all F all Z_2 all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z_2),G),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1)) -> hAPP(fun(X_b,bool),X_a,Fa,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_1),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,Fa,A_1)),hAPP(fun(X_b,bool),X_a,Fa,B_1)))))) # label(fact_259_folding__image__simple__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 333 (all X_b all X_a all B_1 all A_1 all F all Z_2 all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z_2),G),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_1),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,Fa,B_1)),hAPP(fun(X_b,bool),X_a,Fa,A_1)) = hAPP(fun(X_b,bool),X_a,Fa,A_1))))) # label(fact_260_folding__image__simple__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 334 (all X_b all X_a all F1 all F2 all A_2 hAPP(option(X_b),X_a,hAPP(fun(X_b,X_a),fun(option(X_b),X_a),hAPP(X_a,fun(fun(X_b,X_a),fun(option(X_b),X_a)),option_rec(X_a,X_b),F1),F2),hAPP(X_b,option(X_b),some(X_b),A_2)) = hAPP(X_b,X_a,F2,A_2)) # label(fact_261_option_Orecs_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 335 (all X_b all X_a all X_2 all F all Z_2 all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z_2),G),Fa)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),X_2) = ti(X_a,X_2))) # label(fact_262_folding__image__simple__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 336 (all X_b all X_a all X_2 all A_1 all F all Z_2 all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z_2),G),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_b,X_a,G,X_2)),hAPP(fun(X_b,bool),X_a,Fa,A_1)) = hAPP(fun(X_b,bool),X_a,Fa,A_1))))) # label(fact_263_folding__image__simple__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 337 (all X_a all X_2 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),Fa)) -> hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = ti(X_a,X_2))) # label(fact_264_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 338 (all X_b all X_a all X_2 all A_1 all F all Z_2 all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z_2),G),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> hAPP(fun(X_b,bool),X_a,Fa,hAPP(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_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_b,X_a,G,X_2)),hAPP(fun(X_b,bool),X_a,Fa,A_1))))) # label(fact_265_folding__image__simple__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 339 (all X_a all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> ((all X_1 all Y_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_1),Y_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_1),bot_bot(fun(X_a,bool))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(fun(X_a,bool),X_a,Fa,A_1)),A_1))))))) # label(fact_266_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 340 (all X_a all X_2 hAPP(fun(X_a,bool),X_a,the_1(X_a),hAPP(X_a,fun(X_a,bool),fequal(X_a),X_2)) = ti(X_a,X_2)) # label(fact_267_the__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 341 (all X_a all A_2 hAPP(fun(X_a,bool),X_a,the_1(X_a),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2)) = ti(X_a,A_2)) # label(fact_268_the__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 342 (all X_a all X_2 all Y_2 all P_1 ((hBOOL(P_1) -> ti(X_a,X_2) = hAPP(fun(X_a,bool),X_a,the_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),hAPP(bool,fun(bool,bool),fimplies,P_1)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_2)))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,P_1))),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),Y_2))))) & (-hBOOL(P_1) -> ti(X_a,Y_2) = hAPP(fun(X_a,bool),X_a,the_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),hAPP(bool,fun(bool,bool),fimplies,P_1)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_2)))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,P_1))),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),Y_2))))))) # label(fact_269_If__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 343 (all X_b all X_a all F all G all M all N (ti(fun(X_a,bool),M) = ti(fun(X_a,bool),N) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),N)) -> hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,G,X_1))) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),M) = hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),G),N)))) # label(fact_270_image__cong) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 344 (all X_a all Q_2 all P_1 ((all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(hAPP(X_a,bool,Q_2,X_1)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_2))))) # label(fact_271_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 345 (all X_a all Q_2 all P_1 ((all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(hAPP(X_a,bool,Q_2,X_1)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),P_1),Q_2)))) # label(fact_272_predicate1I) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 346 (all X_a all P_1 all A_2 (hBOOL(hAPP(X_a,bool,P_1,A_2)) -> ((all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> ti(X_a,X_1) = ti(X_a,A_2))) -> hAPP(fun(X_a,bool),X_a,the_1(X_a),P_1) = ti(X_a,A_2)))) # label(fact_273_the__equality) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 347 (all X_a all P_1 all A_2 (hBOOL(hAPP(X_a,bool,P_1,A_2)) -> ((all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> ti(X_a,X_1) = ti(X_a,A_2))) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,the_1(X_a),P_1)))))) # label(fact_274_theI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 348 (all X_a all A_2 all P_1 ((exists X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) & (all Y_1 (hBOOL(hAPP(X_a,bool,P_1,Y_1)) -> ti(X_a,Y_1) = ti(X_a,X_1))))) -> (hBOOL(hAPP(X_a,bool,P_1,A_2)) -> hAPP(fun(X_a,bool),X_a,the_1(X_a),P_1) = ti(X_a,A_2)))) # label(fact_275_the1__equality) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 349 (all X_a all P_1 ((exists X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) & (all Y_1 (hBOOL(hAPP(X_a,bool,P_1,Y_1)) -> ti(X_a,Y_1) = ti(X_a,X_1))))) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,the_1(X_a),P_1))))) # label(fact_276_theI_H) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 350 (all X_a all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1)) -> (exists B_3 (ti(fun(X_a,bool),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),B_3) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),B_3)))))) # label(fact_277_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 351 (all X_a all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> -(all B_3 (ti(fun(X_a,bool),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),B_3) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B_3)))))) # label(fact_278_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 352 (all X_a all A_1 ((all Y_1 -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1))) -> ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)))) # label(fact_279_equals0I) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 353 (all G_2 all C (hBOOL(hoare_511481251gleton) -> (hBOOL(hAPP(fun(hoare_2118899576triple(state),bool),bool,hAPP(fun(hoare_2118899576triple(state),bool),fun(fun(hoare_2118899576triple(state),bool),bool),hoare_1301688828derivs(state),G_2),hAPP(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool),hAPP(hoare_2118899576triple(state),fun(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool)),insert(hoare_2118899576triple(state)),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),hAPP(fun(state,fun(state,fun(state,bool))),fun(state,fun(state,bool)),hAPP(fun(fun(state,fun(state,bool)),fun(state,bool)),fun(fun(state,fun(state,fun(state,bool))),fun(state,fun(state,bool))),combb(fun(state,fun(state,bool)),fun(state,bool),state),hAPP(fun(fun(state,bool),bool),fun(fun(state,fun(state,bool)),fun(state,bool)),combb(fun(state,bool),bool,state),fAll(state))),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,fun(state,bool))),hAPP(fun(fun(state,bool),fun(state,fun(state,bool))),fun(fun(state,fun(state,bool)),fun(state,fun(state,fun(state,bool)))),combb(fun(state,bool),fun(state,fun(state,bool)),state),hAPP(fun(state,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(state,fun(state,bool))),combc(state,fun(state,bool),fun(state,bool)),hAPP(fun(state,fun(state,fun(bool,bool))),fun(state,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(state,fun(state,fun(bool,bool))),fun(state,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),state),combs(state,bool,bool)),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(state,fun(state,bool)),fun(state,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),state),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fimplies)),hAPP(com,fun(state,fun(state,bool)),evalc,C))))),fequal(state)))),C),fequal(state))),bot_bot(fun(hoare_2118899576triple(state),bool))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(state),bool),bool,hAPP(fun(hoare_2118899576triple(state),bool),fun(fun(hoare_2118899576triple(state),bool),bool),hoare_1301688828derivs(state),G_2),hAPP(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool),hAPP(hoare_2118899576triple(state),fun(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool)),insert(hoare_2118899576triple(state)),hAPP(com,hoare_2118899576triple(state),hoare_Mirabelle_MGT,C)),bot_bot(fun(hoare_2118899576triple(state),bool)))))))) # label(fact_280_MGT__alternD) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 354 (all X_b all X_a (order(X_a) & ord(X_b) -> (all C all F all B all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,B)),A_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C),B)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Y_1)),hAPP(X_b,X_a,F,X_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,C)),A_2)))))))) # label(fact_281_xt2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 355 (all X_a (order(X_a) -> (all C all A_2 all F all B (ti(X_a,A_2) = hAPP(X_a,X_a,F,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),B)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,F,Y_1)),hAPP(X_a,X_a,F,X_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,F,C)),A_2)))))))) # label(fact_282_xt1_I15_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 356 (all X_a all X_b (order(X_b) & order(X_a) -> (all C all A_2 all F all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_b,X_a,F,B))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B),C)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_1)),hAPP(X_b,X_a,F,Y_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_b,X_a,F,C))))))))) # label(fact_283_order__subst1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 357 (all X_a all X_b (ord(X_b) & ord(X_a) -> (all C all A_2 all F all B (ti(X_a,A_2) = hAPP(X_b,X_a,F,B) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B),C)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_1)),hAPP(X_b,X_a,F,Y_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_b,X_a,F,C))))))))) # label(fact_284_ord__eq__le__subst) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 358 (all G_2 all C (hBOOL(hAPP(fun(hoare_2118899576triple(state),bool),bool,hAPP(fun(hoare_2118899576triple(state),bool),fun(fun(hoare_2118899576triple(state),bool),bool),hoare_1301688828derivs(state),G_2),hAPP(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool),hAPP(hoare_2118899576triple(state),fun(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool)),insert(hoare_2118899576triple(state)),hAPP(com,hoare_2118899576triple(state),hoare_Mirabelle_MGT,C)),bot_bot(fun(hoare_2118899576triple(state),bool))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(state),bool),bool,hAPP(fun(hoare_2118899576triple(state),bool),fun(fun(hoare_2118899576triple(state),bool),bool),hoare_1301688828derivs(state),G_2),hAPP(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool),hAPP(hoare_2118899576triple(state),fun(fun(hoare_2118899576triple(state),bool),fun(hoare_2118899576triple(state),bool)),insert(hoare_2118899576triple(state)),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),hAPP(fun(state,fun(state,fun(state,bool))),fun(state,fun(state,bool)),hAPP(fun(fun(state,fun(state,bool)),fun(state,bool)),fun(fun(state,fun(state,fun(state,bool))),fun(state,fun(state,bool))),combb(fun(state,fun(state,bool)),fun(state,bool),state),hAPP(fun(fun(state,bool),bool),fun(fun(state,fun(state,bool)),fun(state,bool)),combb(fun(state,bool),bool,state),fAll(state))),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,fun(state,bool))),hAPP(fun(fun(state,bool),fun(state,fun(state,bool))),fun(fun(state,fun(state,bool)),fun(state,fun(state,fun(state,bool)))),combb(fun(state,bool),fun(state,fun(state,bool)),state),hAPP(fun(state,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(state,fun(state,bool))),combc(state,fun(state,bool),fun(state,bool)),hAPP(fun(state,fun(state,fun(bool,bool))),fun(state,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(state,fun(state,fun(bool,bool))),fun(state,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),state),combs(state,bool,bool)),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(state,fun(state,bool)),fun(state,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),state),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fimplies)),hAPP(com,fun(state,fun(state,bool)),evalc,C))))),fequal(state)))),C),fequal(state))),bot_bot(fun(hoare_2118899576triple(state),bool))))))) # label(fact_285_MGT__alternI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 359 (all C hAPP(com,hoare_2118899576triple(state),hoare_Mirabelle_MGT,C) = 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),fequal(state)),C),hAPP(com,fun(state,fun(state,bool)),evalc,C))) # label(fact_286_MGT__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 360 (all P all S_4 all S1_2 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(pname,com,body_1,P)),S_4),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,P))),S_4),S1_2)))) # label(fact_287_evalc__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 361 (all Pn all S0_1 all 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,Pn))),S0_1),S1_2)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(pname,com,body_1,Pn)),S0_1),S1_2)))) # label(fact_288_evalc_OBody) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 362 (all S_4 all T_4 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,skip),S_4),T_4)) -> T_4 = S_4)) # label(fact_289_evalc__elim__cases_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 363 (all S_4 hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,skip),S_4),S_4))) # label(fact_290_evalc_OSkip) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 364 (all C1 all S2_1 all C0 all S0_1 all S1_2 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C0),S0_1),S1_2)) -> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1),S1_2),S2_1)) -> 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),C1)),S0_1),S2_1))))) # label(fact_291_evalc_OSemi) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 365 (all S2 all C all S1_1 all B all S0 (hBOOL(hAPP(state,bool,B,S0)) -> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C),S0),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),C)),S1_1),S2)) -> 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),C)),S0),S2)))))) # label(fact_292_evalc_OWhileTrue) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 366 (all C all B all S_3 (-hBOOL(hAPP(state,bool,B,S_3)) -> 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),C)),S_3),S_3)))) # label(fact_293_evalc_OWhileFalse) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 367 (all U_1 all C_1 all S_4 all T_4 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S_4),T_4)) -> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S_4),U_1)) -> U_1 = T_4))) # label(fact_294_com__det) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 368 (all C1 all C2 all S_4 all 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),semi,C1),C2)),S_4),T_4)) -> -(all S1 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1),S_4),S1)) -> -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C2),S1),T_4)))))) # label(fact_295_evalc__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 369 (all B all C all S_3 all T_3 (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),C)),S_3),T_3)) -> ((T_3 = S_3 -> hBOOL(hAPP(state,bool,B,S_3))) -> -(hBOOL(hAPP(state,bool,B,S_3)) -> (all S1 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C),S_3),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),C)),S1),T_3)))))))) # label(fact_296_evalc__WHILE__case) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 370 (all X_a all X_b (order(X_b) & order(X_a) -> (all F all C all A_2 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,B)),C)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,F,Y_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,A_2)),C)))))))) # label(fact_297_order__subst2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 371 (all X_a all X_b (ord(X_b) & ord(X_a) -> (all F all C all A_2 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B)) -> (hAPP(X_a,X_b,F,B) = ti(X_b,C) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,F,Y_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,A_2)),C)))))))) # label(fact_298_ord__le__eq__subst) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 372 (all X_a (order(X_a) -> (all F all C all B all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_2)) -> (hAPP(X_a,X_a,F,B) = ti(X_a,C) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,F,Y_1)),hAPP(X_a,X_a,F,X_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),hAPP(X_a,X_a,F,A_2))))))))) # label(fact_299_xt1_I16_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 373 (all X_b all X_a (order(X_a) & order(X_b) -> (all C all F all B all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C),hAPP(X_a,X_b,F,B))) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Y_1)),hAPP(X_a,X_b,F,X_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C),hAPP(X_a,X_b,F,A_2))))))))) # label(fact_300_xt3) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 374 (all X_a all B_1 all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1))),hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_a,bool),X_a,Fa,A_1)),hAPP(fun(X_a,bool),X_a,Fa,B_1))))))) # label(fact_301_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 375 (all X_a all B_1 all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_a,bool),X_a,Fa,A_1)),hAPP(fun(X_a,bool),X_a,Fa,B_1))))))))) # label(fact_302_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 376 (all X_a all X_2 all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = ti(X_a,X_2)) & (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))))))) # label(fact_303_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 377 (all X_a all X_2 all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,Fa,A_1) = ti(X_a,X_2)) & (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,Fa,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))))))))) # label(fact_304_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 378 (all X_b all X -hBOOL(hAPP(option(X_b),bool,is_none(X_b),hAPP(X_b,option(X_b),some(X_b),X)))) # label(fact_305_is__none__code_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 379 (all X_a all Q_2 all G_2 all C all P_1 ((all Z_3 all S_1 (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),P_1,Z_3),S_1)) -> (exists P_2 exists Q_3 (hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),P_2),C),Q_3)),bot_bot(fun(hoare_2118899576triple(X_a),bool))))) & (all S_2 ((all Z_4 (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),P_2,Z_4),S_1)) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Q_3,Z_4),S_2)))) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Q_2,Z_3),S_2)))))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_a),bool),bool,hAPP(fun(hoare_2118899576triple(X_a),bool),fun(fun(hoare_2118899576triple(X_a),bool),bool),hoare_1301688828derivs(X_a),G_2),hAPP(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool),hAPP(hoare_2118899576triple(X_a),fun(fun(hoare_2118899576triple(X_a),bool),fun(hoare_2118899576triple(X_a),bool)),insert(hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_2118899576triple(X_a))),hoare_759811442triple(X_a),P_1),C),Q_2)),bot_bot(fun(hoare_2118899576triple(X_a),bool))))))) # label(fact_306_conseq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 380 (all X_a all A_1 all B_1 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1),X_2)) -> -(hBOOL(hAPP(X_a,bool,A_1,X_2)) -> -hBOOL(hAPP(X_a,bool,B_1,X_2))))) # label(fact_307_inf1E) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 381 (all X_a all B_1 all A_1 all X_2 (hBOOL(hAPP(X_a,bool,A_1,X_2)) -> (hBOOL(hAPP(X_a,bool,B_1,X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1),X_2))))) # label(fact_308_inf1I) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 382 (all X_a all C all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1))) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1)) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),B_1))))) # label(fact_309_IntE) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 383 (all X_a all B_1 all C all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)))))) # label(fact_310_IntI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 384 (all X_a all C all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1))) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),B_1))))) # label(fact_311_DiffE) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 385 (all X_a all B_1 all C all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1)))))) # label(fact_312_DiffI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 386 (all X_a all G_2 all Fa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa)) | hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),G_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),Fa),G_2))))) # label(fact_313_finite__Int) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 387 (all X_a all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1))))) # label(fact_314_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 388 (all X_a all A_1 all B_1 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1),X_2)) -> hBOOL(hAPP(X_a,bool,B_1,X_2)))) # label(fact_315_inf1D2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 389 (all X_a all A_1 all B_1 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1),X_2)) -> hBOOL(hAPP(X_a,bool,A_1,X_2)))) # label(fact_316_inf1D1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 390 (all X_a all R_1 all S all X_1 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)),X_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),R_1),S))))) # label(fact_317_inf__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 391 (all X_a all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_1),A_1)) = bot_bot(fun(X_a,bool))) # label(fact_318_Diff__disjoint) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 392 (all X_a all A_1 all B_1 (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1) = ti(fun(X_a,bool),A_1))) # label(fact_319_Diff__triv) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 393 (all X_a all C all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),B_1)))) # label(fact_320_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 394 (all X_a all C all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),B_1)))) # label(fact_321_IntD2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 395 (all X_a all C all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1)))) # label(fact_322_IntD1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 396 (all X_a all C all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1)))) # label(fact_323_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 397 (all X_a all A_1 all C_2 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),C_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B_1),C_2)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),C_2)),B_1)) # label(fact_324_Diff__Int2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 398 (all X_a all A_1 all B_1 all C_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1)),C_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),C_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B_1),C_2))) # label(fact_325_Diff__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 399 (all X_a all A_1 all B_1 all C_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)),C_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B_1),C_2))) # label(fact_326_Int__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 400 (all X_a all A_1 all B_1 all C_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)),C_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_1),C_2))) # label(fact_327_Int__Diff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 401 (all X_a all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1)),B_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1)) # label(fact_328_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 402 (all X_a all C_2 all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),C_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),C_2),A_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),C_2),B_1))) # label(fact_329_Diff__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 403 (all X_a all C all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),B_1)))) # label(fact_330_Int__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 404 (all X_a all C all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1)) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),B_1)))) # label(fact_331_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 405 (all X_a all A_1 all B_1 all C_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B_1),C_2)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),C_2))) # label(fact_332_Int__left__commute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 406 (all X_a all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)) # label(fact_333_Int__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 407 (all X_a all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B_1),A_1)) # label(fact_334_Int__commute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 408 (all X_a all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_1)))) # label(fact_335_Int__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 409 (all X_a all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_1))))) # label(fact_336_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 410 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),A_1) = ti(fun(X_a,bool),A_1)) # label(fact_337_Int__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 411 (all X_a all X_2 all A_1 all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) & hBOOL(hAPP(X_a,bool,P_1,X_2)))) # label(fact_338_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 412 (all X_a all P_1 all Q_2 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),P_1)),Q_2)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_2))) # label(fact_339_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 413 (all X_b all X_a (lattice(X_a) -> (all F all G all X_2 hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),semilattice_inf_inf(fun(X_b,X_a)),F),G),X_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,G,X_2))))) # label(fact_340_inf__apply) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 414 (all X_b all X_a (minus(X_a) -> (all A_1 all B_1 all X_2 hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),minus_minus(fun(X_b,X_a)),A_1),B_1),X_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_b,X_a,A_1,X_2)),hAPP(X_b,X_a,B_1,X_2))))) # label(fact_341_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 415 (all X_a (semilattice_inf(X_a) -> (all X all Y all 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),Y)),Z) = 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_inf_inf(X_a),Y),Z))))) # label(fact_342_inf__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 416 (all X_a (lattice(X_a) -> (all X all Y all 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),Y)),Z) = 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_inf_inf(X_a),Y),Z))))) # label(fact_343_inf__sup__aci_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 417 (all X_a (semilattice_inf(X_a) -> (all A_3 all B_2 all C_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_inf_inf(X_a),A_3),B_2)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_2),C_1))))) # label(fact_344_inf_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 418 (all X_a (semilattice_inf(X_a) -> (all X all Y all Z 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_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),Z))))) # label(fact_345_inf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 419 (all X_a (lattice(X_a) -> (all X all Y all Z 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_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),Z))))) # label(fact_346_inf__sup__aci_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 420 (all X_a (semilattice_inf(X_a) -> (all B_2 all A_3 all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_3),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_2),C_1))))) # label(fact_347_inf_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 421 (all X_a (semilattice_inf(X_a) -> (all X all Y 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_inf_inf(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)))) # label(fact_348_inf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 422 (all X_a (lattice(X_a) -> (all X all Y 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_inf_inf(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)))) # label(fact_349_inf__sup__aci_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 423 (all X_a (semilattice_inf(X_a) -> (all A_3 all B_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_3),B_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_3),B_2)))) # label(fact_350_inf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 424 (all X_a (semilattice_inf(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),X)))) # label(fact_351_inf__commute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 425 (all X_a (lattice(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),X)))) # label(fact_352_inf__sup__aci_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 426 (all X_a (semilattice_inf(X_a) -> (all A_3 all B_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_3),B_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_2),A_3)))) # label(fact_353_inf_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 427 (all X_a all X_b (lattice(X_b) -> (all F all G all X_1 hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),semilattice_inf_inf(fun(X_a,X_b)),F),G),X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))) # label(fact_354_inf__fun__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 428 (all X_a all X_b (minus(X_b) -> (all A_1 all B_1 all X_1 hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),minus_minus(fun(X_a,X_b)),A_1),B_1),X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,A_1,X_1)),hAPP(X_a,X_b,B_1,X_1))))) # label(fact_355_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 429 (all X_a (semilattice_inf(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),X) = ti(X_a,X)))) # label(fact_356_inf__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 430 (all X_a (semilattice_inf(X_a) -> (all A_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_3),A_3) = ti(X_a,A_3)))) # label(fact_357_inf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 431 (all X_a all A_1 all B_1 all C_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B_1),C_2)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),C_2))) # label(fact_358_Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 432 (all X_a all A_1 all B_1 all C_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B_1),C_2)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),C_2))) # label(fact_359_Diff__Un) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 433 (all X_a all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)) = ti(fun(X_a,bool),A_1)) # label(fact_360_Un__Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 434 (all X_a (lattice(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),X))))) # label(fact_361_inf__sup__ord_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 435 (all X_a (semilattice_inf(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),X))))) # label(fact_362_inf__le1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 436 (all X_a (lattice(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),Y))))) # label(fact_363_inf__sup__ord_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 437 (all X_a (semilattice_inf(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),Y))))) # label(fact_364_inf__le2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 438 (all X_a (semilattice_inf(X_a) -> (all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_2),Y_2) = ti(X_a,X_2))))) # label(fact_365_le__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 439 (all X_a (semilattice_inf(X_a) -> (all X_2 all Y_2 all Z_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y_2),Z_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z_2)))))) # label(fact_366_le__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 440 (all X_a (semilattice_inf(X_a) -> (all B_2 all A_3 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_3),B_2)),X)))))) # label(fact_367_le__infI1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 441 (all X_a (semilattice_inf(X_a) -> (all A_3 all B_2 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_3),B_2)),X)))))) # label(fact_368_le__infI2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 442 (all X_a (semilattice_inf(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y) = ti(X_a,X))))) # label(fact_369_inf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 443 (all X_a (semilattice_inf(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y) = ti(X_a,Y))))) # label(fact_370_inf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.32 444 (all X_a (semilattice_inf(X_a) -> (all B_2 all X all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_3),B_2)))))))) # label(fact_371_le__infI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 445 (all X_a (semilattice_inf(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)))))))) # label(fact_372_inf__greatest) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 446 (all X_a (semilattice_inf(X_a) -> (all B_2 all D all A_3 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_3),B_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),C_1),D)))))))) # label(fact_373_inf__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 447 (all X_a (semilattice_inf(X_a) -> (all X all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_3),B_2))) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_3)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_2))))))) # label(fact_374_le__infE) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 448 (all X_a (bounded_lattice_bot(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),bot_bot(X_a)) = bot_bot(X_a)))) # label(fact_375_inf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 449 (all X_a (bounded_lattice_bot(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),bot_bot(X_a)),X) = bot_bot(X_a)))) # label(fact_376_inf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 450 (all X_a (lattice(X_a) -> (all X all Y 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),X),Y)) = ti(X_a,X)))) # label(fact_377_inf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 451 (all X_a (lattice(X_a) -> (all X all Y 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),X),Y)) = ti(X_a,X)))) # label(fact_378_sup__inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 452 (all X_a (distrib_lattice(X_a) -> (all X all Y all Z 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),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),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Z))))) # label(fact_379_inf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 453 (all X_a (distrib_lattice(X_a) -> (all X all Y all Z 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),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),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Z))))) # label(fact_380_sup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 454 (all X_a (distrib_lattice(X_a) -> (all Y all Z all X 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) = 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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Z),X))))) # label(fact_381_inf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 455 (all X_a (distrib_lattice(X_a) -> (all Y all Z all X 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) = 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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Z),X))))) # label(fact_382_sup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 456 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),A_1) = bot_bot(fun(X_a,bool))) # label(fact_383_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 457 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),bot_bot(fun(X_a,bool))) = ti(fun(X_a,bool),A_1)) # label(fact_384_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 458 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),bot_bot(fun(X_a,bool))),A_1) = bot_bot(fun(X_a,bool))) # label(fact_385_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 459 (all X_a all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1))))) # label(fact_386_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 460 (all X_a all A_1 all X_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)),B_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1))) # label(fact_387_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 461 (all X_a all A_1 all X_2 all B_1 ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)),B_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)),B_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1))))) # label(fact_388_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 462 (all X_a all A_1 all B_1 (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1) = bot_bot(fun(X_a,bool)) <-> (all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),B_1)) -> ti(X_a,X_1) != ti(X_a,Xa))))))) # label(fact_389_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 463 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),bot_bot(fun(X_a,bool))) = bot_bot(fun(X_a,bool))) # label(fact_390_Int__empty__right) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 464 (all X_a all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),bot_bot(fun(X_a,bool))),B_1) = bot_bot(fun(X_a,bool))) # label(fact_391_Int__empty__left) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 465 (all X_a all C_2 all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),C_2)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),C_2),A_1)) = ti(fun(X_a,bool),A_1)))) # label(fact_392_double__diff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 466 (all X_a all D_2 all B_1 all A_1 all C_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),D_2),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),C_2),D_2)))))) # label(fact_393_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 467 (all X_a all A_1 all B_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1)),A_1))) # label(fact_394_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 468 (all X_a all A_1 all B_1 all C_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)),C_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),C_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_1),C_2))) # label(fact_395_Un__Diff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 469 (all X_a all B_1 all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_1),A_1)),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B_1),A_1)) # label(fact_396_Un__Diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 470 (all X_a all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_1),A_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)) # label(fact_397_Un__Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 471 (all X_a all B_1 all A_2 all C_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),C_2)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),B_1)),C_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B_1),C_2)))) # label(fact_398_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 472 (all X_a all B_1 all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)))) # label(fact_399_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 473 (all X_a all B_1 all A_2 all C_2 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),C_2)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),B_1)),C_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B_1),C_2))) # label(fact_400_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 474 (all X_a all B_1 all A_2 all A_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1))) # label(fact_401_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 475 (all X_a all A_2 all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1))) # label(fact_402_insert__inter__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 476 (all X_a all B_1 all A_2 all C_2 ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),C_2)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),B_1)),C_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B_1),C_2))) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),C_2)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),B_1)),C_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B_1),C_2)))) # label(fact_403_Int__insert__left) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 477 (all X_a all B_1 all A_2 all A_1 ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1))) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)))) # label(fact_404_Int__insert__right) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 478 (all X_a all B_1 all D_2 all A_1 all C_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),D_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),C_2),D_2)))))) # label(fact_405_Int__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 479 (all X_a all B_1 all C_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),C_2),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),C_2),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),C_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)))))) # label(fact_406_Int__greatest) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 480 (all X_a all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1) = ti(fun(X_a,bool),B_1))) # label(fact_407_Int__absorb1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 481 (all X_a all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1) = ti(fun(X_a,bool),A_1))) # label(fact_408_Int__absorb2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 482 (all X_a all A_1 all B_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)),B_1))) # label(fact_409_Int__lower2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 483 (all X_a all A_1 all B_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)),A_1))) # label(fact_410_Int__lower1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 484 (all X_a all A_1 all B_1 all C_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B_1),C_2))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),C_2),A_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B_1),C_2))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),C_2),A_1))) # label(fact_411_Un__Int__crazy) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 485 (all X_a all B_1 all C_2 all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B_1),C_2)),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B_1),A_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),C_2),A_1))) # label(fact_412_Un__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 486 (all X_a all B_1 all C_2 all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B_1),C_2)),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B_1),A_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),C_2),A_1))) # label(fact_413_Int__Un__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 487 (all X_a all A_1 all B_1 all C_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B_1),C_2)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),C_2))) # label(fact_414_Un__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 488 (all X_a all A_1 all B_1 all C_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B_1),C_2)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),C_2))) # label(fact_415_Int__Un__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 489 (all X_a (lattice(X_a) -> (all X all Y all Z hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(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),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Z))),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),Z))))))) # label(fact_416_distrib__inf__le) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 490 (all X_a (lattice(X_a) -> (all X all Y all Z hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),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),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),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Z))))))) # label(fact_417_distrib__sup__le) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 491 (all X_a all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),bot_bot(fun(X_a,bool))))) = ti(fun(X_a,bool),A_1))) # label(fact_418_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 492 (all X_a all X_2 all A_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = ti(fun(X_a,bool),A_1))) # label(fact_419_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 493 (all X_a all A_2 all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),bot_bot(fun(X_a,bool))))) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1)) # label(fact_420_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 494 (all X_a all A_1 all A_2 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),bot_bot(fun(X_a,bool))))),B_1)) # label(fact_421_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 495 (all X_a all A_1 all A_2 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),bot_bot(fun(X_a,bool))))) # label(fact_422_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 496 (all X_a all A_1 all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),B_1)))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1))))) # label(fact_423_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 497 (all X_a all X_b all F all A_1 all B_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),B_1))),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),B_1))))) # label(fact_424_image__diff__subset) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 498 (all X_a all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_1),A_1)) = ti(fun(X_a,bool),B_1))) # label(fact_425_Diff__partition) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 499 (all X_a all A_1 all B_1 all C_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1)),C_2)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B_1),C_2))))) # label(fact_426_Diff__subset__conv) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 500 (all X_a all X_b all F all A_1 all B_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),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_1),B_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),B_1))))) # label(fact_427_image__Int__subset) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 501 (all X_a all A_1 all B_1 all C_2 (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)),C_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B_1),C_2)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),C_2),A_1)))) # label(fact_428_Un__Int__assoc__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 502 (all X_b all X_a all P_1 all F all G all S hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_b,fun(X_a,fun(X_a,X_a))),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combs(X_b,X_a,fun(X_a,X_a)),hAPP(fun(X_b,bool),fun(X_b,fun(X_a,fun(X_a,X_a))),hAPP(fun(bool,fun(X_a,fun(X_a,X_a))),fun(fun(X_b,bool),fun(X_b,fun(X_a,fun(X_a,X_a)))),combb(bool,fun(X_a,fun(X_a,X_a)),X_b),if(X_a)),P_1)),F)),G)),S) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),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),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),P_1)))),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),G),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),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),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),P_1)))))) # label(fact_429_if__image__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 503 (all X_a all X_b all P_1 all F all G hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),hAPP(fun(X_a,option(X_b)),fun(X_a,option(X_b)),hAPP(fun(X_a,fun(option(X_b),option(X_b))),fun(fun(X_a,option(X_b)),fun(X_a,option(X_b))),combs(X_a,option(X_b),option(X_b)),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),option(X_b))),hAPP(fun(X_a,fun(option(X_b),fun(option(X_b),option(X_b)))),fun(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),option(X_b)))),combs(X_a,option(X_b),fun(option(X_b),option(X_b))),hAPP(fun(X_a,bool),fun(X_a,fun(option(X_b),fun(option(X_b),option(X_b)))),hAPP(fun(bool,fun(option(X_b),fun(option(X_b),option(X_b)))),fun(fun(X_a,bool),fun(X_a,fun(option(X_b),fun(option(X_b),option(X_b))))),combb(bool,fun(option(X_b),fun(option(X_b),option(X_b))),X_a),if(option(X_b))),P_1)),F)),G)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),F)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),G)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),P_1))))) # label(fact_430_dom__if) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 504 (all X_a all A_1 all X_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),B_1)))))) # label(fact_431_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 505 (all X_a all A_1 all X_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),B_1))) <-> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))),B_1))) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1))))) # label(fact_432_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 506 (all X_a all P_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,P_1,A_1)) -> ((all A_4 all A_5 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_5)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_4),A_5)) -> (hBOOL(hAPP(fun(X_a,bool),bool,P_1,A_5)) -> hBOOL(hAPP(fun(X_a,bool),bool,P_1,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_5),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_4),bot_bot(fun(X_a,bool)))))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,P_1,bot_bot(fun(X_a,bool)))))))) # label(fact_433_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 507 (all X_a all X_b all F all G all A_1 hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b)))),override_on(X_a,option(X_b)),F),G),A_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),F)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),G)))))),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),G)))))) # label(fact_434_dom__override__on) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 508 (all X_a all Q_2 all P_1 all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(hAPP(X_a,bool,Q_2,X_1))))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B_1),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_2))))))) # label(fact_435_Int__Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 509 (all X_a (lattice(X_a) -> (all X all Y all Z ((all X_1 all Y_1 all Z_1 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_1),Z_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),X_1),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Z_1))) -> 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),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),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Z)))))) # label(fact_436_distrib__imp2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 510 (all X_a (lattice(X_a) -> (all X all Y all Z ((all X_1 all Y_1 all Z_1 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_1),Z_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),X_1),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Z_1))) -> 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),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),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Z)))))) # label(fact_437_distrib__imp1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 511 (all X_b all X_a all B_1 all A_1 all F all Z_2 all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z_2),G),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B_1) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_a,Fa,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_1),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,Fa,A_1)),hAPP(fun(X_b,bool),X_a,Fa,B_1))))))) # label(fact_438_folding__image__simple_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 512 (all X_b all X_a all F all Z_2 all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z_2),G),Fa)) -> hAPP(fun(X_b,bool),X_a,Fa,bot_bot(fun(X_b,bool))) = ti(X_a,Z_2))) # label(fact_439_folding__image__simple_Oempty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 513 (all X_b all X_a all X_2 all A_1 all F all Z_2 all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z_2),G),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> hAPP(fun(X_b,bool),X_a,Fa,hAPP(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_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_b,X_a,G,X_2)),hAPP(fun(X_b,bool),X_a,Fa,A_1)))))) # label(fact_440_folding__image__simple_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 514 (all X_b all X_a all B_1 all A_1 all F all Z_2 all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z_2),G),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,Fa,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_1),B_1))),hAPP(fun(X_b,bool),X_a,Fa,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_1),B_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,Fa,A_1)),hAPP(fun(X_b,bool),X_a,Fa,B_1)))))) # label(fact_441_folding__image__simple_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 515 (all X_b all X_a all X_2 all A_1 all F all Z_2 all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z_2),G),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> hAPP(fun(X_b,bool),X_a,Fa,hAPP(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_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_b,X_a,G,X_2)),hAPP(fun(X_b,bool),X_a,Fa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_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))))))))) # label(fact_442_folding__image__simple_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 516 (all X_b all X_a all X_2 all A_1 all F all Z_2 all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z_2),G),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> hAPP(fun(X_b,bool),X_a,Fa,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_b,X_a,G,X_2)),hAPP(fun(X_b,bool),X_a,Fa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_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)))))))))) # label(fact_443_folding__image__simple_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 517 (all X_b all X_a all B_1 all A_1 all F all Z_2 all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z_2),G),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1)) -> ((all X_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B_1))) -> hAPP(X_b,X_a,G,X_1) = ti(X_a,Z_2))) -> hAPP(fun(X_b,bool),X_a,Fa,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_1),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,Fa,A_1)),hAPP(fun(X_b,bool),X_a,Fa,B_1))))))) # label(fact_444_folding__image__simple_Ounion__inter__neutral) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 518 (all X_b all X_a all A_1 all F all Z_2 all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z_2),G),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> ((all X_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) -> hAPP(X_b,X_a,G,X_1) = ti(X_a,Z_2))) -> hAPP(fun(X_b,bool),X_a,Fa,A_1) = ti(X_a,Z_2))))) # label(fact_445_folding__image__simple_Oneutral) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 519 (all X_a all X_b all F all G hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b))),override_on(X_a,X_b),F),G),bot_bot(fun(X_a,bool))) = ti(fun(X_a,X_b),F)) # label(fact_446_override__on__emptyset) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 520 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B all C all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C),D_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D_1))))))) # label(fact_447_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 521 (all X_a (ab_group_add(X_a) -> (all A_2 all B all C all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C),D_1) -> (ti(X_a,A_2) = ti(X_a,B) <-> ti(X_a,C) = ti(X_a,D_1)))))) # label(fact_448_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 522 (all X_b all X_a all F all G all A_1 all X_1 ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hAPP(X_a,X_b,hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b))),override_on(X_a,X_b),F),G),A_1),X_1) = hAPP(X_a,X_b,G,X_1)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hAPP(X_a,X_b,hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b))),override_on(X_a,X_b),F),G),A_1),X_1) = hAPP(X_a,X_b,F,X_1)))) # label(fact_449_override__on__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 523 (all X_b all X_a all F all G all A_2 all A_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1)) -> hAPP(X_a,X_b,hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b))),override_on(X_a,X_b),F),G),A_1),A_2) = hAPP(X_a,X_b,F,A_2))) # label(fact_450_override__on__apply__notin) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 524 (all X_b all X_a all F all G all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1)) -> hAPP(X_a,X_b,hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b))),override_on(X_a,X_b),F),G),A_1),A_2) = hAPP(X_a,X_b,G,A_2))) # label(fact_451_override__on__apply__in) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 525 (all X_a all A_1 all B ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),bot_bot(fun(X_a,bool))))) -> hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),partial_flat_lub(X_a),B),A_1) = ti(X_a,B)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),bot_bot(fun(X_a,bool))))) -> hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),partial_flat_lub(X_a),B),A_1) = hAPP(fun(X_a,bool),X_a,the_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),bot_bot(fun(X_a,bool))))))))) # label(fact_452_flat__lub__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 526 (all X_a hBOOL(hAPP(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),bool,finite_comp_fun_idem(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),combb(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),X_a),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool))),combc(fun(X_a,bool),fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)))),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(X_a,fun(X_a,bool))),combc(X_a,fun(X_a,bool),fun(X_a,bool)),insert(X_a)),bot_bot(fun(X_a,bool))))))) # label(fact_453_comp__fun__idem__remove) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 527 (all X_b all X_a all F all Y_2 all X_2 all A_1 ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),X_2),Y_2)),A_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))))) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),X_2),Y_2)),A_1) = hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))) # label(fact_454_fun__upd__image) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 528 (all X_b all X_a all F all Z_2 all Y_2 all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),fold_graph(X_a,X_b),F),Z_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),fold_graph(X_a,X_b),F),Z_2),A_1),hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),Y_2)))))) # label(fact_455_fold__graph_H_Ointros_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 529 (all X_b all X_a all F all X_2 hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),X_2),hAPP(X_a,X_b,F,X_2)) = ti(fun(X_a,X_b),F)) # label(fact_456_fun__upd__triv) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 530 (all X_b all X_a all F all X_2 all Y_2 (hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),X_2),Y_2) = ti(fun(X_a,X_b),F) <-> hAPP(X_a,X_b,F,X_2) = ti(X_b,Y_2))) # label(fact_457_fun__upd__idem__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 531 (all X_b all X_a all F all X_2 all Y_2 all Z_2 hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),X_2),Y_2)),X_2),Z_2) = hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),X_2),Z_2)) # label(fact_458_fun__upd__upd) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 532 (all X_b all X_a all F all X_2 all Y_2 hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),hAPP(X_b,fun(X_a,fun(X_b,X_a)),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,fun(X_b,X_a))),fun_upd(X_b,X_a),F),X_2),Y_2),X_2) = ti(X_a,Y_2)) # label(fact_459_fun__upd__same) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 533 (all X_b all X_a all F all Y_2 all Z_2 all X_2 ((ti(X_a,Z_2) = ti(X_a,X_2) -> hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),X_2),Y_2),Z_2) = ti(X_b,Y_2)) & (ti(X_a,Z_2) != ti(X_a,X_2) -> hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),X_2),Y_2),Z_2) = hAPP(X_a,X_b,F,Z_2)))) # label(fact_460_fun__upd__apply) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 534 (all X_b all X_a all M_1 all B all D_1 all A_2 all C (ti(X_a,A_2) != ti(X_a,C) -> hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),M_1),A_2),B)),C),D_1) = hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),M_1),C),D_1)),A_2),B))) # label(fact_461_fun__upd__twist) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 535 (all X_b all X_a all F all Y_2 all Z_2 all X_2 (ti(X_a,Z_2) != ti(X_a,X_2) -> hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),X_2),Y_2),Z_2) = hAPP(X_a,X_b,F,Z_2))) # label(fact_462_fun__upd__other) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 536 (all X_b all X_a all F all X_2 all Y_2 (hAPP(X_b,X_a,F,X_2) = ti(X_a,Y_2) -> hAPP(X_a,fun(X_b,X_a),hAPP(X_b,fun(X_a,fun(X_b,X_a)),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,fun(X_b,X_a))),fun_upd(X_b,X_a),F),X_2),Y_2) = ti(fun(X_b,X_a),F))) # label(fact_463_fun__upd__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 537 (all X_b all X_a all F all B all A_2 all X_1 ((ti(X_a,X_1) = ti(X_a,A_2) -> hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),A_2),B),X_1) = ti(X_b,B)) & (ti(X_a,X_1) != ti(X_a,A_2) -> hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),A_2),B),X_1) = hAPP(X_a,X_b,F,X_1)))) # label(fact_464_fun__upd__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 538 (all X_a all X_b all X_2 all Z_2 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_a,X_b),F)) -> hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),Z_2)) = hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),Z_2))) # label(fact_465_comp__fun__idem_Ofun__left__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.33 539 (all X_b all X_a all M_1 all Y_2 all X_2 all A_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),fun(option(X_b),bool),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(option(X_b),bool)),image(X_a,option(X_b)),hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),M_1),X_2),hAPP(X_b,option(X_b),some(X_b),Y_2))),A_1) = hAPP(fun(X_a,bool),fun(option(X_b),bool),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(option(X_b),bool)),image(X_a,option(X_b)),M_1),A_1))) # label(fact_466_image__map__upd) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 540 (all X_b all X_a all M_1 all A_2 all X_2 all N_1 all Y_2 (hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),M_1),A_2),hAPP(X_b,option(X_b),some(X_b),X_2)) = hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),N_1),A_2),hAPP(X_b,option(X_b),some(X_b),Y_2)) -> ti(X_b,X_2) = ti(X_b,Y_2))) # label(fact_467_map__upd__eqD1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 541 (all X_b all X_a all T_3 all K all X_2 (hAPP(X_b,option(X_a),T_3,K) = hAPP(X_a,option(X_a),some(X_a),X_2) -> hAPP(option(X_a),fun(X_b,option(X_a)),hAPP(X_b,fun(option(X_a),fun(X_b,option(X_a))),hAPP(fun(X_b,option(X_a)),fun(X_b,fun(option(X_a),fun(X_b,option(X_a)))),fun_upd(X_b,option(X_a)),T_3),K),hAPP(X_a,option(X_a),some(X_a),X_2)) = ti(fun(X_b,option(X_a)),T_3))) # label(fact_468_map__upd__triv) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 542 (all X_b all X_a all M_1 all A_2 all B all X_2 all Y_2 (hAPP(X_b,option(X_a),hAPP(option(X_a),fun(X_b,option(X_a)),hAPP(X_b,fun(option(X_a),fun(X_b,option(X_a))),hAPP(fun(X_b,option(X_a)),fun(X_b,fun(option(X_a),fun(X_b,option(X_a)))),fun_upd(X_b,option(X_a)),M_1),A_2),hAPP(X_a,option(X_a),some(X_a),B)),X_2) = hAPP(X_a,option(X_a),some(X_a),Y_2) <-> ti(X_b,X_2) = ti(X_b,A_2) & ti(X_a,B) = ti(X_a,Y_2) | ti(X_b,X_2) != ti(X_b,A_2) & hAPP(X_b,option(X_a),M_1,X_2) = hAPP(X_a,option(X_a),some(X_a),Y_2))) # label(fact_469_map__upd__Some__unfold) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 543 (all X_b all X_a all F all Z_2 hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),fold_graph(X_a,X_b),F),Z_2),bot_bot(fun(X_a,bool))),Z_2))) # label(fact_470_fold__graph_H_Ointros_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 544 (all X_a hBOOL(hAPP(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),bool,finite_comp_fun_idem(X_a,fun(X_a,bool)),insert(X_a)))) # label(fact_471_comp__fun__idem__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 545 (all X_a (semilattice_sup(X_a) -> hBOOL(hAPP(fun(X_a,fun(X_a,X_a)),bool,finite_comp_fun_idem(X_a,X_a),semilattice_sup_sup(X_a))))) # label(fact_472_comp__fun__idem__sup) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 546 (all X_a (semilattice_inf(X_a) -> hBOOL(hAPP(fun(X_a,fun(X_a,X_a)),bool,finite_comp_fun_idem(X_a,X_a),semilattice_inf_inf(X_a))))) # label(fact_473_comp__fun__idem__inf) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 547 (all X_a all X_b all F all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),B_1)) & hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1))),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_1),A_1))) = bot_bot(fun(X_b,bool)))) # label(fact_474_inj__on__Un) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 548 (all X_a all X_b all F all X_2 (hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),F) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))) <-> (exists V ti(fun(X_a,option(X_b)),F) = hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),hAPP(option(X_b),fun(X_a,option(X_b)),combk(option(X_b),X_a),none(X_b))),X_2),hAPP(X_b,option(X_b),some(X_b),V))))) # label(fact_475_dom__eq__singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 549 (all X_a all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_1),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool))),finite_fold(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),combb(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),X_a),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool))),combc(fun(X_a,bool),fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)))),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(X_a,fun(X_a,bool))),combc(X_a,fun(X_a,bool),fun(X_a,bool)),insert(X_a)),bot_bot(fun(X_a,bool))))),B_1),A_1))) # label(fact_476_minus__fold__remove) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 550 (all X_b all X_a all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1) = hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_b,bool),fun(fun(X_a,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_b,bool),fun(fun(X_a,bool),fun(X_b,bool)))),finite_fold_image(fun(X_b,bool),X_a),semilattice_sup_sup(fun(X_b,bool))),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_a,X_b),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_a,X_b),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool)))),combb(X_b,fun(fun(X_b,bool),fun(X_b,bool)),X_a),insert(X_b)),F)),bot_bot(fun(X_b,bool)))),bot_bot(fun(X_b,bool))),A_1))) # label(fact_477_image__eq__fold__image) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 551 (all X_a all X_b all F hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),bot_bot(fun(X_a,bool))))) # label(fact_478_inj__on__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 552 (all X_a all X_b all X_2 all X_1 hAPP(X_a,option(X_b),hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),hAPP(option(X_b),fun(X_a,option(X_b)),combk(option(X_b),X_a),none(X_b))),X_2),none(X_b)),X_1) = none(X_b)) # label(fact_479_empty__upd__none) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 553 (all X_a all X_b all T_3 all K all X_2 -(all X_1 hAPP(X_a,option(X_b),hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),T_3),K),hAPP(X_b,option(X_b),some(X_b),X_2)),X_1) = none(X_b))) # label(fact_480_map__upd__nonempty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 554 (all X_a all A_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,option(X_a)),fun(fun(X_a,bool),bool),inj_on(X_a,option(X_a)),some(X_a)),A_1))) # label(fact_481_inj__Some) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 555 (all X_b all X_a all F all Z_2 hAPP(fun(X_b,bool),X_a,hAPP(X_a,fun(fun(X_b,bool),X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,bool),X_a)),finite_fold(X_b,X_a),F),Z_2),bot_bot(fun(X_b,bool))) = ti(X_a,Z_2)) # label(fact_482_fold__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 556 (all X_a all A_8 none(X_a) != hAPP(X_a,option(X_a),some(X_a),A_8)) # label(fact_483_option_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 557 (all X_a all A_8 hAPP(X_a,option(X_a),some(X_a),A_8) != none(X_a)) # label(fact_484_option_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 558 (all X_a all X_2 ((all Y_1 ti(option(X_a),X_2) != hAPP(X_a,option(X_a),some(X_a),Y_1)) <-> ti(option(X_a),X_2) = none(X_a))) # label(fact_485_not__Some__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 559 (all X_a all X_2 (ti(option(X_a),X_2) != none(X_a) <-> (exists Y_1 ti(option(X_a),X_2) = hAPP(X_a,option(X_a),some(X_a),Y_1)))) # label(fact_486_not__None__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 560 (all X_b all X_a all F all G all Z_2 hAPP(fun(X_b,bool),X_a,hAPP(X_a,fun(fun(X_b,bool),X_a),hAPP(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a))),finite_fold_image(X_a,X_b),F),G),Z_2),bot_bot(fun(X_b,bool))) = ti(X_a,Z_2)) # label(fact_487_fold__image__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 561 (all X_a all X_b all M_1 hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),M_1) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(option(X_b),fun(X_a,bool),hAPP(fun(X_a,fun(option(X_b),bool)),fun(option(X_b),fun(X_a,bool)),combc(X_a,option(X_b),bool),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),bool)),hAPP(fun(option(X_b),fun(option(X_b),bool)),fun(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),bool))),combb(option(X_b),fun(option(X_b),bool),X_a),fequal(option(X_b))),M_1)),none(X_b))))) # label(fact_488_dom__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 562 (all X_a all X_b all A_2 all M_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),M_1))) <-> hAPP(X_a,option(X_b),M_1,A_2) != none(X_b))) # label(fact_489_domIff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 563 (all X_b all X_a all F all G hAPP(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a))),finite_fold_image(X_a,X_b),F),G) = hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,bool),X_a)),finite_fold(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),F),G))) # label(fact_490_fold__image__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 564 (all X_a all X_b all X_2 all Y_2 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> (hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_2) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_2),A_1)) -> ti(X_a,X_2) = ti(X_a,Y_2)))))) # label(fact_491_inj__onD) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 565 (all X_a all X_b all Y_2 all X_2 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_2),A_1)) -> (hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_2) <-> ti(X_a,X_2) = ti(X_a,Y_2)))))) # label(fact_492_inj__on__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 566 (all X_a all X_b all X_2 all Y_2 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> (ti(X_a,X_2) != ti(X_a,Y_2) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_2),A_1)) -> hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,Y_2)))))) # label(fact_493_inj__on__contraD) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 567 (all X_a all X_b all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) <-> (all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_1)) -> (hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Xa) -> ti(X_a,X_1) = ti(X_a,Xa)))))))) # label(fact_494_inj__on__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 568 (all X_a all A_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),combi(X_a)),A_1))) # label(fact_495_inj__on__id2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 569 (all X_a all X_b all A_1 all F all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))))) # label(fact_496_subset__inj__on) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 570 (all X_a all X_b all B_1 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)))))) # label(fact_497_inj__on__Int) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 571 (all X_a all X_b all B_1 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1))))) # label(fact_498_inj__on__diff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 572 (all X_a all X_b all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),inj_on(X_b,X_a),F),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1))))) # label(fact_499_finite__imageD) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 573 (all X_a all X_b all F all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1))) -> (hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1) = hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B_1) <-> ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B_1)))) # label(fact_500_inj__on__Un__image__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 574 (all X_a all X_2 (hBOOL(hAPP(option(X_a),bool,is_none(X_a),X_2)) <-> ti(option(X_a),X_2) = none(X_a))) # label(fact_501_is__none__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 575 (all X_a hBOOL(hAPP(option(X_a),bool,is_none(X_a),none(X_a)))) # label(fact_502_is__none__code_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 576 (all X_a all X_b all X_2 all Y_2 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),X_2),Y_2)),A_1))))) # label(fact_503_inj__on__fun__updI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 577 (all X_a (semilattice_sup(X_a) -> (all B all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B)),hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),semilattice_sup_sup(X_a)),B),A_1)))))))) # label(fact_504_sup__le__fold__sup) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 578 (all X_a (semilattice_inf(X_a) -> (all B all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),semilattice_inf_inf(X_a)),B),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B)))))))) # label(fact_505_fold__inf__le__inf) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 579 (all X_a (semilattice_sup(X_a) -> (all B all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),semilattice_sup_sup(X_a)),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),semilattice_sup_sup(X_a)),B),A_1)))))) # label(fact_506_fold__sup__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 580 (all X_a (semilattice_inf(X_a) -> (all B all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),semilattice_inf_inf(X_a)),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),semilattice_inf_inf(X_a)),B),A_1)))))) # label(fact_507_fold__inf__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 581 (all X_a all X_b all F (hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),F) = bot_bot(fun(X_a,bool)) <-> (all X_1 hAPP(X_a,option(X_b),F,X_1) = none(X_b)))) # label(fact_508_dom__eq__empty__conv) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 582 (all X_b all X_a all F1 all F2 hAPP(option(X_b),X_a,hAPP(fun(X_b,X_a),fun(option(X_b),X_a),hAPP(X_a,fun(fun(X_b,X_a),fun(option(X_b),X_a)),option_rec(X_a,X_b),F1),F2),none(X_b)) = ti(X_a,F1)) # label(fact_509_option_Orecs_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 583 (all X_a all X_b hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),hAPP(option(X_b),fun(X_a,option(X_b)),combk(option(X_b),X_a),none(X_b))) = bot_bot(fun(X_a,bool))) # label(fact_510_dom__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 584 (all X_a hAPP(option(X_a),fun(X_a,bool),set(X_a),none(X_a)) = bot_bot(fun(X_a,bool))) # label(fact_511_Option_Oset_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 585 (all X_a all Xo (hAPP(option(X_a),fun(X_a,bool),set(X_a),Xo) = bot_bot(fun(X_a,bool)) <-> ti(option(X_a),Xo) = none(X_a))) # label(fact_512_set__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 586 (all X_b all X_a all A_1 all F all Z_2 all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z_2),G),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> hAPP(fun(X_b,bool),X_a,Fa,A_1) = hAPP(fun(X_b,bool),X_a,hAPP(X_a,fun(fun(X_b,bool),X_a),hAPP(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a))),finite_fold_image(X_a,X_b),F),G),Z_2),A_1)))) # label(fact_513_folding__image__simple_Oeq__fold__g) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 587 (all X_a all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),A_1)),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),F),A_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),A_1) = ti(fun(X_a,bool),A_1))))) # label(fact_514_endo__inj__surj) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 588 (all X_a all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),A_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),F),A_1))))) # label(fact_515_finite__surj__inj) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 589 (all X_a all X_b all B_1 all A_1 all F all C_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),C_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),C_2)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B_1)))))) # label(fact_516_inj__on__image__Int) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 590 (all X_a all X_b all B_1 all A_1 all F all C_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),C_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),C_2)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B_1)))))) # label(fact_517_inj__on__image__set__diff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 591 (all X_a all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool))),finite_fold(X_a,fun(X_a,bool)),insert(X_a)),B_1),A_1))) # label(fact_518_union__fold__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 592 (all X_b all X_a all A_1 all F all X_2 (hAPP(X_b,option(X_a),F,X_2) = none(X_a) -> hAPP(fun(X_b,bool),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,option(X_a)),fun(X_b,bool),dom(X_b,X_a),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),X_2),A_1)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,option(X_a)),fun(X_b,bool),dom(X_b,X_a),F)),A_1))) # label(fact_519_dom__minus) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 593 (all X_a all X_b all Z_2 all X_2 all A_1 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_a,X_b),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_2),A_1))))) # label(fact_520_comp__fun__idem_Ofold__insert__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 594 (all X_a all X_b all Z_2 all X_2 all A_1 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_a,X_b),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),Z_2)),A_1)))) # label(fact_521_comp__fun__idem_Ofold__insert__idem2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 595 (all X_a (lattice(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),X) = ti(X_a,X)))) # label(fact_522_Sup__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 596 (all X_a all X_2 all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),F),X_2),A_1))))) # label(fact_523_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 597 (all X_a (lattice(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),X) = ti(X_a,X)))) # label(fact_524_Inf__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 598 (all X_a all A_2 all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),F),A_2),A_1)))) # label(fact_525_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 599 (all Pn (hAPP(pname,option(com),body,Pn) != none(com) -> hBOOL(hAPP(com,bool,wt,hAPP(pname,com,body_1,Pn))))) # label(fact_526_WT_OBody) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 600 (all X_a all X_b all F all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,A_2)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),bot_bot(fun(X_a,bool))))))))) # label(fact_527_inj__on__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 601 (all X_b all X_a all F all X_2 all Y_2 ((ti(option(X_a),Y_2) = none(X_a) -> hAPP(fun(X_b,option(X_a)),fun(X_b,bool),dom(X_b,X_a),hAPP(option(X_a),fun(X_b,option(X_a)),hAPP(X_b,fun(option(X_a),fun(X_b,option(X_a))),hAPP(fun(X_b,option(X_a)),fun(X_b,fun(option(X_a),fun(X_b,option(X_a)))),fun_upd(X_b,option(X_a)),F),X_2),Y_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,option(X_a)),fun(X_b,bool),dom(X_b,X_a),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),X_2),bot_bot(fun(X_b,bool))))) & (ti(option(X_a),Y_2) != none(X_a) -> hAPP(fun(X_b,option(X_a)),fun(X_b,bool),dom(X_b,X_a),hAPP(option(X_a),fun(X_b,option(X_a)),hAPP(X_b,fun(option(X_a),fun(X_b,option(X_a))),hAPP(fun(X_b,option(X_a)),fun(X_b,fun(option(X_a),fun(X_b,option(X_a)))),fun_upd(X_b,option(X_a)),F),X_2),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_2),hAPP(fun(X_b,option(X_a)),fun(X_b,bool),dom(X_b,X_a),F))))) # label(fact_528_dom__fun__upd) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 602 (all X_a (semilattice_inf(X_a) -> (all C all B all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X_1)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B),C)),hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),semilattice_inf_inf(X_a)),C),A_1)))))))) # label(fact_529_inf__le__fold__inf) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 603 (all X_a (semilattice_sup(X_a) -> (all C all B all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),B)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),semilattice_sup_sup(X_a)),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B),C)))))))) # label(fact_530_fold__sup__le__sup) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 604 (all X_b all X_a all A_7 all A_1 (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> ((exists F_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F_1),A_1)) & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F_1),A_1)),A_7)))) <-> (exists G_1 hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),G_1),A_7) = ti(fun(X_a,bool),A_1))))) # label(fact_531_inj__on__iff__surj) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 605 (all X_a all Y (ti(option(X_a),Y) != none(X_a) -> -(all A_4 ti(option(X_a),Y) != hAPP(X_a,option(X_a),some(X_a),A_4)))) # label(fact_532_option_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 606 (all X_b all X_a all B all M_1 all A_2 (hAPP(X_b,option(X_a),M_1,A_2) = none(X_a) -> hAPP(fun(X_b,option(X_a)),fun(X_a,bool),ran(X_b,X_a),hAPP(option(X_a),fun(X_b,option(X_a)),hAPP(X_b,fun(option(X_a),fun(X_b,option(X_a))),hAPP(fun(X_b,option(X_a)),fun(X_b,fun(option(X_a),fun(X_b,option(X_a)))),fun_upd(X_b,option(X_a)),M_1),A_2),hAPP(X_a,option(X_a),some(X_a),B))) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),hAPP(fun(X_b,option(X_a)),fun(X_a,bool),ran(X_b,X_a),M_1)))) # label(fact_533_ran__map__upd) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 607 (all X_b all X_a all G all F all A_1 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_1)) -> (hAPP(X_a,X_b,G,hAPP(X_a,X_a,F,X_1)) = hAPP(X_a,X_b,G,hAPP(X_a,X_a,F,Xa)) <-> hAPP(X_a,X_b,G,X_1) = hAPP(X_a,X_b,G,Xa)))))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),F),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),G),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),A_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),G),A_1)))))) # label(fact_534_inj__on__image__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 608 (all X_a all X_b all Z_2 all X_2 all A_1 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite100568337ommute(X_a,X_b),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))))))) # label(fact_535_comp__fun__commute_Ofold__insert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 609 (all X_a all X_b all Z_2 all X_2 all A_1 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite100568337ommute(X_a,X_b),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_2),A_1) = hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))))))) # label(fact_536_comp__fun__commute_Ofold__rec) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 610 (all X_a all X_b all X_2 all Y_2 all Z_2 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite100568337ommute(X_a,X_b),F)) -> hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,Y_2),Z_2)) = hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,Y_2),hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),Z_2)))) # label(fact_537_comp__fun__commute_Ofun__left__comm) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 611 (all X_b all X_a all M_1 all A_2 all B (hAPP(X_b,option(X_a),M_1,A_2) = hAPP(X_a,option(X_a),some(X_a),B) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B),hAPP(fun(X_b,option(X_a)),fun(X_a,bool),ran(X_b,X_a),M_1))))) # label(fact_538_ranI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 612 (all X_a all X_b all X_2 all Z_2 all A_1 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite100568337ommute(X_a,X_b),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_2),A_1)) = hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),Z_2)),A_1)))) # label(fact_539_comp__fun__commute_Ofold__fun__comm) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 613 (all X_a all X_b all Z_2 all X_2 all A_1 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite100568337ommute(X_a,X_b),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_2),A_1)))))) # label(fact_540_comp__fun__commute_Ofold__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 614 (all X_a all X_b all Z_2 all X_2 all A_1 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite100568337ommute(X_a,X_b),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),Z_2)),A_1))))) # label(fact_541_comp__fun__commute_Ofold__insert2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 615 (all X_b all X_a hAPP(fun(X_b,option(X_a)),fun(X_a,bool),ran(X_b,X_a),hAPP(option(X_a),fun(X_b,option(X_a)),combk(option(X_a),X_b),none(X_a))) = bot_bot(fun(X_a,bool))) # label(fact_542_ran__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 616 (all X_a all X_b all A_2 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,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))))),A_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),hAPP(fun(X_a,bool),X_a,the_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),hAPP(X_b,fun(X_a,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,bool))),combb(X_b,fun(X_b,bool),X_a),fequal(X_b)),F)),A_2)))),bot_bot(fun(X_a,bool))))))) # label(fact_543_inj__on__vimage__singleton) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 617 (all X_b all X_a all M_1 all X_2 all D_2 ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),D_2)) -> hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),M_1),D_2)),X_2),none(X_b)) = hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),M_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),D_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),D_2)) -> hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),M_1),D_2)),X_2),none(X_b)) = hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),M_1),D_2)))) # label(fact_544_fun__upd__None__restrict) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 618 (all X_b all X_a all G all B_1 all F all A_1 exists A_6 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_6),A_1)) & (all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_6)) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),G),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_6))))))) & (exists H_1 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_6)) -> hAPP(X_a,X_b,H_1,X_1) = hAPP(X_a,X_b,F,X_1))) & (all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),A_6))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,H_1,X_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_6)))) & ti(X_a,X_1) = hAPP(X_b,X_a,G,hAPP(X_a,X_b,H_1,X_1)))))))) # label(fact_545_Cantor__Bernstein__aux) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 619 (all X_b all X_a all G all A_1 all F all Z_2 all Fa (hBOOL(hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool,hAPP(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool)),big_comm_monoid_big(X_a,X_b),F),Z_2),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,G),A_1) = hAPP(fun(X_b,bool),X_a,hAPP(X_a,fun(fun(X_b,bool),X_a),hAPP(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a))),finite_fold_image(X_a,X_b),F),G),Z_2),A_1)) & (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,G),A_1) = ti(X_a,Z_2)))) # label(fact_546_comm__monoid__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 620 (all X_b all X_a all B_1 all F all A_2 all B (hAPP(X_b,X_a,F,A_2) = ti(X_a,B) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),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_a,bool),fun(X_b,bool),hAPP(fun(X_b,X_a),fun(fun(X_a,bool),fun(X_b,bool)),vimage(X_b,X_a),F),B_1)))))) # label(fact_547_vimageI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 621 (all X_b all X_a all F all P_1 hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),P_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,X_b),fun(X_a,bool),hAPP(fun(X_b,bool),fun(fun(X_a,X_b),fun(X_a,bool)),combb(X_b,bool,X_a),P_1),F))) # label(fact_548_vimage__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 622 (all X_a all X_b all A_2 all F all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),B_1))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,A_2)),B_1)))) # label(fact_549_vimage__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 623 (all X_a all X_b all F all A_1 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),A_1),X_2)) <-> hBOOL(hAPP(X_b,bool,A_1,hAPP(X_a,X_b,F,X_2))))) # label(fact_550_vimage__code) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 624 (all X_b all X_a all M_1 all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(X_a,option(X_b),hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),M_1),A_1),X_2) = hAPP(X_a,option(X_b),M_1,X_2))) # label(fact_551_restrict__in) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 625 (all X_a all X_b all A_2 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),A_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,A_2)),A_1)))) # label(fact_552_vimageD) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 626 (all X_a all X_b all F all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_b,X_a,F,A_2)),A_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_a,bool),fun(X_b,bool),hAPP(fun(X_b,X_a),fun(fun(X_a,bool),fun(X_b,bool)),vimage(X_b,X_a),F),A_1))))) # label(fact_553_vimageI2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 627 (all X_b all X_a all F all B_1 hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),B_1) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_a,bool)),combc(X_a,fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(X_a,fun(fun(X_b,bool),bool)),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_a,X_b),fun(X_a,fun(fun(X_b,bool),bool))),combb(X_b,fun(fun(X_b,bool),bool),X_a),member(X_b)),F)),B_1))) # label(fact_554_vimage__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 628 (all X_a all Y_3 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),vimage(X_a,X_a),combi(X_a)),Y_3) = ti(fun(X_a,bool),Y_3)) # label(fact_555_vimage__ident) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 629 (all X_b all X_a all F all A_1 all B_1 hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),A_1)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),B_1))) # label(fact_556_vimage__Diff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 630 (all X_b all X_a all F all A_1 all B_1 hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),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_1),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),A_1)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),B_1))) # label(fact_557_vimage__Un) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 631 (all X_b all X_a all F all A_1 all B_1 hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),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_1),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),A_1)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),B_1))) # label(fact_558_vimage__Int) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 632 (all X_b all X_a all F all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_b,X_a),fun(fun(X_a,bool),fun(X_b,bool)),vimage(X_b,X_a),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_b,X_a),fun(fun(X_a,bool),fun(X_b,bool)),vimage(X_b,X_a),F),B_1))))) # label(fact_559_vimage__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 633 (all X_b all X_a all F hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),bot_bot(fun(X_b,bool))) = bot_bot(fun(X_a,bool))) # label(fact_560_vimage__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 634 (all X_b all X_a all M_1 all X_2 all A_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(X_a,option(X_b),hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),M_1),A_1),X_2) = none(X_b))) # label(fact_561_restrict__out) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 635 (all X_b all X_a all M_1 all A_1 all X_1 ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hAPP(X_a,option(X_b),hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),M_1),A_1),X_1) = hAPP(X_a,option(X_b),M_1,X_1)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hAPP(X_a,option(X_b),hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),M_1),A_1),X_1) = none(X_b)))) # label(fact_562_restrict__map__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 636 (all X_a all X_b all M_1 all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),M_1),A_1)),B_1) = hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),M_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1))) # label(fact_563_restrict__restrict) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 637 (all X_a all X_b all D_2 all X_1 hAPP(X_a,option(X_b),hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),hAPP(option(X_b),fun(X_a,option(X_b)),combk(option(X_b),X_a),none(X_b))),D_2),X_1) = none(X_b)) # label(fact_564_restrict__map__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 638 (all X_a all X_b all A_2 all F all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,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),B),bot_bot(fun(X_b,bool)))))) <-> hAPP(X_a,X_b,F,A_2) = ti(X_b,B))) # label(fact_565_vimage__singleton__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 639 (all X_a all X_b all F all A_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_b,X_a),fun(fun(X_a,bool),fun(X_b,bool)),vimage(X_b,X_a),F),A_1))),A_1))) # label(fact_566_image__vimage__subset) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 640 (all X_a all X_b all M_1 all X_1 hAPP(X_a,option(X_b),hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),M_1),bot_bot(fun(X_a,bool))),X_1) = none(X_b)) # label(fact_567_restrict__map__to__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 641 (all X_a all X_b all F all A_2 all A_1 hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1)) = hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),F),A_1)),A_2),hAPP(X_a,option(X_b),F,A_2))) # label(fact_568_restrict__map__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 642 (all X_a all X_b all M_1 all A_1 hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),M_1),A_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),M_1)),A_1)) # label(fact_569_dom__restrict) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.34 643 (all X_b all X_a all F all A_2 all B_1 hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,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),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,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))))),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),B_1))) # label(fact_570_vimage__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 644 (all X_b all X_a all H all A_1 all Fa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),inj_on(X_b,X_a),H),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_b,X_a),fun(fun(X_a,bool),fun(X_b,bool)),vimage(X_b,X_a),H),Fa)),A_1)))))) # label(fact_571_finite__vimage__IntI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 645 (all X_b all X_a all G all A_1 all F all Z_2 all Fa (hBOOL(hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool,hAPP(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool)),big_comm_monoid_big(X_a,X_b),F),Z_2),Fa)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,G),A_1) = ti(X_a,Z_2)))) # label(fact_572_comm__monoid__big_Oinfinite) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 646 (all X_b all X_a all M_1 all Y_2 all X_2 all D_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),D_2)) -> hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),M_1),D_2)),X_2),Y_2) = hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),M_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),D_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))),X_2),Y_2))) # label(fact_573_fun__upd__restrict__conv) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 647 (all X_b all X_a all M_1 all D_2 all X_2 all Y_2 hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),M_1),D_2)),X_2),Y_2) = hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),M_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),D_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))),X_2),Y_2)) # label(fact_574_fun__upd__restrict) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 648 (all X_b all X_a all M_1 all Y_2 all X_2 all D_2 ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),D_2)) -> hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),M_1),X_2),Y_2)),D_2) = hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),M_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),D_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))),X_2),Y_2)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),D_2)) -> hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),M_1),X_2),Y_2)),D_2) = hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),M_1),D_2)))) # label(fact_575_restrict__fun__upd) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 649 (all X_a all X_b all Y_2 all M_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_2),hAPP(fun(X_b,option(X_a)),fun(X_a,bool),ran(X_b,X_a),hAPP(fun(X_b,bool),fun(X_b,option(X_a)),hAPP(fun(X_b,option(X_a)),fun(fun(X_b,bool),fun(X_b,option(X_a))),restrict_map(X_b,X_a),M_1),A_1)))) -> (exists X_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) & hAPP(X_b,option(X_a),M_1,X_1) = hAPP(X_a,option(X_a),some(X_a),Y_2))))) # label(fact_576_ran__restrictD) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 650 (all X_a all X_b all A_2 all F all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),B_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,A_2)),B_1)))) # label(fact_577_vimageE) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 651 (all X_b all X_a all Y_2 all F all G all S ((all W (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),W),S)) -> hAPP(X_a,X_b,F,W) = hAPP(X_a,X_b,G,W))) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),Y_2)),S) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),G),Y_2)),S))) # label(fact_578_vimage__inter__cong) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 652 (all X_b all X_a all H all G all A_1 all B_1 all F all Z_2 all Fa (hBOOL(hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool,hAPP(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool)),big_comm_monoid_big(X_a,X_b),F),Z_2),Fa)) -> (ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B_1) -> ((all X_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)) -> hAPP(X_b,X_a,H,X_1) = hAPP(X_b,X_a,G,X_1))) -> hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,H),A_1) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,G),B_1))))) # label(fact_579_comm__monoid__big_OF__cong) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 653 (all X_a all X_b all A_2 all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,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))))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),hAPP(fun(X_a,bool),X_a,the_1(X_a),hAPP(X_b,fun(X_a,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,bool))),combb(X_b,fun(X_b,bool),X_a),fequal(X_b)),F)),A_2))),bot_bot(fun(X_a,bool))))))) # label(fact_580_inj__vimage__singleton) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 654 (all X_a (lattice(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),A_1)),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),B_1)))))))))) # label(fact_581_Inf__fin_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 655 (all X_a (lattice(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1))),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),A_1)),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),B_1)))))))) # label(fact_582_Inf__fin_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 656 (all X_a all X_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),top_top(fun(X_a,bool))))) # label(fact_583_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 657 (all X_a all X_2 hBOOL(hAPP(X_a,bool,top_top(fun(X_a,bool)),X_2))) # label(fact_584_top1I) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 658 (all X_b all X_a all X_c all F all G hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_b,X_c),fun(X_b,X_a),hAPP(fun(X_c,X_a),fun(fun(X_b,X_c),fun(X_b,X_a)),combb(X_c,X_a,X_b),F),G)),top_top(fun(X_b,bool))) = hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),F),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),top_top(fun(X_b,bool))))) # label(fact_585_range__composition) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 659 (all X_a all X_b all F all X_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool)))))) # label(fact_586_rangeI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 660 (all X_a all X_b all B all F all X_2 (ti(X_a,B) = hAPP(X_b,X_a,F,X_2) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))))))) # label(fact_587_range__eqI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 661 (all X_a (bounded_lattice_top(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),top_top(X_a)) = top_top(X_a)))) # label(fact_588_sup__top__right) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 662 (all X_a (bounded_lattice_top(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),top_top(X_a)),X) = top_top(X_a)))) # label(fact_589_sup__top__left) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 663 (all X_a (bounded_lattice_top(X_a) -> (all X_2 all Y_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_2),Y_2) = top_top(X_a) <-> ti(X_a,X_2) = top_top(X_a) & ti(X_a,Y_2) = top_top(X_a))))) # label(fact_590_inf__eq__top__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 664 (all X_a (bounded_lattice_top(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),top_top(X_a)) = ti(X_a,X)))) # label(fact_591_inf__top__right) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 665 (all X_a (bounded_lattice_top(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),top_top(X_a)),X) = ti(X_a,X)))) # label(fact_592_inf__top__left) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 666 (all X_b all X_a (top(X_a) -> (all X_2 hAPP(X_b,X_a,top_top(fun(X_b,X_a)),X_2) = top_top(X_a)))) # label(fact_593_top__apply) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 667 (all X_a top_top(fun(X_a,bool)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(bool,fun(X_a,bool),combk(bool,X_a),fTrue))) # label(fact_594_UNIV__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 668 (all X_b all X_a (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),top_top(fun(X_a,bool)))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),top_top(fun(X_b,bool)))) -> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,finite_finite(product_prod(X_a,X_b)),top_top(fun(product_prod(X_a,X_b),bool))))))) # label(fact_595_finite__Prod__UNIV) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 669 (all X_a (hBOOL(hAPP(fun(option(X_a),bool),bool,finite_finite(option(X_a)),top_top(fun(option(X_a),bool)))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),top_top(fun(X_a,bool)))))) # label(fact_596_finite__option__UNIV) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 670 (all X_a all X_b (hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite(sum_sum(X_a,X_b)),top_top(fun(sum_sum(X_a,X_b),bool)))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),top_top(fun(X_a,bool)))) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),top_top(fun(X_b,bool)))))) # label(fact_597_finite__Plus__UNIV__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 671 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),top_top(fun(X_a,bool))) = top_top(fun(X_a,bool))) # label(fact_598_Un__UNIV__right) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 672 (all X_a all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),top_top(fun(X_a,bool))),B_1) = top_top(fun(X_a,bool))) # label(fact_599_Un__UNIV__left) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 673 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),top_top(fun(X_a,bool))) = ti(fun(X_a,bool),A_1)) # label(fact_600_Int__UNIV__right) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 674 (all X_a all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),top_top(fun(X_a,bool))),B_1) = ti(fun(X_a,bool),B_1)) # label(fact_601_Int__UNIV__left) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 675 (all X_a all A_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),top_top(fun(X_a,bool))))) # label(fact_602_subset__UNIV) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 676 (all X_a (finite_finite_1(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),top_top(fun(X_a,bool)))))) # label(fact_603_finite__UNIV) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 677 (all X_a top_top(fun(X_a,bool)) != bot_bot(fun(X_a,bool))) # label(fact_604_UNIV__not__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 678 (all X_a all X_b (hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,finite_finite(fun(X_a,X_b)),top_top(fun(fun(X_a,X_b),bool)))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),top_top(fun(X_b,bool)))))) # label(fact_605_finite__fun__UNIVD2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 679 (all X_a (top(X_a) -> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),top_top(X_a)),A_3)) -> ti(X_a,A_3) = top_top(X_a))))) # label(fact_606_top__le) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 680 (all X_a (top(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),top_top(X_a)),A_2)) <-> ti(X_a,A_2) = top_top(X_a))))) # label(fact_607_top__unique) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 681 (all X_a (top(X_a) -> (all A_3 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),top_top(X_a)))))) # label(fact_608_top__greatest) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 682 (all X_a all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),P_1)))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),top_top(fun(X_a,bool))))))) # label(fact_609_finite__Collect__not) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 683 (all X_a all P_1 ((hBOOL(P_1) -> hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(bool,fun(X_a,bool),combk(bool,X_a),P_1)) = top_top(fun(X_a,bool))) & (-hBOOL(P_1) -> hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(bool,fun(X_a,bool),combk(bool,X_a),P_1)) = bot_bot(fun(X_a,bool))))) # label(fact_610_Collect__const) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 684 (all X_a all X_b all X_2 all Y_2 all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) -> (hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_2) <-> ti(X_a,X_2) = ti(X_a,Y_2)))) # label(fact_611_inj__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 685 (all X_a all X_b all X_2 all Y_2 all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) -> (hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_2) -> ti(X_a,X_2) = ti(X_a,Y_2)))) # label(fact_612_injD) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 686 (all X_c all X_a all X_b all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,fun(X_c,X_b)),fun(fun(X_a,bool),bool),inj_on(X_a,fun(X_c,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_c,X_b)),hAPP(fun(X_b,fun(X_c,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_c,X_b))),combb(X_b,fun(X_c,X_b),X_a),combk(X_b,X_c)),F)),top_top(fun(X_a,bool)))))) # label(fact_613_inj__fun) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 687 (all X_b all X_a all F hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool))) # label(fact_614_vimage__UNIV) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 688 (all X_a top_top(fun(option(X_a),bool)) = hAPP(fun(option(X_a),bool),fun(option(X_a),bool),hAPP(option(X_a),fun(fun(option(X_a),bool),fun(option(X_a),bool)),insert(option(X_a)),none(X_a)),hAPP(fun(X_a,bool),fun(option(X_a),bool),hAPP(fun(X_a,option(X_a)),fun(fun(X_a,bool),fun(option(X_a),bool)),image(X_a,option(X_a)),some(X_a)),top_top(fun(X_a,bool))))) # label(fact_615_UNIV__option__conv) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 689 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),top_top(fun(X_a,bool))) = bot_bot(fun(X_a,bool))) # label(fact_616_Diff__UNIV) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 690 (all X_a all X_b all B all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),top_top(fun(X_a,bool))))) <-> (exists X_1 (ti(X_b,B) = hAPP(X_a,X_b,F,X_1) & (all Y_1 (ti(X_b,B) = hAPP(X_a,X_b,F,Y_1) -> ti(X_a,Y_1) = ti(X_a,X_1)))))))) # label(fact_617_range__ex1__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 691 (all X_a all X_b all A_2 all A_1 all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,A_2)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1))))) # label(fact_618_inj__image__mem__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 692 (all X_a all X_b all A_1 all B_1 all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) -> (hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1) = hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B_1) <-> ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B_1)))) # label(fact_619_inj__image__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 693 (all X_b all X_a all A_1 all F (hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool)) -> hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_b,X_a),fun(fun(X_a,bool),fun(X_b,bool)),vimage(X_b,X_a),F),A_1)) = ti(fun(X_a,bool),A_1))) # label(fact_620_surj__image__vimage__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 694 (all X_a (lattice(X_a) -> (all X_2 hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = ti(X_a,X_2)))) # label(fact_621_Inf__fin_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 695 (all X_a (lattice(X_a) -> (all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),A_1)) = ti(X_a,A_2)))))) # label(fact_622_sup__Inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 696 (all X_a (lattice(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),A_1)) = hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),A_1)))))) # label(fact_623_Inf__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 697 (all X_a hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,fun(X_a,bool)),fun(fun(X_a,bool),bool),inj_on(X_a,fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(X_a,fun(X_a,bool))),combc(X_a,fun(X_a,bool),fun(X_a,bool)),insert(X_a)),bot_bot(fun(X_a,bool)))),top_top(fun(X_a,bool))))) # label(fact_624_inj__singleton) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 698 (all X_c all X_a all X_b all F all G (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),G),top_top(fun(X_b,bool))))) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(fun(X_b,X_a),fun(X_b,X_c),hAPP(fun(X_a,X_c),fun(fun(X_b,X_a),fun(X_b,X_c)),combb(X_a,X_c,X_b),F),G)),top_top(fun(X_b,bool))))))) # label(fact_625_finite__range__imageI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 699 (all X_b all X_a all C all A_1 ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_b,X_a),fun(fun(X_a,bool),fun(X_b,bool)),vimage(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),C)),A_1) = top_top(fun(X_b,bool))) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_b,X_a),fun(fun(X_a,bool),fun(X_b,bool)),vimage(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),C)),A_1) = bot_bot(fun(X_b,bool))))) # label(fact_626_vimage__const) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 700 (all X_a all X_b all F hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,option(X_b)),hAPP(fun(X_b,option(X_b)),fun(fun(X_a,X_b),fun(X_a,option(X_b))),combb(X_b,option(X_b),X_a),some(X_b)),F)) = top_top(fun(X_a,bool))) # label(fact_627_dom__const) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 701 (all X_a all F (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),top_top(fun(X_a,bool)))) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),top_top(fun(X_a,bool))) = top_top(fun(X_a,bool)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),F),top_top(fun(X_a,bool))))))) # label(fact_628_finite__UNIV__surj__inj) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 702 (all X_a all F (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),top_top(fun(X_a,bool)))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),F),top_top(fun(X_a,bool)))) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),top_top(fun(X_a,bool))) = top_top(fun(X_a,bool))))) # label(fact_629_finite__UNIV__inj__surj) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 703 (all X_a all X_b all A_1 all B_1 all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1))))) # label(fact_630_inj__image__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 704 (all X_a all X_b all A_1 all B_1 all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B_1)))) # label(fact_631_image__Int) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 705 (all X_a all X_b all A_1 all B_1 all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B_1)))) # label(fact_632_image__set__diff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 706 (all X_b all X_a all A_1 all F (hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool)) -> (hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_b,X_a),fun(fun(X_a,bool),fun(X_b,bool)),vimage(X_b,X_a),F),A_1) = bot_bot(fun(X_b,bool)) <-> ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool))))) # label(fact_633_surj__vimage__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 707 (all X_a all X_b all H all Fa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),H),Fa))) -> (hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),H),top_top(fun(X_a,bool))) = top_top(fun(X_b,bool)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),Fa))))) # label(fact_634_finite__vimageD) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 708 (all X_b all X_a all B_1 all A_1 all F (hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_b,X_a),fun(fun(X_a,bool),fun(X_b,bool)),vimage(X_b,X_a),F),B_1)),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))))) # label(fact_635_vimage__subsetD) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 709 (all X_b all X_a all F all A_1 hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_b,X_a),fun(fun(X_a,bool),fun(X_b,bool)),vimage(X_b,X_a),F),A_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))))) # label(fact_636_image__vimage__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 710 (all X_b all X_a all H all Fa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),inj_on(X_b,X_a),H),top_top(fun(X_b,bool)))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_b,X_a),fun(fun(X_a,bool),fun(X_b,bool)),vimage(X_b,X_a),H),Fa)))))) # label(fact_637_finite__vimageI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 711 (all X_a all X_b all A_1 all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) -> hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)) = ti(fun(X_a,bool),A_1))) # label(fact_638_inj__vimage__image__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 712 (all X_a all X_b all A_2 all B all F (hBOOL(hAPP(fun(option(X_a),bool),bool,finite_finite(option(X_a)),hAPP(fun(X_b,bool),fun(option(X_a),bool),hAPP(fun(X_b,option(X_a)),fun(fun(X_b,bool),fun(option(X_a),bool)),image(X_b,option(X_a)),F),top_top(fun(X_b,bool))))) -> hBOOL(hAPP(fun(option(X_a),bool),bool,finite_finite(option(X_a)),hAPP(fun(X_b,bool),fun(option(X_a),bool),hAPP(fun(X_b,option(X_a)),fun(fun(X_b,bool),fun(option(X_a),bool)),image(X_b,option(X_a)),hAPP(option(X_a),fun(X_b,option(X_a)),hAPP(X_b,fun(option(X_a),fun(X_b,option(X_a))),hAPP(fun(X_b,option(X_a)),fun(X_b,fun(option(X_a),fun(X_b,option(X_a)))),fun_upd(X_b,option(X_a)),F),A_2),hAPP(X_a,option(X_a),some(X_a),B))),top_top(fun(X_b,bool))))))) # label(fact_639_finite__range__updI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 713 (all X_a all X_b all B_1 all A_1 all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),B_1)),A_1))))) # label(fact_640_vimage__subsetI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 714 (all X_a (lattice(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),A_1))))))) # label(fact_641_Inf__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 715 (all X_a (lattice(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),A_1)))))))) # label(fact_642_Inf__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 716 (all X_a (lattice(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),B_1)),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),A_1)) = hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),A_1))))))) # label(fact_643_Inf__fin_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 717 (all X_a (lattice(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),A_1)),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),B_1))))))))) # label(fact_644_Inf__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 718 (all X_a (lattice(X_a) -> (all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),semilattice_inf_inf(X_a)),A_2),A_1))))) # label(fact_645_Inf__fin_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 719 (all X_a (lattice(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),semilattice_inf_inf(X_a)),X_2),A_1)))))) # label(fact_646_Inf__fin_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 720 (all X_a (lattice(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),A_1) = ti(X_a,X_2)) & (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))))))))) # label(fact_647_Inf__fin_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 721 (all X_a (lattice(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = ti(X_a,X_2)) & (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))))))))) # label(fact_648_Inf__fin_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 722 (all X_a (lattice(X_a) -> (all N all H ((all X_1 all Y_1 hAPP(X_a,X_a,H,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,H,X_1)),hAPP(X_a,X_a,H,Y_1))) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),N)) -> (ti(fun(X_a,bool),N) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,H,hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),N)) = hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),H),N)))))))) # label(fact_649_Inf__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 723 (all X_a (lattice(X_a) -> (all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> ((all X_1 all Y_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_1),bot_bot(fun(X_a,bool))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),A_1)),A_1)))))))) # label(fact_650_Inf__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 724 (all X_a all X_b all F (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),F))) -> (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),top_top(fun(X_a,bool)))) -> (exists X_1 hAPP(X_a,option(X_b),F,X_1) = none(X_b))))) # label(fact_651_finite__map__freshness) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 725 (all X_a all X_b all B all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))))) -> -(all X_1 ti(X_a,B) != hAPP(X_b,X_a,F,X_1)))) # label(fact_652_rangeE) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 726 (all X_a all X_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),top_top(fun(X_a,bool))))) # label(fact_653_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 727 (all X_a all X_b all F ((all X_1 all Y_1 (hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Y_1) -> ti(X_a,X_1) = ti(X_a,Y_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))))) # label(fact_654_injI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 728 (all X_b all X_a all F (hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool)) <-> (all Y_1 exists X_1 ti(X_a,Y_1) = hAPP(X_b,X_a,F,X_1)))) # label(fact_655_surj__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 729 (all X_b all X_a all G all F ((all X_1 hAPP(X_b,X_a,G,hAPP(X_a,X_b,F,X_1)) = ti(X_a,X_1)) -> hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),G),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool)))) # label(fact_656_surjI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 730 (all X_b all X_a all Y_2 all F (hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool)) -> (exists X_1 ti(X_a,Y_2) = hAPP(X_b,X_a,F,X_1)))) # label(fact_657_surjD) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 731 (all X_b all X_a all Y_2 all F (hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool)) -> -(all X_1 ti(X_a,Y_2) != hAPP(X_b,X_a,F,X_1)))) # label(fact_658_surjE) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 732 (all X_a all A_1 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),top_top(fun(X_a,bool)))) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (exists A_4 -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_4),A_1)))))) # label(fact_659_ex__new__if__finite) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 733 (all X_a (lattice(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1))),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),A_1)),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),B_1)))))))) # label(fact_660_Sup__fin_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 734 (all X_a (lattice(X_a) -> (all X_2 hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = ti(X_a,X_2)))) # label(fact_661_Sup__fin_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 735 (all X_a (lattice(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),A_1)) = hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),A_1)))))) # label(fact_662_Sup__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 736 (all X_a (lattice(X_a) -> (all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),A_1)) = ti(X_a,A_2)))))) # label(fact_663_inf__Sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 737 (all X_a (lattice(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),A_1))))))) # label(fact_664_Sup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 738 (all X_a (lattice(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),A_1)))))))) # label(fact_665_Sup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 739 (all X_a (lattice(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),B_1)),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),A_1)) = hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),A_1))))))) # label(fact_666_Sup__fin_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 740 (all X_a (lattice(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),A_1)),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),B_1))))))))) # label(fact_667_Sup__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 741 (all X_a (lattice(X_a) -> (all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),A_1)),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),A_1)))))))) # label(fact_668_Inf__le__Sup) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 742 (all X_a (lattice(X_a) -> (all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),semilattice_sup_sup(X_a)),A_2),A_1))))) # label(fact_669_Sup__fin_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 743 (all X_a (lattice(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),semilattice_sup_sup(X_a)),X_2),A_1)))))) # label(fact_670_Sup__fin_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 744 (all X_a (lattice(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = ti(X_a,X_2)) & (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))))))))) # label(fact_671_Sup__fin_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 745 (all X_a (lattice(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),A_1) = ti(X_a,X_2)) & (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))))))))) # label(fact_672_Sup__fin_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 746 (all X_a (lattice(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),A_1)),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),B_1)))))))))) # label(fact_673_Sup__fin_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 747 (all X_a (lattice(X_a) -> (all N all H ((all X_1 all Y_1 hAPP(X_a,X_a,H,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,H,X_1)),hAPP(X_a,X_a,H,Y_1))) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),N)) -> (ti(fun(X_a,bool),N) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,H,hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),N)) = hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),H),N)))))))) # label(fact_674_Sup__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 748 (all X_a (lattice(X_a) -> (all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> ((all X_1 all Y_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_1),bot_bot(fun(X_a,bool))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),A_1)),A_1)))))))) # label(fact_675_Sup__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 749 (all X_a all X_b all M_1 all X_2 all Y_2 hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),M_1),X_2),hAPP(X_b,option(X_b),some(X_b),Y_2))),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))) = hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),M_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))) # label(fact_676_restrict__upd__same) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 750 (all X_a all C all A_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1))))) # label(fact_677_ComplI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 751 (all X_a (ordered_ab_group_add(X_a) -> (all A_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),uminus_uminus(X_a)),A_1))))) # label(fact_678_inj__uminus) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 752 (all X_a (boolean_algebra(X_a) -> (all X all Y hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))) # label(fact_679_compl__inf) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 753 (all X_a (boolean_algebra(X_a) -> (all X all Y hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))) # label(fact_680_compl__sup) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 754 (all X_b all X_a all F all A_1 hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),A_1))) # label(fact_681_vimage__Compl) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 755 (all X_a all P_1 all Q_2 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fimplies),P_1)),Q_2)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_2))) # label(fact_682_Collect__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 756 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y)))))) # label(fact_683_compl__le__swap2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 757 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,uminus_uminus(X_a),X))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))))) # label(fact_684_compl__le__swap1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 758 (all X_a (boolean_algebra(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y)),hAPP(X_a,X_a,uminus_uminus(X_a),X))))))) # label(fact_685_compl__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 759 (all X_a (boolean_algebra(X_a) -> (all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X_2)),hAPP(X_a,X_a,uminus_uminus(X_a),Y_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_2)))))) # label(fact_686_compl__le__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 760 (all X_a all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_1)))) # label(fact_687_Compl__subset__Compl__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.35 761 (all X_a all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_1)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1))))) # label(fact_688_Compl__anti__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 762 (all X_a all P_1 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),P_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) # label(fact_689_Collect__neg__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 763 (all X_a all C all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1)))) # label(fact_690_ComplE) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 764 (all X_a all C all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1)))) # label(fact_691_ComplD) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 765 (all X_a all A_1 all B_1 (hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_1) <-> ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B_1))) # label(fact_692_Compl__eq__Compl__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 766 (all X_a all C all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1))) <-> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1)))) # label(fact_693_Compl__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 767 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1)) = ti(fun(X_a,bool),A_1)) # label(fact_694_double__complement) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 768 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1)))) # label(fact_695_Compl__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 769 (all X_a (boolean_algebra(X_a) -> (all X_2 all Y_2 (hAPP(X_a,X_a,uminus_uminus(X_a),X_2) = hAPP(X_a,X_a,uminus_uminus(X_a),Y_2) <-> ti(X_a,X_2) = ti(X_a,Y_2))))) # label(fact_696_compl__eq__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 770 (all X_b all X_a (uminus(X_a) -> (all A_1 all X_2 hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),uminus_uminus(fun(X_b,X_a)),A_1),X_2) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_b,X_a,A_1,X_2))))) # label(fact_697_uminus__apply) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 771 (all X_a (boolean_algebra(X_a) -> (all X hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = ti(X_a,X)))) # label(fact_698_double__compl) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 772 (all X_a all X_b (uminus(X_b) -> (all A_1 all X_1 hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),uminus_uminus(fun(X_a,X_b)),A_1),X_1) = hAPP(X_b,X_b,uminus_uminus(X_b),hAPP(X_a,X_b,A_1,X_1))))) # label(fact_699_fun__Compl__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 773 (all X_a (group_add(X_a) -> (all A_2 all B (hAPP(X_a,X_a,uminus_uminus(X_a),A_2) = hAPP(X_a,X_a,uminus_uminus(X_a),B) <-> ti(X_a,A_2) = ti(X_a,B))))) # label(fact_700_neg__equal__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 774 (all X_a (group_add(X_a) -> (all A_2 all B (hAPP(X_a,X_a,uminus_uminus(X_a),A_2) = ti(X_a,B) <-> hAPP(X_a,X_a,uminus_uminus(X_a),B) = ti(X_a,A_2))))) # label(fact_701_minus__equation__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 775 (all X_a (group_add(X_a) -> (all A_2 all B (ti(X_a,A_2) = hAPP(X_a,X_a,uminus_uminus(X_a),B) <-> ti(X_a,B) = hAPP(X_a,X_a,uminus_uminus(X_a),A_2))))) # label(fact_702_equation__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 776 (all X_a (group_add(X_a) -> (all A_3 hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_3)) = ti(X_a,A_3)))) # label(fact_703_minus__minus) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 777 (all X_a (ordered_ab_group_add(X_a) -> (all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B_2)),hAPP(X_a,X_a,uminus_uminus(X_a),A_3))))))) # label(fact_704_le__imp__neg__le) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 778 (all X_a (ordered_ab_group_add(X_a) -> (all B all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B)),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B)))))) # label(fact_705_neg__le__iff__le) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 779 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),B)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B)),A_2)))))) # label(fact_706_minus__le__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 780 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_a,X_a,uminus_uminus(X_a),B))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))))))) # label(fact_707_le__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 781 (all X_a (ab_group_add(X_a) -> (all A_3 all B_2 hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_3),B_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B_2),A_3)))) # label(fact_708_minus__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 782 (all X_a (boolean_algebra(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))) # label(fact_709_diff__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 783 (all X_a (boolean_algebra(X_a) -> hAPP(X_a,X_a,uminus_uminus(X_a),bot_bot(X_a)) = top_top(X_a))) # label(fact_710_compl__bot__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 784 (all X_a (boolean_algebra(X_a) -> hAPP(X_a,X_a,uminus_uminus(X_a),top_top(X_a)) = bot_bot(X_a))) # label(fact_711_compl__top__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 785 (all X_a (boolean_algebra(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = bot_bot(X_a)))) # label(fact_712_inf__compl__bot) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 786 (all X_a (boolean_algebra(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),X) = bot_bot(X_a)))) # label(fact_713_compl__inf__bot) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 787 (all X_a (boolean_algebra(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),X) = top_top(X_a)))) # label(fact_714_compl__sup__top) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 788 (all X_a (boolean_algebra(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = top_top(X_a)))) # label(fact_715_sup__compl__top) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 789 (all X_a all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1))) <-> ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)))) # label(fact_716_subset__Compl__self__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 790 (all X_a hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),bot_bot(fun(X_a,bool))) = top_top(fun(X_a,bool))) # label(fact_717_Compl__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 791 (all X_a hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),top_top(fun(X_a,bool))) = bot_bot(fun(X_a,bool))) # label(fact_718_Compl__UNIV__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 792 (all X_a all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),top_top(fun(X_a,bool))))))) # label(fact_719_finite__compl) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 793 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1)) = bot_bot(fun(X_a,bool))) # label(fact_720_Compl__disjoint) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 794 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1)),A_1) = bot_bot(fun(X_a,bool))) # label(fact_721_Compl__disjoint2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 795 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1)) = top_top(fun(X_a,bool))) # label(fact_722_Compl__partition) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 796 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1)),A_1) = top_top(fun(X_a,bool))) # label(fact_723_Compl__partition2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 797 (all X_a all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_1))) # label(fact_724_Compl__Int) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 798 (all X_a all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_1))) # label(fact_725_Compl__Un) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 799 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),top_top(fun(X_a,bool))),A_1)) # label(fact_726_Compl__eq__Diff__UNIV) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 800 (all X_a all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)) # label(fact_727_Diff__Compl) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 801 (all X_a all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_1))) # label(fact_728_Diff__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 802 (all X_a all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1)),B_1)) # label(fact_729_Compl__Diff__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 803 (all X_a all A_1 all B_1 (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1) = bot_bot(fun(X_a,bool)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_1))))) # label(fact_730_disjoint__eq__subset__Compl) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 804 (all X_b all X_a all A_1 all F (hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_1)))))) # label(fact_731_surj__Compl__image__subset) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 805 (all X_b all X_a all B_1 all D_1 all C all A_1 ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),D_1),A_1)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_b,X_a),fun(fun(X_a,bool),fun(X_b,bool)),vimage(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(X_a,fun(X_b,fun(X_a,X_a)),hAPP(fun(X_b,fun(X_a,fun(X_a,X_a))),fun(X_a,fun(X_b,fun(X_a,X_a))),combc(X_b,X_a,fun(X_a,X_a)),hAPP(fun(X_b,bool),fun(X_b,fun(X_a,fun(X_a,X_a))),hAPP(fun(bool,fun(X_a,fun(X_a,X_a))),fun(fun(X_b,bool),fun(X_b,fun(X_a,fun(X_a,X_a)))),combb(bool,fun(X_a,fun(X_a,X_a)),X_b),if(X_a)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_1))),C)),D_1)),A_1) = top_top(fun(X_b,bool))) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),D_1),A_1)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_b,X_a),fun(fun(X_a,bool),fun(X_b,bool)),vimage(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(X_a,fun(X_b,fun(X_a,X_a)),hAPP(fun(X_b,fun(X_a,fun(X_a,X_a))),fun(X_a,fun(X_b,fun(X_a,X_a))),combc(X_b,X_a,fun(X_a,X_a)),hAPP(fun(X_b,bool),fun(X_b,fun(X_a,fun(X_a,X_a))),hAPP(fun(bool,fun(X_a,fun(X_a,X_a))),fun(fun(X_b,bool),fun(X_b,fun(X_a,fun(X_a,X_a)))),combb(bool,fun(X_a,fun(X_a,X_a)),X_b),if(X_a)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_1))),C)),D_1)),A_1) = ti(fun(X_b,bool),B_1))) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),D_1),A_1)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_b,X_a),fun(fun(X_a,bool),fun(X_b,bool)),vimage(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(X_a,fun(X_b,fun(X_a,X_a)),hAPP(fun(X_b,fun(X_a,fun(X_a,X_a))),fun(X_a,fun(X_b,fun(X_a,X_a))),combc(X_b,X_a,fun(X_a,X_a)),hAPP(fun(X_b,bool),fun(X_b,fun(X_a,fun(X_a,X_a))),hAPP(fun(bool,fun(X_a,fun(X_a,X_a))),fun(fun(X_b,bool),fun(X_b,fun(X_a,fun(X_a,X_a)))),combb(bool,fun(X_a,fun(X_a,X_a)),X_b),if(X_a)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_1))),C)),D_1)),A_1) = hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),B_1)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),D_1),A_1)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_b,X_a),fun(fun(X_a,bool),fun(X_b,bool)),vimage(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(X_a,fun(X_b,fun(X_a,X_a)),hAPP(fun(X_b,fun(X_a,fun(X_a,X_a))),fun(X_a,fun(X_b,fun(X_a,X_a))),combc(X_b,X_a,fun(X_a,X_a)),hAPP(fun(X_b,bool),fun(X_b,fun(X_a,fun(X_a,X_a))),hAPP(fun(bool,fun(X_a,fun(X_a,X_a))),fun(fun(X_b,bool),fun(X_b,fun(X_a,fun(X_a,X_a)))),combb(bool,fun(X_a,fun(X_a,X_a)),X_b),if(X_a)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_1))),C)),D_1)),A_1) = bot_bot(fun(X_b,bool)))))) # label(fact_732_vimage__if) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 806 (all X_a (boolean_algebra(X_a) -> (all X all Y (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y) = bot_bot(X_a) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y) = top_top(X_a) -> hAPP(X_a,X_a,uminus_uminus(X_a),X) = ti(X_a,Y)))))) # label(fact_733_compl__unique) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 807 (all X_a all X_b all A_1 all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1))),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))))) # label(fact_734_inj__image__Compl__subset) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 808 (all X_b all X_a all P_1 all H all G all A_1 all F all Z_2 all Fa (hBOOL(hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool,hAPP(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool)),big_comm_monoid_big(X_a,X_b),F),Z_2),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_b,fun(X_a,fun(X_a,X_a))),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combs(X_b,X_a,fun(X_a,X_a)),hAPP(fun(X_b,bool),fun(X_b,fun(X_a,fun(X_a,X_a))),hAPP(fun(bool,fun(X_a,fun(X_a,X_a))),fun(fun(X_b,bool),fun(X_b,fun(X_a,fun(X_a,X_a)))),combb(bool,fun(X_a,fun(X_a,X_a)),X_b),if(X_a)),P_1)),H)),G)),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,H),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_1),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),P_1)))),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,G),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_1),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),P_1)))))))) # label(fact_735_comm__monoid__big_OIf__cases) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 809 (all X_a all X_b all F all X_2 hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),restrict_map(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))) = hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),F),X_2),none(X_b))) # label(fact_736_restrict__complement__singleton__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 810 (all X_b all X_a all Q_2 all P_1 all F ((all X_1 (hBOOL(hAPP(X_b,bool,P_1,hAPP(X_a,X_b,F,X_1))) <-> hBOOL(hAPP(X_a,bool,Q_2,X_1)))) -> hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_a,X_b),fun(fun(X_b,bool),fun(X_a,bool)),vimage(X_a,X_b),F),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),P_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_2))) # label(fact_737_vimage__Collect) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 811 (all X_a all X_b all B_1 all X_2 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),A_1),F),X_2)),B_1)))))) # label(fact_738_the__inv__into__into) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 812 (all X_a (comple44059174attice(X_a) -> (all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),A_1) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),semilattice_inf_inf(X_a)),top_top(X_a)),A_1))))) # label(fact_739_Inf__fold__inf) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 813 (all X_a all M ((exists X_1 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_1),M)) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),X_1)))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),M))))) # label(fact_740_finite__Inter) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 814 (all X_a all X_b all X_2 all Y_2 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> (hAPP(X_a,X_b,F,X_2) = ti(X_b,Y_2) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),A_1),F),Y_2) = ti(X_a,X_2))))) # label(fact_741_the__inv__into__f__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 815 (all X_a all X_b all X_2 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),A_1),F),hAPP(X_a,X_b,F,X_2)) = ti(X_a,X_2)))) # label(fact_742_the__inv__into__f__f) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 816 (all X_a all X_b all A_1 all F all X_1 hAPP(X_a,X_b,hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),the_inv_into(X_b,X_a),A_1),F),X_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(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_1))),hAPP(X_a,fun(X_b,bool),hAPP(fun(X_b,fun(X_a,bool)),fun(X_a,fun(X_b,bool)),combc(X_b,X_a,bool),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,bool)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,bool))),combb(X_a,fun(X_a,bool),X_b),fequal(X_a)),F)),X_1)))) # label(fact_743_the__inv__into__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 817 (all X_a all X_b all X_2 all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) -> hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F),hAPP(X_a,X_b,F,X_2)) = ti(X_a,X_2))) # label(fact_744_the__inv__f__f) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 818 (all X_a all X_b all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),inj_on(X_b,X_a),hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),A_1),F)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))))) # label(fact_745_inj__on__the__inv__into) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 819 (all X_a all X_b all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),A_1),F)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)) = ti(fun(X_a,bool),A_1))) # label(fact_746_the__inv__into__onto) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 820 (all X_a all X_b all Y_2 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) -> hAPP(X_a,X_b,F,hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),A_1),F),Y_2)) = ti(X_b,Y_2)))) # label(fact_747_f__the__inv__into__f) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 821 (all X_a (comple44059174attice(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_1),hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),A_1)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),semilattice_inf_inf(X_a)),B_1),A_1))))) # label(fact_748_inf__Inf__fold__inf) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 822 (all X_a (comple44059174attice(X_a) -> (all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),A_1) = hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),A_1)))))) # label(fact_749_Inf__fin__Inf) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 823 (all X_a (comple44059174attice(X_a) -> (all A_2 all B hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),bot_bot(fun(X_a,bool))))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B)))) # label(fact_750_Inf__binary) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 824 (all X_a (comple44059174attice(X_a) -> (all A_1 all B_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),A_1)),hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),B_1))),hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1))))))) # label(fact_751_less__eq__Inf__inter) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 825 (all X_a all X_4 all A_1 all C_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),C_2))) -> (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_4),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),X_4))))) # label(fact_752_InterE) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 826 (all X_a all X_4 all A_1 all C_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),C_2))) -> (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_4),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),X_4))))) # label(fact_753_InterD) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 827 (all X_a hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),top_top(fun(fun(X_a,bool),bool))) = bot_bot(fun(X_a,bool))) # label(fact_754_Inter__UNIV) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 828 (all X_a all B_1 all A_1 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),B_1),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),A_1)),B_1)))) # label(fact_755_Inter__lower) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 829 (all X_a all B_1 all A_1 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),B_1),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),A_1)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),B_1))))) # label(fact_756_Inter__anti__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 830 (all X_a hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),bot_bot(fun(fun(X_a,bool),bool))) = top_top(fun(X_a,bool))) # label(fact_757_Inter__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 831 (all X_a all A_1 all B_1 hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),semilattice_sup_sup(fun(fun(X_a,bool),bool)),A_1),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),A_1)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),B_1))) # label(fact_758_Inter__Un__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 832 (all X_a all A_2 all B_1 hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),insert(fun(X_a,bool)),A_2),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_2),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),B_1))) # label(fact_759_Inter__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 833 (all X_a all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1) = hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),insert(fun(X_a,bool)),A_1),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),insert(fun(X_a,bool)),B_1),bot_bot(fun(fun(X_a,bool),bool)))))) # label(fact_760_Int__eq__Inter) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 834 (all X_a all A_1 all B_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),A_1)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),B_1))),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),semilattice_inf_inf(fun(fun(X_a,bool),bool)),A_1),B_1))))) # label(fact_761_Inter__Un__subset) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 835 (all X_a (comple44059174attice(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),A_1))) <-> (all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X_1)))))))) # label(fact_762_le__Inf__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 836 (all X_a (comple44059174attice(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),A_1)),X_2)))))) # label(fact_763_Inf__lower) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 837 (all X_a (comple44059174attice(X_a) -> (all V_1 all U all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),U),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),U),V_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),A_1)),V_1))))))) # label(fact_764_Inf__lower2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 838 (all X_a (comple44059174attice(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),A_1)),hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),B_1))))))) # label(fact_765_Inf__superset__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 839 (all X_a (comple44059174attice(X_a) -> (all A_2 hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),bot_bot(fun(X_a,bool)))) = ti(X_a,A_2)))) # label(fact_766_Inf__singleton) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 840 (all X_a (comple44059174attice(X_a) -> hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),bot_bot(fun(X_a,bool))) = top_top(X_a))) # label(fact_767_Inf__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 841 (all X_a (comple44059174attice(X_a) -> hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),top_top(fun(X_a,bool))) = bot_bot(X_a))) # label(fact_768_Inf__UNIV) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 842 (all X_a (comple44059174attice(X_a) -> (all A_2 all A_1 hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),A_1))))) # label(fact_769_Inf__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 843 (all X_a (comple1742628961attice(X_a) -> (all B_1 all A_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),B_1)),A_2) = top_top(X_a) <-> (all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),A_2) = top_top(X_a))))))) # label(fact_770_Inf__sup__eq__top__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 844 (all X_a (comple44059174attice(X_a) -> (all A_1 all B_1 hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),A_1)),hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),B_1))))) # label(fact_771_Inf__union__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 845 (all X_a all A_1 all C_2 ((all X_3 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_3),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),X_3)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),C_2))))) # label(fact_772_InterI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 846 (all X_a (comple44059174attice(X_a) -> (all U all A_1 ((all V (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),V),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),V),U)))) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),A_1)),U))))))) # label(fact_773_Inf__less__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 847 (all X_b all X_a all F all S (ti(fun(fun(X_a,bool),bool),S) != bot_bot(fun(fun(X_a,bool),bool)) -> ((all A_5 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_5),S)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_5)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),S)))))) # label(fact_774_inj__on__Inter) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 848 (all X_a all B_1 all A_1 ((all X_3 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_3),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),X_3),B_1)))) -> (ti(fun(fun(X_a,bool),bool),A_1) != bot_bot(fun(fun(X_a,bool),bool)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),A_1)),B_1))))) # label(fact_775_Inter__subset) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 849 (all X_a all C_2 all A_1 ((all X_3 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_3),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),C_2),X_3)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),C_2),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Inf_Inf(fun(X_a,bool)),A_1))))) # label(fact_776_Inter__greatest) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 850 (all X_a (comple44059174attice(X_a) -> (all Z_2 all A_1 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_2),X_1)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_2),hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),A_1))))))) # label(fact_777_Inf__greatest) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 851 (all X_a all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),powp(X_a),A_1)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),powp(X_a),B_1))))) # label(fact_778_Powp__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 852 (all X_b all X_a all F all A_1 ((all X_1 all Y_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1)) -> (hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Y_1) -> ti(X_a,X_1) = ti(X_a,Y_1))))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)))) # label(fact_779_inj__onI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 853 (all X_b all X_a all G all F all A_1 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hAPP(X_b,X_a,G,hAPP(X_a,X_b,F,X_1)) = ti(X_a,X_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)))) # label(fact_780_inj__on__inverseI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 854 (all X_b all X_a all F all G all A_1 ((all A_4 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_4),A_1)) -> hAPP(X_a,X_b,F,A_4) = hAPP(X_a,X_b,G,A_4))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),G),A_1))))) # label(fact_781_inj__on__cong) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 855 (all X_a (comple44059174attice(X_a) -> (all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_1) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),semilattice_sup_sup(X_a)),bot_bot(X_a)),A_1))))) # label(fact_782_Sup__fold__sup) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 856 (all X_a exists X_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),top_top(fun(X_a,bool))))) # label(fact_783_UNIV__witness) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 857 (all X_a (comple44059174attice(X_a) -> hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),top_top(fun(X_a,bool))) = top_top(X_a))) # label(fact_784_Sup__UNIV) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 858 (all X_a (comple44059174attice(X_a) -> (all A_2 all A_1 hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_1))))) # label(fact_785_Sup__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 859 (all X_a all C_2 all A_1 (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),C_2)),A_1) = bot_bot(fun(X_a,bool)) <-> (all X_1 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_1),C_2)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),X_1),A_1) = bot_bot(fun(X_a,bool)))))) # label(fact_786_Union__disjoint) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 860 (all X_a all A_1 all B_1 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),A_1),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_1)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),B_1))))) # label(fact_787_Union__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 861 (all X_a all B_1 all A_1 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),B_1),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_1))))) # label(fact_788_Union__upper) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 862 (all X_a hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),bot_bot(fun(fun(X_a,bool),bool))) = bot_bot(fun(X_a,bool))) # label(fact_789_Union__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 863 (all X_a (comple44059174attice(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_1)),B)) <-> (all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),B)))))))) # label(fact_790_Sup__le__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 864 (all X_a (comple44059174attice(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_1))))))) # label(fact_791_Sup__upper) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 865 (all X_a (comple44059174attice(X_a) -> (all V_1 all U all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),U),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),V_1),U)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),V_1),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_1)))))))) # label(fact_792_Sup__upper2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 866 (all X_a all A_2 all B_1 hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),insert(fun(X_a,bool)),A_2),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_2),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),B_1))) # label(fact_793_Union__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 867 (all X_a (comple44059174attice(X_a) -> (all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_1)),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),B_1))))))) # label(fact_794_Sup__subset__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 868 (all X_a (comple44059174attice(X_a) -> hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),bot_bot(fun(X_a,bool))) = bot_bot(X_a))) # label(fact_795_Sup__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 869 (all X_a (comple1742628961attice(X_a) -> (all B_1 all A_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),B_1)),A_2) = bot_bot(X_a) <-> (all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),A_2) = bot_bot(X_a))))))) # label(fact_796_Sup__inf__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 870 (all X_a (comple44059174attice(X_a) -> (all A_2 hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),bot_bot(fun(X_a,bool)))) = ti(X_a,A_2)))) # label(fact_797_Sup__singleton) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 871 (all X_a all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_1))) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite(fun(X_a,bool)),A_1)))) # label(fact_798_finite__UnionD) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 872 (all X_a (comple44059174attice(X_a) -> (all A_1 all B_1 hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_1)),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),B_1))))) # label(fact_799_Sup__union__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 873 (all X_a hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),top_top(fun(fun(X_a,bool),bool))) = top_top(fun(X_a,bool))) # label(fact_800_Union__UNIV) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 874 (all X_a all A_1 all B_1 hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),semilattice_sup_sup(fun(fun(X_a,bool),bool)),A_1),B_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_1)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),B_1))) # label(fact_801_Union__Un__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 875 (all X_a all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1) = hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),insert(fun(X_a,bool)),A_1),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),insert(fun(X_a,bool)),B_1),bot_bot(fun(fun(X_a,bool),bool)))))) # label(fact_802_Un__eq__Union) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 876 (all X_a (comple44059174attice(X_a) -> (all A_1 all B_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_1)),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),B_1))))))) # label(fact_803_Sup__inter__less__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 877 (all X_a (comple44059174attice(X_a) -> (all A_2 all B hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),bot_bot(fun(X_a,bool))))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B)))) # label(fact_804_Sup__binary) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 878 (all X_a all A_1 all B_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),semilattice_inf_inf(fun(fun(X_a,bool),bool)),A_1),B_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_1)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),B_1))))) # label(fact_805_Union__Int__subset) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 879 (all X_a (comple44059174attice(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_1),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_1)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),semilattice_sup_sup(X_a)),B_1),A_1))))) # label(fact_806_sup__Sup__fold__sup) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 880 (all X_a (comple61589808lgebra(X_a) -> (all A_1 hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),A_1)) = hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),uminus_uminus(X_a)),A_1))))) # label(fact_807_uminus__Inf) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 881 (all X_a (comple61589808lgebra(X_a) -> (all A_1 hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_1)) = hAPP(fun(X_a,bool),X_a,complete_Inf_Inf(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),uminus_uminus(X_a)),A_1))))) # label(fact_808_uminus__Sup) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 882 (all X_a (comple44059174attice(X_a) -> (all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),A_1) = hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_1)))))) # label(fact_809_Sup__fin__Sup) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 883 (all X_a all A_1 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite(fun(X_a,bool)),A_1)) -> ((all M_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),M_2),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),M_2)))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_1)))))) # label(fact_810_finite__Union) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 884 (all X_a all X_2 all Fa (-hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_2),Fa)) -> ((all X_1 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_1),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),insert(fun(X_a,bool)),X_2),Fa))) -> (all Xa (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),Xa),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),insert(fun(X_a,bool)),X_2),Fa))) -> (ti(fun(X_a,bool),X_1) != ti(fun(X_a,bool),Xa) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),X_1),Xa) = bot_bot(fun(X_a,bool))))))) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),X_2),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),Fa)) = bot_bot(fun(X_a,bool))))) # label(fact_811_insert__partition) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 885 (all X_a all A_1 all X_4 all C_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_4),C_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),X_4)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),C_2)))))) # label(fact_812_UnionI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 886 (all X_a all A_1 all C_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),C_2))) -> -(all X_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),X_3)) -> -hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_3),C_2)))))) # label(fact_813_UnionE) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 887 (all X_a (comple44059174attice(X_a) -> (all U all A_1 ((all V (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),V),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),U),V)))) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),U),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_1)))))))) # label(fact_814_less__eq__Sup) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 888 (all X_a all C_2 all A_1 ((all X_3 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_3),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),X_3),C_2)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_1)),C_2)))) # label(fact_815_Union__least) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 889 (all X_a (comple44059174attice(X_a) -> (all Z_2 all A_1 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z_2)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_1)),Z_2)))))) # label(fact_816_Sup__least) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 890 (all X_a all A_1 ((all X_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))) -> top_top(fun(X_a,bool)) = ti(fun(X_a,bool),A_1))) # label(fact_817_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 891 (all X_a all A_1 all B_1 hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),semilattice_sup_sup(fun(fun(X_a,bool),bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_1)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_1))),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1))))) # label(fact_818_Un__Pow__subset) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 892 (all X_a all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_1))))) # label(fact_819_PowI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 893 (all X_a all A_1 hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_1)) = ti(fun(X_a,bool),A_1)) # label(fact_820_Union__Pow__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 894 (all X_a all A_1 all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),powp(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1)),X_1)) <-> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_1),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_1))))) # label(fact_821_Powp__Pow__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 895 (all X_a all B_1 hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),bot_bot(fun(X_a,bool))),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_1)))) # label(fact_822_Pow__bottom) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 896 (all X_a all A_1 all B_1 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)))) # label(fact_823_PowD) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 897 (all X_a all A_1 all B_1 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)))) # label(fact_824_Pow__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 898 (all X_a all A_1 hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_1) = hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),combc(fun(X_a,bool),fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool))),A_1))) # label(fact_825_Pow__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 899 (all X_a all A_1 hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_1) != bot_bot(fun(fun(X_a,bool),bool))) # label(fact_826_Pow__not__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 900 (all X_a all A_1 hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_1)))) # label(fact_827_Pow__top) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 901 (all X_b all X_a all F all A_1 all B_1 (hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1) = ti(fun(X_a,bool),B_1) -> hAPP(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_b,bool),fun(X_a,bool)),fun(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool)),image(fun(X_b,bool),fun(X_a,bool)),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),pow(X_b),A_1)) = hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_1))) # label(fact_828_image__Pow__surj) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 902 (all X_a all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_1)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_1))))) # label(fact_829_Pow__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 903 (all X_a all A_1 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)))) # label(fact_830_finite__Pow__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 904 (all X_a all A_1 hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),A_1),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_1))))) # label(fact_831_subset__Pow__Union) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 905 (all X_a all A_2 all A_1 hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1)) = hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),semilattice_sup_sup(fun(fun(X_a,bool),bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_1)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),image(fun(X_a,bool),fun(X_a,bool)),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_1)))) # label(fact_832_Pow__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 906 (all X_a hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),top_top(fun(X_a,bool))) = top_top(fun(fun(X_a,bool),bool))) # label(fact_833_Pow__UNIV) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 907 (all X_a all A_1 all B_1 hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1)) = hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),semilattice_inf_inf(fun(fun(X_a,bool),bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_1)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_1))) # label(fact_834_Pow__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 908 (all X_a all X_b all F all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)),B_1)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_b,bool),fun(X_a,bool)),fun(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool)),image(fun(X_b,bool),fun(X_a,bool)),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),pow(X_b),A_1))),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_1))))) # label(fact_835_image__Pow__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 909 (all X_a hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),bot_bot(fun(X_a,bool))) = hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),insert(fun(X_a,bool)),bot_bot(fun(X_a,bool))),bot_bot(fun(fun(X_a,bool),bool)))) # label(fact_836_Pow__empty) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 910 (all X_a (distrib_lattice(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),A_1)),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),B_1)) = hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,fun(X_a,bool)),fun(X_a,bool)),combb(fun(X_a,bool),bool,X_a),fEx(X_a)),hAPP(fun(X_a,fun(X_a,fun(X_a,bool))),fun(X_a,fun(X_a,bool)),hAPP(fun(fun(X_a,fun(X_a,bool)),fun(X_a,bool)),fun(fun(X_a,fun(X_a,fun(X_a,bool))),fun(X_a,fun(X_a,bool))),combb(fun(X_a,fun(X_a,bool)),fun(X_a,bool),X_a),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,fun(X_a,bool)),fun(X_a,bool)),combb(fun(X_a,bool),bool,X_a),fEx(X_a))),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(X_a,bool))),hAPP(fun(X_a,fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(X_a,bool)))),combc(X_a,fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool))),hAPP(fun(X_a,fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),fun(X_a,fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)))),hAPP(fun(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)))),fun(fun(X_a,fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),fun(X_a,fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool))))),combb(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool))),X_a),combs(X_a,fun(X_a,bool),fun(X_a,bool))),hAPP(fun(X_a,fun(X_a,fun(X_a,fun(bool,bool)))),fun(X_a,fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),hAPP(fun(fun(X_a,fun(X_a,fun(bool,bool))),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),fun(fun(X_a,fun(X_a,fun(X_a,fun(bool,bool)))),fun(X_a,fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))))),combb(fun(X_a,fun(X_a,fun(bool,bool))),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),X_a),hAPP(fun(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,fun(X_a,fun(bool,bool))),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),combb(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),X_a),combs(X_a,bool,bool))),hAPP(fun(X_a,fun(X_a,fun(X_a,bool))),fun(X_a,fun(X_a,fun(X_a,fun(bool,bool)))),hAPP(fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(bool,bool)))),fun(fun(X_a,fun(X_a,fun(X_a,bool))),fun(X_a,fun(X_a,fun(X_a,fun(bool,bool))))),combb(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(bool,bool))),X_a),hAPP(fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(bool,bool)))),combb(fun(X_a,bool),fun(X_a,fun(bool,bool)),X_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj))),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,fun(X_a,bool))),hAPP(fun(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,bool)))),fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,fun(X_a,bool)))),combc(X_a,fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,bool))),hAPP(fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool))),fun(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,bool)))),hAPP(fun(fun(fun(X_a,X_a),fun(X_a,bool)),fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,bool)))),fun(fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool))),fun(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,bool))))),combb(fun(fun(X_a,X_a),fun(X_a,bool)),fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,bool))),X_a),combb(fun(X_a,X_a),fun(X_a,bool),X_a)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool))),hAPP(fun(fun(X_a,bool),fun(fun(X_a,X_a),fun(X_a,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool)))),combb(fun(X_a,bool),fun(fun(X_a,X_a),fun(X_a,bool)),X_a),combb(X_a,bool,X_a)),fequal(X_a)))),semilattice_inf_inf(X_a)))))),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(X_a,fun(X_a,bool))),combc(X_a,fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),combb(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),X_a),combb(bool,bool,X_a)),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1)))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_1)))))))))))))) # label(fact_837_inf__Sup2__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 911 (all X_a (distrib_lattice(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),A_1)) = hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,fun(X_a,bool)),fun(X_a,bool)),combb(fun(X_a,bool),bool,X_a),fEx(X_a)),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(X_a,fun(X_a,bool))),combc(X_a,fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,fun(bool,bool))),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,fun(X_a,fun(bool,bool))),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),combb(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),X_a),combs(X_a,bool,bool)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(bool,bool))),hAPP(fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(bool,bool)))),combb(fun(X_a,bool),fun(X_a,fun(bool,bool)),X_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj)),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool))),fun(fun(X_a,X_a),fun(X_a,fun(X_a,bool))),combc(X_a,fun(X_a,X_a),fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool))),hAPP(fun(fun(X_a,bool),fun(fun(X_a,X_a),fun(X_a,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool)))),combb(fun(X_a,bool),fun(fun(X_a,X_a),fun(X_a,bool)),X_a),combb(X_a,bool,X_a)),fequal(X_a))),hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_2))))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1)))))))))) # label(fact_838_inf__Sup1__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 912 (all X_b all X_a all F all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_b,fun(X_a,bool)),fun(X_b,bool)),combb(fun(X_a,bool),bool,X_b),fEx(X_a)),hAPP(fun(X_a,bool),fun(X_b,fun(X_a,bool)),hAPP(fun(X_b,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(X_b,fun(X_a,bool))),combc(X_b,fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_b,fun(X_a,fun(bool,bool))),fun(X_b,fun(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_b,fun(X_a,fun(bool,bool))),fun(X_b,fun(fun(X_a,bool),fun(X_a,bool)))),combb(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),X_b),combs(X_a,bool,bool)),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,fun(bool,bool))),hAPP(fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,fun(bool,bool)))),combb(fun(X_a,bool),fun(X_a,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj)),hAPP(fun(X_a,X_b),fun(X_b,fun(X_a,bool)),hAPP(fun(X_b,fun(fun(X_a,X_b),fun(X_a,bool))),fun(fun(X_a,X_b),fun(X_b,fun(X_a,bool))),combc(X_b,fun(X_a,X_b),fun(X_a,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_a,X_b),fun(X_a,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_a,X_b),fun(X_a,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_a,X_b),fun(X_a,bool)))),combb(fun(X_b,bool),fun(fun(X_a,X_b),fun(X_a,bool)),X_b),combb(X_b,bool,X_a)),fequal(X_b))),F)))),P_1))))))) # label(fact_839_finite__image__set) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 913 (all X_b all X_a all Q_2 all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_b,fun(X_a,bool)),fun(X_b,bool)),combb(fun(X_a,bool),bool,X_b),fEx(X_a)),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_b),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),P_1))),Q_2))))) <-> (all Y_1 (hBOOL(hAPP(X_a,bool,P_1,Y_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_a,fun(X_b,bool),hAPP(fun(X_b,fun(X_a,bool)),fun(X_a,fun(X_b,bool)),combc(X_b,X_a,bool),Q_2),Y_1))))))))) # label(fact_840_finite__Collect__bounded__ex) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 914 (all X_a all A_1 hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_1)) = hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),bool),hAPP(fun(fun(fun(X_a,bool),bool),bool),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),bool)),combb(fun(fun(X_a,bool),bool),bool,fun(X_a,bool)),fEx(fun(X_a,bool))),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(fun(X_a,bool),bool))),combc(fun(X_a,bool),fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),hAPP(fun(fun(fun(X_a,bool),fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)))),combb(fun(fun(X_a,bool),fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),fun(X_a,bool)),combs(fun(X_a,bool),bool,bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),hAPP(fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool)))),combb(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool)),fun(X_a,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X_a,bool)),fconj)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool))),combc(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool))),hAPP(fun(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool)))),combb(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool)),fun(X_a,bool)),combb(fun(X_a,bool),bool,fun(X_a,bool))),fequal(fun(X_a,bool)))),uminus_uminus(fun(X_a,bool)))))),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),bool),hAPP(fun(fun(fun(X_a,bool),bool),bool),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),bool)),combb(fun(fun(X_a,bool),bool),bool,fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_1)),pow(X_a)))))) # label(fact_841_Pow__Compl) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 915 (all X_b all X_a all M_1 hAPP(fun(X_b,option(X_a)),fun(X_a,bool),ran(X_b,X_a),M_1) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_a,fun(X_b,bool)),fun(X_a,bool)),combb(fun(X_b,bool),bool,X_a),fEx(X_b)),hAPP(fun(X_a,option(X_a)),fun(X_a,fun(X_b,bool)),hAPP(fun(option(X_a),fun(X_b,bool)),fun(fun(X_a,option(X_a)),fun(X_a,fun(X_b,bool))),combb(option(X_a),fun(X_b,bool),X_a),hAPP(fun(X_b,fun(option(X_a),bool)),fun(option(X_a),fun(X_b,bool)),combc(X_b,option(X_a),bool),hAPP(fun(X_b,option(X_a)),fun(X_b,fun(option(X_a),bool)),hAPP(fun(option(X_a),fun(option(X_a),bool)),fun(fun(X_b,option(X_a)),fun(X_b,fun(option(X_a),bool))),combb(option(X_a),fun(option(X_a),bool),X_b),fequal(option(X_a))),M_1))),some(X_a))))) # label(fact_842_ran__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 916 (all X_a (distrib_lattice(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),A_1)) = hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,fun(X_a,bool)),fun(X_a,bool)),combb(fun(X_a,bool),bool,X_a),fEx(X_a)),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(X_a,fun(X_a,bool))),combc(X_a,fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,fun(bool,bool))),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,fun(X_a,fun(bool,bool))),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),combb(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),X_a),combs(X_a,bool,bool)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(bool,bool))),hAPP(fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(bool,bool)))),combb(fun(X_a,bool),fun(X_a,fun(bool,bool)),X_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj)),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool))),fun(fun(X_a,X_a),fun(X_a,fun(X_a,bool))),combc(X_a,fun(X_a,X_a),fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool))),hAPP(fun(fun(X_a,bool),fun(fun(X_a,X_a),fun(X_a,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool)))),combb(fun(X_a,bool),fun(fun(X_a,X_a),fun(X_a,bool)),X_a),combb(X_a,bool,X_a)),fequal(X_a))),hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2))))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1)))))))))) # label(fact_843_sup__Inf1__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 917 (all X_a (distrib_lattice(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),A_1)),hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),B_1)) = hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,fun(X_a,bool)),fun(X_a,bool)),combb(fun(X_a,bool),bool,X_a),fEx(X_a)),hAPP(fun(X_a,fun(X_a,fun(X_a,bool))),fun(X_a,fun(X_a,bool)),hAPP(fun(fun(X_a,fun(X_a,bool)),fun(X_a,bool)),fun(fun(X_a,fun(X_a,fun(X_a,bool))),fun(X_a,fun(X_a,bool))),combb(fun(X_a,fun(X_a,bool)),fun(X_a,bool),X_a),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,fun(X_a,bool)),fun(X_a,bool)),combb(fun(X_a,bool),bool,X_a),fEx(X_a))),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(X_a,bool))),hAPP(fun(X_a,fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(X_a,bool)))),combc(X_a,fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool))),hAPP(fun(X_a,fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),fun(X_a,fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)))),hAPP(fun(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)))),fun(fun(X_a,fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),fun(X_a,fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool))))),combb(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool))),X_a),combs(X_a,fun(X_a,bool),fun(X_a,bool))),hAPP(fun(X_a,fun(X_a,fun(X_a,fun(bool,bool)))),fun(X_a,fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),hAPP(fun(fun(X_a,fun(X_a,fun(bool,bool))),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),fun(fun(X_a,fun(X_a,fun(X_a,fun(bool,bool)))),fun(X_a,fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))))),combb(fun(X_a,fun(X_a,fun(bool,bool))),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),X_a),hAPP(fun(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,fun(X_a,fun(bool,bool))),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),combb(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),X_a),combs(X_a,bool,bool))),hAPP(fun(X_a,fun(X_a,fun(X_a,bool))),fun(X_a,fun(X_a,fun(X_a,fun(bool,bool)))),hAPP(fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(bool,bool)))),fun(fun(X_a,fun(X_a,fun(X_a,bool))),fun(X_a,fun(X_a,fun(X_a,fun(bool,bool))))),combb(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(bool,bool))),X_a),hAPP(fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(bool,bool)))),combb(fun(X_a,bool),fun(X_a,fun(bool,bool)),X_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj))),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,fun(X_a,bool))),hAPP(fun(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,bool)))),fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,fun(X_a,bool)))),combc(X_a,fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,bool))),hAPP(fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool))),fun(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,bool)))),hAPP(fun(fun(fun(X_a,X_a),fun(X_a,bool)),fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,bool)))),fun(fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool))),fun(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,bool))))),combb(fun(fun(X_a,X_a),fun(X_a,bool)),fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,bool))),X_a),combb(fun(X_a,X_a),fun(X_a,bool),X_a)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool))),hAPP(fun(fun(X_a,bool),fun(fun(X_a,X_a),fun(X_a,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool)))),combb(fun(X_a,bool),fun(fun(X_a,X_a),fun(X_a,bool)),X_a),combb(X_a,bool,X_a)),fequal(X_a)))),semilattice_sup_sup(X_a)))))),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(X_a,fun(X_a,bool))),combc(X_a,fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),combb(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),X_a),combb(bool,bool,X_a)),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1)))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_1)))))))))))))) # label(fact_844_sup__Inf2__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 918 (all X_a all P_1 ((exists X1 hBOOL(hAPP(X_a,bool,P_1,X1))) <-> (all Q_1 ((all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(Q_1))) -> hBOOL(Q_1))))) # label(fact_845_Ex__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 919 (all X_a (linorder(X_a) -> (all M all N (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),M),N)) -> (ti(fun(X_a,bool),M) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),M)),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),N))))))))) # label(fact_846_Max__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 920 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_1)))))))) # label(fact_847_Max__ge) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 921 (all X_a (linorder(X_a) -> (all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_1)),A_1))))))) # label(fact_848_Max__in) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 922 (all X_a (linorder(X_a) -> (all X_2 hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = ti(X_a,X_2)))) # label(fact_849_Max_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 923 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> ((all Y_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_2)))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_1) = ti(X_a,X_2))))))) # label(fact_850_Max__eqI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 924 (all X_a (linord219039673up_add(X_a) -> (all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),S)) -> (ti(fun(X_a,bool),S) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),S)) = hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),uminus_uminus(X_a)),S))))))) # label(fact_851_minus__Min__eq__Max) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 925 (all X_a (linorder(X_a) -> (all X_2 hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = ti(X_a,X_2)))) # label(fact_852_Min_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 926 (all X_a (linorder(X_a) -> (all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_1)),A_1))))))) # label(fact_853_Min__in) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 927 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_1)),X_2))))))) # label(fact_854_Min__le) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 928 (all X_a (linorder(X_a) -> (all M all N (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),M),N)) -> (ti(fun(X_a,bool),M) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),N)),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),M))))))))) # label(fact_855_Min__antimono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 929 (all X_a (linord219039673up_add(X_a) -> (all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),S)) -> (ti(fun(X_a,bool),S) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),S)) = hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),uminus_uminus(X_a)),S))))))) # label(fact_856_minus__Max__eq__Min) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 930 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> ((all Y_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_1) = ti(X_a,X_2))))))) # label(fact_857_Min__eqI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 931 (all X_a (linorder(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1))),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_1)),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),B_1)))))))) # label(fact_858_Min_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 932 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_1)) = hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_1)))))) # label(fact_859_Min_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 933 (all X_a (semilattice_inf(X_a) & linorder(X_a) -> semilattice_inf_inf(X_a) = ord_min(X_a))) # label(fact_860_inf__min) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 934 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),X))))) # label(fact_861_min__max_Oinf__le1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 935 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Y))))) # label(fact_862_min__max_Oinf__le2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 936 (all X_a (linorder(X_a) -> (all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),Y_2) = ti(X_a,X_2))))) # label(fact_863_min__max_Ole__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 937 (all X_a (linorder(X_a) -> (all X_2 all Y_2 all Z_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y_2),Z_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z_2)))))) # label(fact_864_min__max_Ole__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 938 (all X_a (linorder(X_a) -> (all B_2 all A_3 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),B_2)),X)))))) # label(fact_865_min__max_Ole__infI1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 939 (all X_a (linorder(X_a) -> (all A_3 all B_2 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),B_2)),X)))))) # label(fact_866_min__max_Ole__infI2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 940 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y) = ti(X_a,X))))) # label(fact_867_min__max_Oinf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 941 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y) = ti(X_a,Y))))) # label(fact_868_min__max_Oinf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 942 (all X_a (linorder(X_a) -> (all B_2 all X all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),B_2)))))))) # label(fact_869_min__max_Ole__infI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 943 (all X_a (linorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z)))))))) # label(fact_870_min__max_Oinf__greatest) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 944 (all X_a (linorder(X_a) -> (all B_2 all D all A_3 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),B_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),C_1),D)))))))) # label(fact_871_min__max_Oinf__mono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 945 (all X_a (linorder(X_a) -> (all X all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),B_2))) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_3)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_2))))))) # label(fact_872_min__max_Ole__infE) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 946 (all X_a (linorder(X_a) -> (all X_2 all Y_2 all Z_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),Y_2)),Z_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),Z_2)))))) # label(fact_873_min__le__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 947 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z))))) # label(fact_874_min__max_Oinf__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 948 (all X_a (linorder(X_a) -> (all A_3 all B_2 all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),B_2)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B_2),C_1))))) # label(fact_875_min__max_Oinf_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 949 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z))))) # label(fact_876_min__max_Oinf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 950 (all X_a (linorder(X_a) -> (all B_2 all A_3 all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B_2),C_1))))) # label(fact_877_min__max_Oinf_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 951 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)))) # label(fact_878_min__max_Oinf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 952 (all X_a (linorder(X_a) -> (all A_3 all B_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),B_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),B_2)))) # label(fact_879_min__max_Oinf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 953 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),X)))) # label(fact_880_min__max_Oinf__commute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 954 (all X_a (linorder(X_a) -> (all A_3 all B_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),B_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B_2),A_3)))) # label(fact_881_min__max_Oinf_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 955 (all X_a (linorder(X_a) -> (all A_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),A_3) = ti(X_a,A_3)))) # label(fact_882_min__max_Oinf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 956 (all X_a (ordered_ab_group_add(X_a) -> (all X all Y all Z 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),ord_min(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z))))) # label(fact_883_min__diff__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 957 (all X_a (linorder(X_a) -> hBOOL(hAPP(fun(X_a,fun(X_a,X_a)),bool,finite_comp_fun_idem(X_a,X_a),ord_min(X_a))))) # label(fact_884_min__max_Ocomp__fun__idem__inf) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 958 (all X_a (linorder(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),X) = ti(X_a,X)))) # label(fact_885_Min_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 959 (all X_a (linorder(X_a) -> (all B all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_min(X_a)),B),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_2),B)))))))) # label(fact_886_min__max_Ofold__inf__le__inf) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 960 (all X_a (linorder(X_a) -> (all B all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_min(X_a)),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_2),hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_min(X_a)),B),A_1)))))) # label(fact_887_min__max_Ofold__inf__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 961 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_1)))))))) # label(fact_888_Min_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 962 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_1))))))) # label(fact_889_Min__insert) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 963 (all X_a (linorder(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),B_1)),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_1)) = hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_1))))))) # label(fact_890_Min_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 964 (all X_a (linorder(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_1)),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),B_1))))))))) # label(fact_891_Min__Un) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 965 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_min(X_a)),X_2),A_1)))))) # label(fact_892_Min_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 966 (all X_a (linorder(X_a) -> (all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_min(X_a)),A_2),A_1))))) # label(fact_893_Min_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 967 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = ti(X_a,X_2)) & (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))))))))) # label(fact_894_Min_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 968 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_1) = ti(X_a,X_2)) & (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))))))))) # label(fact_895_Min_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 969 (all X_a (linorder(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_1)),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),B_1)))))))))) # label(fact_896_Min_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 970 (all X_a (linorder(X_a) -> (all N all H ((all X_1 all Y_1 hAPP(X_a,X_a,H,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,H,X_1)),hAPP(X_a,X_a,H,Y_1))) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),N)) -> (ti(fun(X_a,bool),N) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,H,hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),N)) = hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),H),N)))))))) # label(fact_897_Min_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 971 (all X_a (linorder(X_a) -> (all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> ((all X_1 all Y_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_1),bot_bot(fun(X_a,bool))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_1)),A_1)))))))) # label(fact_898_Min_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 972 (all X_a (linorder(X_a) -> (all C all B all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X_1)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),C)),hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_min(X_a)),C),A_1)))))))) # label(fact_899_min__max_Oinf__le__fold__inf) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 973 (all X_a (linorder(X_a) -> hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),max(X_a),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),ord_less_eq(X_a))) = ord_min(X_a))) # label(fact_900_dual__max) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 974 (all X_a (order(X_a) -> (all X all Least ((all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_1))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Least) = ti(X_a,Least))))) # label(fact_901_min__leastR) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 975 (all X_a (ord(X_a) -> (all X all Least ((all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_1))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Least),X) = ti(X_a,Least))))) # label(fact_902_min__leastL) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 976 (all X_a (ord(X_a) -> ord_min(X_a) = hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),min(X_a),ord_less_eq(X_a)))) # label(fact_903_min__ord__min) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 977 (all X_a (linorder(X_a) -> (all B_1 all A_1 (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),ord_min(X_a)),B_1)),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),ord_min(X_a)),A_1))))))))) # label(fact_904_fold1__antimono) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 978 (all X_a all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_a,Fa,A_1) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),F),A_1)))) # label(fact_905_folding__one_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 979 (all X_a all A_2 all G all F (G = hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),F) -> hAPP(fun(X_a,bool),X_a,G,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),bot_bot(fun(X_a,bool)))) = ti(X_a,A_2))) # label(fact_906_fold1__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 980 (all X_a all F all A_2 hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),bot_bot(fun(X_a,bool)))) = ti(X_a,A_2)) # label(fact_907_fold1__singleton) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 981 (all X_a (semilattice_inf(X_a) -> (all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),semilattice_inf_inf(X_a)),A_1)),A_2))))))) # label(fact_908_fold1__belowI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 982 (all X_a (linorder(X_a) -> (all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),ord_min(X_a)),A_1)),A_2))))))) # label(fact_909_min__max_Ofold1__belowI) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 983 (all X_a (lattice(X_a) -> (all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Sup_fin(X_a),A_1) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),semilattice_sup_sup(X_a)),A_1))))) # label(fact_910_Sup__fin_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.37 984 (all X_a (lattice(X_a) -> (all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_a,big_lattice_Inf_fin(X_a),A_1) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),semilattice_inf_inf(X_a)),A_1))))) # label(fact_911_Inf__fin_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.37 985 (all X_a (linorder(X_a) -> (all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_1) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),ord_min(X_a)),A_1))))) # label(fact_912_Min_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.37 986 (all X_a (semilattice_inf(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),semilattice_inf_inf(X_a)),A_1))) <-> (all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),X_1)))))))))) # label(fact_913_below__fold1__iff) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.37 987 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),ord_min(X_a)),A_1)),X_2)) <-> (exists X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),X_2)))))))))) # label(fact_914_fold1__below__iff) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.37 988 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),ord_min(X_a)),A_1))) <-> (all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),X_1)))))))))) # label(fact_915_min__max_Obelow__fold1__iff) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.37 989 (all X_a all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),big_semilattice_big(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_a,Fa,A_1) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),F),A_1)))) # label(fact_916_semilattice__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.37 990 (all X_a (linorder(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_1)),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),B_1)))))))))) # label(fact_917_min__max_OInf__fin_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.37 991 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_1)) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_1)))))) # label(fact_918_min__max_OInf__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 992 (all X_a (linorder(X_a) -> (all X_2 hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = ti(X_a,X_2)))) # label(fact_919_min__max_OInf__fin_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 993 (all X_a (linorder(X_a) -> (all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_1) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),ord_min(X_a)),A_1))))) # label(fact_920_min__max_OInf__fin_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 994 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_1))))))) # label(fact_921_min__max_OInf__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 995 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_1)))))))) # label(fact_922_min__max_OInf__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 996 (all X_a (linorder(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),B_1)),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_1)) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_1))))))) # label(fact_923_min__max_OInf__fin_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 997 (all X_a (linorder(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_1)),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),B_1))))))))) # label(fact_924_min__max_OInf__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 998 (all X_a (linorder(X_a) -> (all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_min(X_a)),A_2),A_1))))) # label(fact_925_min__max_OInf__fin_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 999 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_min(X_a)),X_2),A_1)))))) # label(fact_926_min__max_OInf__fin_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1000 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_1) = ti(X_a,X_2)) & (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))))))))) # label(fact_927_min__max_OInf__fin_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1001 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = ti(X_a,X_2)) & (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))))))))) # label(fact_928_min__max_OInf__fin_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1002 (all X_a (linorder(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1))),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_1)),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),B_1)))))))) # label(fact_929_min__max_OInf__fin_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1003 (all X_a (linorder(X_a) -> (all N all H ((all X_1 all Y_1 hAPP(X_a,X_a,H,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,H,X_1)),hAPP(X_a,X_a,H,Y_1))) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),N)) -> (ti(fun(X_a,bool),N) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,H,hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),N)) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),H),N)))))))) # label(fact_930_min__max_OInf__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1004 (all X_a (linorder(X_a) -> (all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> ((all X_1 all Y_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_1),bot_bot(fun(X_a,bool))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_1)),A_1)))))))) # label(fact_931_min__max_OInf__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1005 (all X_a all F all A_1 hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),F),A_1) = hAPP(fun(X_a,bool),X_a,the_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool)),finite_fold1Set(X_a),F),A_1))) # label(fact_932_fold1__def) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1006 (all X_a (linorder(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_1)),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),B_1)) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,fun(X_a,bool)),fun(X_a,bool)),combb(fun(X_a,bool),bool,X_a),fEx(X_a)),hAPP(fun(X_a,fun(X_a,fun(X_a,bool))),fun(X_a,fun(X_a,bool)),hAPP(fun(fun(X_a,fun(X_a,bool)),fun(X_a,bool)),fun(fun(X_a,fun(X_a,fun(X_a,bool))),fun(X_a,fun(X_a,bool))),combb(fun(X_a,fun(X_a,bool)),fun(X_a,bool),X_a),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,fun(X_a,bool)),fun(X_a,bool)),combb(fun(X_a,bool),bool,X_a),fEx(X_a))),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(X_a,bool))),hAPP(fun(X_a,fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(X_a,bool)))),combc(X_a,fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool))),hAPP(fun(X_a,fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),fun(X_a,fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)))),hAPP(fun(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)))),fun(fun(X_a,fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),fun(X_a,fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool))))),combb(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool))),X_a),combs(X_a,fun(X_a,bool),fun(X_a,bool))),hAPP(fun(X_a,fun(X_a,fun(X_a,fun(bool,bool)))),fun(X_a,fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),hAPP(fun(fun(X_a,fun(X_a,fun(bool,bool))),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),fun(fun(X_a,fun(X_a,fun(X_a,fun(bool,bool)))),fun(X_a,fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))))),combb(fun(X_a,fun(X_a,fun(bool,bool))),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),X_a),hAPP(fun(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,fun(X_a,fun(bool,bool))),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),combb(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),X_a),combs(X_a,bool,bool))),hAPP(fun(X_a,fun(X_a,fun(X_a,bool))),fun(X_a,fun(X_a,fun(X_a,fun(bool,bool)))),hAPP(fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(bool,bool)))),fun(fun(X_a,fun(X_a,fun(X_a,bool))),fun(X_a,fun(X_a,fun(X_a,fun(bool,bool))))),combb(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(bool,bool))),X_a),hAPP(fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(bool,bool)))),combb(fun(X_a,bool),fun(X_a,fun(bool,bool)),X_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj))),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,fun(X_a,bool))),hAPP(fun(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,bool)))),fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,fun(X_a,bool)))),combc(X_a,fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,bool))),hAPP(fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool))),fun(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,bool)))),hAPP(fun(fun(fun(X_a,X_a),fun(X_a,bool)),fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,bool)))),fun(fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool))),fun(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,bool))))),combb(fun(fun(X_a,X_a),fun(X_a,bool)),fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,bool))),X_a),combb(fun(X_a,X_a),fun(X_a,bool),X_a)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool))),hAPP(fun(fun(X_a,bool),fun(fun(X_a,X_a),fun(X_a,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool)))),combb(fun(X_a,bool),fun(fun(X_a,X_a),fun(X_a,bool)),X_a),combb(X_a,bool,X_a)),fequal(X_a)))),ord_max(X_a)))))),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(X_a,fun(X_a,bool))),combc(X_a,fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),combb(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),X_a),combb(bool,bool,X_a)),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1)))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_1)))))))))))))) # label(fact_933_min__max_Osup__Inf2__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1007 (all X_a (linorder(X_a) -> (all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_1) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),ord_max(X_a)),A_1))))) # label(fact_934_Max_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1008 (all X_a (ord(X_a) -> ord_max(X_a) = hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),max(X_a),ord_less_eq(X_a)))) # label(fact_935_max__ord__max) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1009 (all X_a (linorder(X_a) -> (all X all Y all Z hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z))))))) # label(fact_936_min__max_Odistrib__inf__le) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1010 (all X_a (linorder(X_a) -> (all X all Y all Z hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z))))))) # label(fact_937_min__max_Odistrib__sup__le) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1011 (all X_a (linord219039673up_add(X_a) -> (all X all Y hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))) # label(fact_938_minus__min__eq__max) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1012 (all X_a (linord219039673up_add(X_a) -> (all X all Y hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))) # label(fact_939_minus__max__eq__min) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1013 (all X_a (linorder(X_a) -> (all Y all Z all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Z),X))))) # label(fact_940_min__max_Oinf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1014 (all X_a (linorder(X_a) -> (all Y all Z all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Z),X))))) # label(fact_941_min__max_Osup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1015 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z))))) # label(fact_942_min__max_Oinf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1016 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z))))) # label(fact_943_min__max_Osup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1017 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)) = ti(X_a,X)))) # label(fact_944_min__max_Oinf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1018 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)) = ti(X_a,X)))) # label(fact_945_min__max_Osup__inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1019 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_1)) = hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_1)))))) # label(fact_946_Max_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1020 (all X_a (linorder(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),X) = ti(X_a,X)))) # label(fact_947_Max_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1021 (all X_a (linorder(X_a) -> hBOOL(hAPP(fun(X_a,fun(X_a,X_a)),bool,finite_comp_fun_idem(X_a,X_a),ord_max(X_a))))) # label(fact_948_min__max_Ocomp__fun__idem__sup) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1022 (all X_a (ordered_ab_group_add(X_a) -> (all X all Y all Z 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),ord_max(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z))))) # label(fact_949_max__diff__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1023 (all X_a (linorder(X_a) -> (all A_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),A_3) = ti(X_a,A_3)))) # label(fact_950_min__max_Osup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1024 (all X_a (linorder(X_a) -> (all A_3 all B_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),B_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_2),A_3)))) # label(fact_951_min__max_Osup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1025 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),X)))) # label(fact_952_min__max_Osup__commute) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1026 (all X_a (linorder(X_a) -> (all A_3 all B_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),B_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),B_2)))) # label(fact_953_min__max_Osup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1027 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))) # label(fact_954_min__max_Osup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1028 (all X_a (linorder(X_a) -> (all B_2 all A_3 all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_2),C_1))))) # label(fact_955_min__max_Osup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1029 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z))))) # label(fact_956_min__max_Osup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1030 (all X_a (linorder(X_a) -> (all A_3 all B_2 all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),B_2)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_2),C_1))))) # label(fact_957_min__max_Osup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1031 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z))))) # label(fact_958_min__max_Osup__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1032 (all X_a all F all X_2 -hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool)),finite_fold1Set(X_a),F),bot_bot(fun(X_a,bool))),X_2))) # label(fact_959_empty__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1033 (all X_a all F all A_1 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool)),finite_fold1Set(X_a),F),A_1),X_2)) -> ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)))) # label(fact_960_fold1Set__nonempty) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1034 (all X_a (linorder(X_a) -> (all Z_2 all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),Y_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_2),X_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_2),Y_2)))))) # label(fact_961_le__max__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1035 (all X_a (linorder(X_a) -> (all A_3 all B_2 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),B_2)),X)) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),X)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),X))))))) # label(fact_962_min__max_Ole__supE) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1036 (all X_a (linorder(X_a) -> (all B_2 all D all A_3 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),B_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),C_1),D)))))))) # label(fact_963_min__max_Osup__mono) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1037 (all X_a (linorder(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)),X))))))) # label(fact_964_min__max_Osup__least) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1038 (all X_a (linorder(X_a) -> (all B_2 all A_3 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),B_2)),X))))))) # label(fact_965_min__max_Ole__supI) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1039 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y) = ti(X_a,X))))) # label(fact_966_min__max_Osup__absorb1) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1040 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y) = ti(X_a,Y))))) # label(fact_967_min__max_Osup__absorb2) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1041 (all X_a (linorder(X_a) -> (all A_3 all X all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),B_2))))))) # label(fact_968_min__max_Ole__supI2) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1042 (all X_a (linorder(X_a) -> (all B_2 all X all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),B_2))))))) # label(fact_969_min__max_Ole__supI1) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1043 (all X_a (linorder(X_a) -> (all X_2 all Y_2 all Z_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),Y_2)),Z_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),Z_2)))))) # label(fact_970_min__max_Ole__sup__iff) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1044 (all X_a (linorder(X_a) -> (all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),Y_2) = ti(X_a,Y_2))))) # label(fact_971_min__max_Ole__iff__sup) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1045 (all X_a (linorder(X_a) -> (all Y all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))))) # label(fact_972_le__maxI2) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1046 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))))) # label(fact_973_le__maxI1) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1047 (all X_a (semilattice_sup(X_a) & linorder(X_a) -> semilattice_sup_sup(X_a) = ord_max(X_a))) # label(fact_974_sup__max) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1048 (all X_a (linorder(X_a) -> (all B all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_max(X_a)),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_max(X_a)),B),A_1)))))) # label(fact_975_min__max_Ofold__sup__insert) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1049 (all X_a (linorder(X_a) -> (all B all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B)),hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_max(X_a)),B),A_1)))))))) # label(fact_976_min__max_Osup__le__fold__sup) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1050 (all X_a (linorder(X_a) -> (all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_1)) = ti(X_a,A_2)))))) # label(fact_977_min__max_Osup__Inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1051 (all X_a (linorder(X_a) -> hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),min(X_a),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),ord_less_eq(X_a))) = ord_max(X_a))) # label(fact_978_dual__min) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1052 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_1))))))) # label(fact_979_Max__insert) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1053 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_1)))))))) # label(fact_980_Max_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1054 (all X_a (linorder(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),B_1)),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_1)) = hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_1))))))) # label(fact_981_Max_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1055 (all X_a (linorder(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_1)),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),B_1))))))))) # label(fact_982_Max__Un) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1056 (all X_a all F all A_2 all B (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool)),finite_fold1Set(X_a),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),bot_bot(fun(X_a,bool)))),B)) <-> ti(X_a,A_2) = ti(X_a,B))) # label(fact_983_fold1Set__sing) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1057 (all X_a (linorder(X_a) -> (all A_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),A_1)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_max(X_a)),A_2),A_1))))) # label(fact_984_Max_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1058 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_max(X_a)),X_2),A_1)))))) # label(fact_985_Max_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1059 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_1) = ti(X_a,X_2)) & (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))))))))) # label(fact_986_Max_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1060 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = ti(X_a,X_2)) & (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))))))))) # label(fact_987_Max_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1061 (all X_a (linorder(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1))),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_1)),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),B_1)))))))) # label(fact_988_Max_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1062 (all X_a (linorder(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B_1)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B_1) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_1)),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),B_1)))))))))) # label(fact_989_Max_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1063 (all X_a (linorder(X_a) -> (all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_1)) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,fun(X_a,bool)),fun(X_a,bool)),combb(fun(X_a,bool),bool,X_a),fEx(X_a)),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(X_a,fun(X_a,bool))),combc(X_a,fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,fun(bool,bool))),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,fun(X_a,fun(bool,bool))),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),combb(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),X_a),combs(X_a,bool,bool)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(bool,bool))),hAPP(fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,fun(bool,bool)))),combb(fun(X_a,bool),fun(X_a,fun(bool,bool)),X_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj)),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool))),fun(fun(X_a,X_a),fun(X_a,fun(X_a,bool))),combc(X_a,fun(X_a,X_a),fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool))),hAPP(fun(fun(X_a,bool),fun(fun(X_a,X_a),fun(X_a,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(X_a,X_a),fun(X_a,bool)))),combb(fun(X_a,bool),fun(fun(X_a,X_a),fun(X_a,bool)),X_a),combb(X_a,bool,X_a)),fequal(X_a))),hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2))))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1)))))))))) # label(fact_990_min__max_Osup__Inf1__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1064 (all X_a (linorder(X_a) -> (all N all H ((all X_1 all Y_1 hAPP(X_a,X_a,H,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,H,X_1)),hAPP(X_a,X_a,H,Y_1))) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),N)) -> (ti(fun(X_a,bool),N) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,H,hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),N)) = hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),H),N)))))))) # label(fact_991_Max_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1065 (all X_a (linorder(X_a) -> (all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> ((all X_1 all Y_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_1),bot_bot(fun(X_a,bool))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_1)),A_1)))))))) # label(fact_992_Max_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1066 (all X_a (linorder(X_a) -> (all C all B all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),B)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_max(X_a)),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),C)))))))) # label(fact_993_min__max_Ofold__sup__le__sup) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1067 (all X_a all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (exists X1 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool)),finite_fold1Set(X_a),F),A_1),X1)))))) # label(fact_994_finite__nonempty__imp__fold1Set) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1068 (all X_a (linorder(X_a) -> (all X all Y all Z ((all X_1 all Y_1 all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y_1),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Z_1))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z)))))) # label(fact_995_min__max_Odistrib__imp1) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1069 (all X_a (linorder(X_a) -> (all X all Y all Z ((all X_1 all Y_1 all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y_1),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Z_1))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z)))))) # label(fact_996_min__max_Odistrib__imp2) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1070 (all X_a (order(X_a) -> (all X all Least ((all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_1))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Least) = ti(X_a,X))))) # label(fact_997_max__leastR) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1071 (all X_a (ord(X_a) -> (all X all Least ((all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_1))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Least),X) = ti(X_a,X))))) # label(fact_998_max__leastL) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1072 (all T_2 all T_1 (bounded_lattice(T_1) -> bounded_lattice(fun(T_2,T_1)))) # label(arity_fun___Lattices_Obounded__lattice) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1073 (all T_2 all T_1 (comple1742628961attice(T_1) -> comple1742628961attice(fun(T_2,T_1)))) # label(arity_fun___Complete__Lattice_Ocomplete__distrib__lattice) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1074 (all T_2 all T_1 (comple61589808lgebra(T_1) -> comple61589808lgebra(fun(T_2,T_1)))) # label(arity_fun___Complete__Lattice_Ocomplete__boolean__algebra) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1075 (all T_2 all T_1 (comple44059174attice(T_1) -> comple44059174attice(fun(T_2,T_1)))) # label(arity_fun___Complete__Lattice_Ocomplete__lattice) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1076 (all T_2 all T_1 (bounded_lattice(T_1) -> bounded_lattice_top(fun(T_2,T_1)))) # label(arity_fun___Lattices_Obounded__lattice__top) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1077 (all T_2 all T_1 (bounded_lattice(T_1) -> bounded_lattice_bot(fun(T_2,T_1)))) # label(arity_fun___Lattices_Obounded__lattice__bot) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1078 (all T_2 all T_1 (lattice(T_1) -> semilattice_sup(fun(T_2,T_1)))) # label(arity_fun___Lattices_Osemilattice__sup) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1079 (all T_2 all T_1 (lattice(T_1) -> semilattice_inf(fun(T_2,T_1)))) # label(arity_fun___Lattices_Osemilattice__inf) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1080 (all T_2 all T_1 (distrib_lattice(T_1) -> distrib_lattice(fun(T_2,T_1)))) # label(arity_fun___Lattices_Odistrib__lattice) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1081 (all T_2 all T_1 (boolean_algebra(T_1) -> boolean_algebra(fun(T_2,T_1)))) # label(arity_fun___Lattices_Oboolean__algebra) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1082 (all T_2 all T_1 (preorder(T_1) -> preorder(fun(T_2,T_1)))) # label(arity_fun___Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1083 (all T_2 all T_1 (finite_finite_1(T_1) & finite_finite_1(T_2) -> finite_finite_1(fun(T_2,T_1)))) # label(arity_fun___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1084 (all T_2 all T_1 (lattice(T_1) -> lattice(fun(T_2,T_1)))) # label(arity_fun___Lattices_Olattice) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1085 (all T_2 all T_1 (order(T_1) -> order(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oorder) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1086 (all T_2 all T_1 (top(T_1) -> top(fun(T_2,T_1)))) # label(arity_fun___Orderings_Otop) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1087 (all T_2 all T_1 (ord(T_1) -> ord(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oord) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1088 (all T_2 all T_1 (bot(T_1) -> bot(fun(T_2,T_1)))) # label(arity_fun___Orderings_Obot) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1089 (all T_2 all T_1 (uminus(T_1) -> uminus(fun(T_2,T_1)))) # label(arity_fun___Groups_Ouminus) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1090 (all T_2 all T_1 (minus(T_1) -> minus(fun(T_2,T_1)))) # label(arity_fun___Groups_Ominus) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1091 (all T_2 all T_1 (finite_finite_1(T_1) & finite_finite_1(T_2) -> finite_finite_1(sum_sum(T_2,T_1)))) # label(arity_sum___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1092 (all T_1 (finite_finite_1(T_1) -> finite_finite_1(option(T_1)))) # label(arity_Option_Ooption___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1093 (all T_2 all T_1 (finite_finite_1(T_1) & finite_finite_1(T_2) -> finite_finite_1(product_prod(T_2,T_1)))) # label(arity_prod___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1094 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1095 (all X_a all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y) = ti(X_a,X)) # label(help_If_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1096 (all X_a all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X),Y) = ti(X_a,Y)) # label(help_If_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1097 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_If_3_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1098 (all X_a all P all X (-hBOOL(hAPP(X_a,bool,P,X)) | hBOOL(hAPP(fun(X_a,bool),bool,fEx(X_a),P)))) # label(help_fEx_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1099 (all X_a all X all P (-hBOOL(hAPP(fun(X_a,bool),bool,fAll(X_a),P)) | hBOOL(hAPP(X_a,bool,P,X)))) # label(help_fAll_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1100 (all P (-hBOOL(hAPP(bool,bool,fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1101 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1102 (all X_a all X_c all X_b all P all Q all 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))) # label(help_COMBB_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.14/2.38 1103 (all X_a all X_c all X_b all P all Q all 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)) # label(help_COMBC_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.29/2.57 1104 (all X_a all P hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P)) # label(help_COMBI_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.29/2.57 1105 (all X_b all X_a all P all 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)) # label(help_COMBK_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.29/2.57 1106 (all X_a all X_c all X_b all P all Q all 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))) # label(help_COMBS_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.29/2.57 1107 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fTrue_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.29/2.57 1108 (all Q all P (-hBOOL(P) | -hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.29/2.57 1109 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.29/2.57 1110 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.29/2.57 1111 (all Q all P (-hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.29/2.57 1112 (all P all Q (-hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.29/2.57 1113 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | hBOOL(P) | hBOOL(Q))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.29/2.57 1114 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.29/2.57 1115 (all X_a all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) | ti(X_a,X) = ti(X_a,Y))) # label(help_fequal_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.29/2.57 1116 (all X_a all X all Y (ti(X_a,X) != ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)))) # label(help_fequal_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.29/2.57 1117 (all Q all P (hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.29/2.57 1118 (all P all Q (-hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.29/2.57 1119 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)) | -hBOOL(P) | hBOOL(Q))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.29/2.57
% 2.29/2.57 ============================== end of process non-clausal formulas ===
% 2.29/2.57
% 2.29/2.57 ============================== PROCESS INITIAL CLAUSES ===============
% 2.29/2.57
% 2.29/2.57 ============================== PREDICATE ELIMINATION =================
% 2.29/2.57 1120 -lattice(A) | semilattice_inf(fun(B,A)) # label(arity_fun___Lattices_Osemilattice__inf) # label(axiom). [clausify(1079)].
% 2.29/2.57 1121 -semilattice_inf(A) | semilattice_inf_inf(A) = ti(fun(A,fun(A,A)),semilattice_inf_inf(A)) # label(tsy_c_Lattices_Osemilattice__inf__class_Oinf_res) # label(axiom). [clausify(40)].
% 2.29/2.57 1122 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D)) # label(fact_342_inf__assoc) # label(axiom). [clausify(415)].
% 2.29/2.57 1123 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D)) # label(fact_344_inf_Oassoc) # label(axiom). [clausify(417)].
% 2.29/2.57 1124 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),D)) # label(fact_345_inf__left__commute) # label(axiom). [clausify(418)].
% 2.29/2.57 1125 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),D)) # label(fact_347_inf_Oleft__commute) # label(axiom). [clausify(420)].
% 2.29/2.57 1126 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) # label(fact_348_inf__left__idem) # label(axiom). [clausify(421)].
% 2.29/2.57 1127 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) # label(fact_350_inf_Oleft__idem) # label(axiom). [clausify(423)].
% 2.29/2.57 1128 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),B) # label(fact_351_inf__commute) # label(axiom). [clausify(424)].
% 2.29/2.57 1129 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),B) # label(fact_353_inf_Ocommute) # label(axiom). [clausify(426)].
% 2.29/2.57 1130 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),B) = ti(A,B) # label(fact_356_inf__idem) # label(axiom). [clausify(429)].
% 2.29/2.57 1131 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),B) = ti(A,B) # label(fact_357_inf_Oidem) # label(axiom). [clausify(430)].
% 2.29/2.57 1132 -semilattice_inf(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C)),B)) # label(fact_362_inf__le1) # label(axiom). [clausify(435)].
% 2.29/2.57 1133 -semilattice_inf(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C)),C)) # label(fact_364_inf__le2) # label(axiom). [clausify(437)].
% 2.29/2.57 1134 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) = ti(A,B) # label(fact_365_le__iff__inf) # label(axiom). [clausify(438)].
% 2.29/2.57 1135 -semilattice_inf(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) != ti(A,B) # label(fact_365_le__iff__inf) # label(axiom). [clausify(438)].
% 2.29/2.57 1136 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_366_le__inf__iff) # label(axiom). [clausify(439)].
% 2.29/2.57 1137 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_366_le__inf__iff) # label(axiom). [clausify(439)].
% 2.29/2.57 1138 -semilattice_inf(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_366_le__inf__iff) # label(axiom). [clausify(439)].
% 2.29/2.57 1139 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),D)),C)) # label(fact_367_le__infI1) # label(axiom). [clausify(440)].
% 2.29/2.57 1140 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),D),B)),C)) # label(fact_368_le__infI2) # label(axiom). [clausify(441)].
% 2.29/2.57 1141 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) = ti(A,B) # label(fact_369_inf__absorb1) # label(axiom). [clausify(442)].
% 2.29/2.57 1142 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),B) = ti(A,B) # label(fact_370_inf__absorb2) # label(axiom). [clausify(443)].
% 2.29/2.57 1143 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) # label(fact_371_le__infI) # label(axiom). [clausify(444)].
% 2.29/2.57 1144 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) # label(fact_372_inf__greatest) # label(axiom). [clausify(445)].
% 2.29/2.57 1145 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),E))) # label(fact_373_inf__mono) # label(axiom). [clausify(446)].
% 2.29/2.57 1146 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_374_le__infE) # label(axiom). [clausify(447)].
% 2.29/2.57 1147 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_374_le__infE) # label(axiom). [clausify(447)].
% 2.29/2.57 1148 -semilattice_inf(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite_comp_fun_idem(A,A),semilattice_inf_inf(A))) # label(fact_473_comp__fun__idem__inf) # label(axiom). [clausify(546)].
% 2.29/2.57 1149 -semilattice_inf(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),semilattice_inf_inf(A)),D),B)),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) # label(fact_505_fold__inf__le__inf) # label(axiom). [clausify(578)].
% 2.29/2.57 1150 -semilattice_inf(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),semilattice_inf_inf(A)),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),D),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),semilattice_inf_inf(A)),C),B)) # label(fact_507_fold__inf__insert) # label(axiom). [clausify(580)].
% 2.29/2.57 1151 -semilattice_inf(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f105(A,C,D,B)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),D),C)),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),semilattice_inf_inf(A)),C),B))) # label(fact_529_inf__le__fold__inf) # label(axiom). [clausify(602)].
% 2.29/2.57 1152 -semilattice_inf(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),f105(A,D,C,B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D)),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),semilattice_inf_inf(A)),D),B))) # label(fact_529_inf__le__fold__inf) # label(axiom). [clausify(602)].
% 2.29/2.57 1153 -semilattice_inf(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),semilattice_inf_inf(A)),B)),C)) # label(fact_908_fold1__belowI) # label(axiom). [clausify(981)].
% 2.29/2.57 1154 -semilattice_inf(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),semilattice_inf_inf(A)),B))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_913_below__fold1__iff) # label(axiom). [clausify(986)].
% 2.29/2.57 1155 -semilattice_inf(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),semilattice_inf_inf(A)),B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f175(A,C,B)),B)) # label(fact_913_below__fold1__iff) # label(axiom). [clausify(986)].
% 2.29/2.57 1156 -semilattice_inf(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),semilattice_inf_inf(A)),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),f175(A,C,B))) # label(fact_913_below__fold1__iff) # label(axiom). [clausify(986)].
% 2.29/2.57 Derived: -lattice(A) | semilattice_inf_inf(fun(B,A)) = ti(fun(fun(B,A),fun(fun(B,A),fun(B,A))),semilattice_inf_inf(fun(B,A))). [resolve(1120,b,1121,a)].
% 2.29/2.57 Derived: -lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D)),E) = hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),E)). [resolve(1120,b,1122,a)].
% 2.29/2.57 Derived: -lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),E)) = hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),E)). [resolve(1120,b,1124,a)].
% 2.29/2.57 Derived: -lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D)) = hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D). [resolve(1120,b,1126,a)].
% 2.29/2.57 Derived: -lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D) = hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),C). [resolve(1120,b,1128,a)].
% 2.29/2.57 Derived: -lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),C) = ti(fun(B,A),C). [resolve(1120,b,1130,a)].
% 2.29/2.57 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D)),C)). [resolve(1120,b,1132,a)].
% 2.29/2.57 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D)),D)). [resolve(1120,b,1133,a)].
% 2.29/2.57 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D) = ti(fun(B,A),C). [resolve(1120,b,1134,a)].
% 2.29/2.57 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D) != ti(fun(B,A),C). [resolve(1120,b,1135,a)].
% 2.29/2.57 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),E))) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)). [resolve(1120,b,1136,a)].
% 2.29/2.57 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),E))) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),E)). [resolve(1120,b,1137,a)].
% 2.29/2.57 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),E))) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),E)). [resolve(1120,b,1138,a)].
% 2.29/2.57 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),E)),D)). [resolve(1120,b,1139,a)].
% 2.29/2.57 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),E),C)),D)). [resolve(1120,b,1140,a)].
% 2.29/2.57 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),C) = ti(fun(B,A),C). [resolve(1120,b,1142,a)].
% 2.29/2.57 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),E),F)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),E)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),F))). [resolve(1120,b,1145,a)].
% 2.29/2.57 Derived: -lattice(A) | hBOOL(hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),bool,finite_comp_fun_idem(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)))). [resolve(1120,b,1148,a)].
% 2.29/2.57 Derived: -lattice(A) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,finite_finite(fun(B,A)),C)) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,hAPP(fun(B,A),fun(fun(fun(B,A),bool),bool),member(fun(B,A)),D),C)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(fun(B,A),bool),fun(B,A),hAPP(fun(B,A),fun(fun(fun(B,A),bool),fun(B,A)),hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),fun(fun(B,A),fun(fun(fun(B,A),bool),fun(B,A))),finite_fold(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A))),E),C)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),E))). [resolve(1120,b,1149,a)].
% 2.29/2.57 Derived: -lattice(A) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,finite_finite(fun(B,A)),C)) | hAPP(fun(fun(B,A),bool),fun(B,A),hAPP(fun(B,A),fun(fun(fun(B,A),bool),fun(B,A)),hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),fun(fun(B,A),fun(fun(fun(B,A),bool),fun(B,A))),finite_fold(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A))),D),hAPP(fun(fun(B,A),bool),fun(fun(B,A),bool),hAPP(fun(B,A),fun(fun(fun(B,A),bool),fun(fun(B,A),bool)),insert(fun(B,A)),E),C)) = hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),E),hAPP(fun(fun(B,A),bool),fun(B,A),hAPP(fun(B,A),fun(fun(fun(B,A),bool),fun(B,A)),hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),fun(fun(B,A),fun(fun(fun(B,A),bool),fun(B,A))),finite_fold(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A))),D),C)). [resolve(1120,b,1150,a)].
% 2.29/2.57 Derived: -lattice(A) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,finite_finite(fun(B,A)),C)) | hBOOL(hAPP(fun(fun(B,A),bool),bool,hAPP(fun(B,A),fun(fun(fun(B,A),bool),bool),member(fun(B,A)),f105(fun(B,A),D,E,C)),C)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),E),D)),hAPP(fun(fun(B,A),bool),fun(B,A),hAPP(fun(B,A),fun(fun(fun(B,A),bool),fun(B,A)),hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),fun(fun(B,A),fun(fun(fun(B,A),bool),fun(B,A))),finite_fold(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A))),D),C))). [resolve(1120,b,1151,a)].
% 2.29/2.57 Derived: -lattice(A) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,finite_finite(fun(B,A)),C)) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),D),f105(fun(B,A),E,D,C))) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),E)),hAPP(fun(fun(B,A),bool),fun(B,A),hAPP(fun(B,A),fun(fun(fun(B,A),bool),fun(B,A)),hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),fun(fun(B,A),fun(fun(fun(B,A),bool),fun(B,A))),finite_fold(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A))),E),C))). [resolve(1120,b,1152,a)].
% 2.29/2.57 Derived: -lattice(A) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,finite_finite(fun(B,A)),C)) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,hAPP(fun(B,A),fun(fun(fun(B,A),bool),bool),member(fun(B,A)),D),C)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(fun(B,A),bool),fun(B,A),hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),fun(fun(fun(B,A),bool),fun(B,A)),finite_fold1(fun(B,A)),semilattice_inf_inf(fun(B,A))),C)),D)). [resolve(1120,b,1153,a)].
% 2.29/2.57 Derived: -lattice(A) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,finite_finite(fun(B,A)),C)) | bot_bot(fun(fun(B,A),bool)) = ti(fun(fun(B,A),bool),C) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),D),hAPP(fun(fun(B,A),bool),fun(B,A),hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),fun(fun(fun(B,A),bool),fun(B,A)),finite_fold1(fun(B,A)),semilattice_inf_inf(fun(B,A))),C))) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,hAPP(fun(B,A),fun(fun(fun(B,A),bool),bool),member(fun(B,A)),E),C)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),D),E)). [resolve(1120,b,1154,a)].
% 2.29/2.57 Derived: -lattice(A) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,finite_finite(fun(B,A)),C)) | bot_bot(fun(fun(B,A),bool)) = ti(fun(fun(B,A),bool),C) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),D),hAPP(fun(fun(B,A),bool),fun(B,A),hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),fun(fun(fun(B,A),bool),fun(B,A)),finite_fold1(fun(B,A)),semilattice_inf_inf(fun(B,A))),C))) | hBOOL(hAPP(fun(fun(B,A),bool),bool,hAPP(fun(B,A),fun(fun(fun(B,A),bool),bool),member(fun(B,A)),f175(fun(B,A),D,C)),C)). [resolve(1120,b,1155,a)].
% 2.29/2.57 Derived: -lattice(A) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,finite_finite(fun(B,A)),C)) | bot_bot(fun(fun(B,A),bool)) = ti(fun(fun(B,A),bool),C) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),D),hAPP(fun(fun(B,A),bool),fun(B,A),hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),fun(fun(fun(B,A),bool),fun(B,A)),finite_fold1(fun(B,A)),semilattice_inf_inf(fun(B,A))),C))) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),D),f175(fun(B,A),D,C))). [resolve(1120,b,1156,a)].
% 2.29/2.57 1157 semilattice_inf(bool) # label(arity_HOL_Obool___Lattices_Osemilattice__inf) # label(axiom). [assumption].
% 2.29/2.57 Derived: semilattice_inf_inf(bool) = ti(fun(bool,fun(bool,bool)),semilattice_inf_inf(bool)). [resolve(1157,a,1121,a)].
% 2.29/2.57 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B)),C) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),C)). [resolve(1157,a,1122,a)].
% 2.29/2.57 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),C)) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),C)). [resolve(1157,a,1124,a)].
% 2.29/2.57 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B)) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B). [resolve(1157,a,1126,a)].
% 2.29/2.57 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),A). [resolve(1157,a,1128,a)].
% 2.29/2.57 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),A) = ti(bool,A). [resolve(1157,a,1130,a)].
% 2.29/2.57 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B)),A)). [resolve(1157,a,1132,a)].
% 2.29/2.57 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B)),B)). [resolve(1157,a,1133,a)].
% 2.29/2.57 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B) = ti(bool,A). [resolve(1157,a,1134,a)].
% 2.29/2.57 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B) != ti(bool,A). [resolve(1157,a,1135,a)].
% 2.29/2.57 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),C))) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)). [resolve(1157,a,1136,a)].
% 2.29/2.57 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),C))) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),C)). [resolve(1157,a,1137,a)].
% 2.29/2.57 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),C))) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),C)). [resolve(1157,a,1138,a)].
% 2.29/2.57 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),C)),B)). [resolve(1157,a,1139,a)].
% 2.29/2.57 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),C),A)),B)). [resolve(1157,a,1140,a)].
% 2.29/2.57 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),A) = ti(bool,A). [resolve(1157,a,1142,a)].
% 2.29/2.57 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),C),D)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),C)),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),D))). [resolve(1157,a,1145,a)].
% 2.29/2.57 Derived: hBOOL(hAPP(fun(bool,fun(bool,bool)),bool,finite_comp_fun_idem(bool,bool),semilattice_inf_inf(bool))). [resolve(1157,a,1148,a)].
% 2.29/2.57 Derived: -hBOOL(hAPP(fun(bool,bool),bool,finite_finite(bool),A)) | -hBOOL(hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),member(bool),B),A)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(fun(bool,bool),bool)),finite_fold(bool,bool),semilattice_inf_inf(bool)),C),A)),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),C))). [resolve(1157,a,1149,a)].
% 2.36/2.66 Derived: -hBOOL(hAPP(fun(bool,bool),bool,finite_finite(bool),A)) | hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(fun(bool,bool),bool)),finite_fold(bool,bool),semilattice_inf_inf(bool)),B),hAPP(fun(bool,bool),fun(bool,bool),hAPP(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),C),A)) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),C),hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(fun(bool,bool),bool)),finite_fold(bool,bool),semilattice_inf_inf(bool)),B),A)). [resolve(1157,a,1150,a)].
% 2.36/2.66 Derived: -hBOOL(hAPP(fun(bool,bool),bool,finite_finite(bool),A)) | hBOOL(hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),member(bool),f105(bool,B,C,A)),A)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),C),B)),hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(fun(bool,bool),bool)),finite_fold(bool,bool),semilattice_inf_inf(bool)),B),A))). [resolve(1157,a,1151,a)].
% 2.36/2.66 Derived: -hBOOL(hAPP(fun(bool,bool),bool,finite_finite(bool),A)) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),B),f105(bool,C,B,A))) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),C)),hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(fun(bool,bool),bool)),finite_fold(bool,bool),semilattice_inf_inf(bool)),C),A))). [resolve(1157,a,1152,a)].
% 2.36/2.66 Derived: -hBOOL(hAPP(fun(bool,bool),bool,finite_finite(bool),A)) | -hBOOL(hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),member(bool),B),A)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(fun(bool,bool),bool,hAPP(fun(bool,fun(bool,bool)),fun(fun(bool,bool),bool),finite_fold1(bool),semilattice_inf_inf(bool)),A)),B)). [resolve(1157,a,1153,a)].
% 2.36/2.66 Derived: -hBOOL(hAPP(fun(bool,bool),bool,finite_finite(bool),A)) | bot_bot(fun(bool,bool)) = ti(fun(bool,bool),A) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),B),hAPP(fun(bool,bool),bool,hAPP(fun(bool,fun(bool,bool)),fun(fun(bool,bool),bool),finite_fold1(bool),semilattice_inf_inf(bool)),A))) | -hBOOL(hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),member(bool),C),A)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),B),C)). [resolve(1157,a,1154,a)].
% 2.36/2.66 Derived: -hBOOL(hAPP(fun(bool,bool),bool,finite_finite(bool),A)) | bot_bot(fun(bool,bool)) = ti(fun(bool,bool),A) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),B),hAPP(fun(bool,bool),bool,hAPP(fun(bool,fun(bool,bool)),fun(fun(bool,bool),bool),finite_fold1(bool),semilattice_inf_inf(bool)),A))) | hBOOL(hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),member(bool),f175(bool,B,A)),A)). [resolve(1157,a,1155,a)].
% 2.36/2.66 Derived: -hBOOL(hAPP(fun(bool,bool),bool,finite_finite(bool),A)) | bot_bot(fun(bool,bool)) = ti(fun(bool,bool),A) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),B),hAPP(fun(bool,bool),bool,hAPP(fun(bool,fun(bool,bool)),fun(fun(bool,bool),bool),finite_fold1(bool),semilattice_inf_inf(bool)),A))) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),B),f175(bool,B,A))). [resolve(1157,a,1156,a)].
% 2.36/2.66 1158 -lattice(A) | semilattice_sup(fun(B,A)) # label(arity_fun___Lattices_Osemilattice__sup) # label(axiom). [clausify(1078)].
% 2.36/2.66 1159 -semilattice_sup(A) | semilattice_sup_sup(A) = ti(fun(A,fun(A,A)),semilattice_sup_sup(A)) # label(tsy_c_Lattices_Osemilattice__sup__class_Osup_res) # label(axiom). [clausify(41)].
% 2.36/2.66 1160 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),B) = ti(A,B) # label(fact_196_sup_Oidem) # label(axiom). [clausify(270)].
% 2.36/2.66 1161 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),B) = ti(A,B) # label(fact_197_sup__idem) # label(axiom). [clausify(271)].
% 2.36/2.66 1162 -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) # label(fact_198_sup_Ocommute) # label(axiom). [clausify(272)].
% 2.36/2.66 1163 -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) # label(fact_200_sup__commute) # label(axiom). [clausify(274)].
% 2.36/2.66 1164 -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) # label(fact_201_sup_Oleft__idem) # label(axiom). [clausify(275)].
% 2.36/2.66 1165 -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) # label(fact_203_sup__left__idem) # label(axiom). [clausify(277)].
% 2.36/2.66 1166 -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)) # label(fact_204_sup_Oleft__commute) # label(axiom). [clausify(278)].
% 2.36/2.66 1167 -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)) # label(fact_206_sup__left__commute) # label(axiom). [clausify(280)].
% 2.36/2.66 1168 -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)) # label(fact_207_sup_Oassoc) # label(axiom). [clausify(281)].
% 2.36/2.66 1169 -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)) # label(fact_209_sup__assoc) # label(axiom). [clausify(283)].
% 2.36/2.66 1170 -semilattice_sup(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C))) # label(fact_211_sup__ge1) # label(axiom). [clausify(285)].
% 2.36/2.66 1171 -semilattice_sup(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),B))) # label(fact_213_sup__ge2) # label(axiom). [clausify(287)].
% 2.36/2.66 1172 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) = ti(A,C) # label(fact_214_le__iff__sup) # label(axiom). [clausify(288)].
% 2.36/2.66 1173 -semilattice_sup(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) != ti(A,C) # label(fact_214_le__iff__sup) # label(axiom). [clausify(288)].
% 2.36/2.66 1174 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_215_le__sup__iff) # label(axiom). [clausify(289)].
% 2.36/2.66 1175 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_215_le__sup__iff) # label(axiom). [clausify(289)].
% 2.36/2.66 1176 -semilattice_sup(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_215_le__sup__iff) # label(axiom). [clausify(289)].
% 2.36/2.66 1177 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),D))) # label(fact_216_le__supI1) # label(axiom). [clausify(290)].
% 2.36/2.66 1178 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),D),C))) # label(fact_217_le__supI2) # label(axiom). [clausify(291)].
% 2.36/2.66 1179 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) = ti(A,C) # label(fact_218_sup__absorb2) # label(axiom). [clausify(292)].
% 2.36/2.66 1180 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),B) = ti(A,C) # label(fact_219_sup__absorb1) # label(axiom). [clausify(293)].
% 2.36/2.66 1181 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),D)),C)) # label(fact_220_le__supI) # label(axiom). [clausify(294)].
% 2.36/2.66 1182 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),D)),C)) # label(fact_221_sup__least) # label(axiom). [clausify(295)].
% 2.36/2.66 1183 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),E))) # label(fact_222_sup__mono) # label(axiom). [clausify(296)].
% 2.36/2.66 1184 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_223_le__supE) # label(axiom). [clausify(297)].
% 2.36/2.66 1185 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_223_le__supE) # label(axiom). [clausify(297)].
% 2.36/2.66 1186 -semilattice_sup(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite_comp_fun_idem(A,A),semilattice_sup_sup(A))) # label(fact_472_comp__fun__idem__sup) # label(axiom). [clausify(545)].
% 2.36/2.66 1187 -semilattice_sup(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),D)),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),semilattice_sup_sup(A)),D),B))) # label(fact_504_sup__le__fold__sup) # label(axiom). [clausify(577)].
% 2.36/2.66 1188 -semilattice_sup(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),semilattice_sup_sup(A)),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),D),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),semilattice_sup_sup(A)),C),B)) # label(fact_506_fold__sup__insert) # label(axiom). [clausify(579)].
% 2.36/2.66 1189 -semilattice_sup(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f106(A,C,D,B)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),semilattice_sup_sup(A)),C),B)),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),D),C))) # label(fact_530_fold__sup__le__sup) # label(axiom). [clausify(603)].
% 2.36/2.66 1190 -semilattice_sup(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f106(A,C,D,B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),semilattice_sup_sup(A)),C),B)),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),D),C))) # label(fact_530_fold__sup__le__sup) # label(axiom). [clausify(603)].
% 2.36/2.66 Derived: -lattice(A) | semilattice_sup_sup(fun(B,A)) = ti(fun(fun(B,A),fun(fun(B,A),fun(B,A))),semilattice_sup_sup(fun(B,A))). [resolve(1158,b,1159,a)].
% 2.36/2.66 Derived: -lattice(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),C) = ti(fun(B,A),C). [resolve(1158,b,1160,a)].
% 2.36/2.66 Derived: -lattice(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) = hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),C). [resolve(1158,b,1162,a)].
% 2.36/2.66 Derived: -lattice(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),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)) = 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). [resolve(1158,b,1164,a)].
% 2.36/2.66 Derived: -lattice(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),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),E)) = hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),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),E)). [resolve(1158,b,1166,a)].
% 2.36/2.66 Derived: -lattice(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)),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(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),E)). [resolve(1158,b,1168,a)].
% 2.36/2.66 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),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))). [resolve(1158,b,1170,a)].
% 2.36/2.66 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),C))). [resolve(1158,b,1171,a)].
% 2.36/2.66 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | 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) = ti(fun(B,A),D). [resolve(1158,b,1172,a)].
% 2.36/2.66 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | 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) != ti(fun(B,A),D). [resolve(1158,b,1173,a)].
% 2.36/2.66 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(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)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),E)). [resolve(1158,b,1174,a)].
% 2.36/2.66 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(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)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),D),E)). [resolve(1158,b,1175,a)].
% 2.36/2.66 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(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)) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),E)) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),D),E)). [resolve(1158,b,1176,a)].
% 2.36/2.66 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),E))). [resolve(1158,b,1177,a)].
% 2.36/2.66 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),E),D))). [resolve(1158,b,1178,a)].
% 2.36/2.66 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),C) = ti(fun(B,A),D). [resolve(1158,b,1180,a)].
% 2.36/2.66 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),E),F)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(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),E)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),F))). [resolve(1158,b,1183,a)].
% 2.36/2.66 Derived: -lattice(A) | hBOOL(hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),bool,finite_comp_fun_idem(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)))). [resolve(1158,b,1186,a)].
% 2.36/2.66 Derived: -lattice(A) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,finite_finite(fun(B,A)),C)) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,hAPP(fun(B,A),fun(fun(fun(B,A),bool),bool),member(fun(B,A)),D),C)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(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)),D),E)),hAPP(fun(fun(B,A),bool),fun(B,A),hAPP(fun(B,A),fun(fun(fun(B,A),bool),fun(B,A)),hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),fun(fun(B,A),fun(fun(fun(B,A),bool),fun(B,A))),finite_fold(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A))),E),C))). [resolve(1158,b,1187,a)].
% 2.36/2.66 Derived: -lattice(A) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,finite_finite(fun(B,A)),C)) | hAPP(fun(fun(B,A),bool),fun(B,A),hAPP(fun(B,A),fun(fun(fun(B,A),bool),fun(B,A)),hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),fun(fun(B,A),fun(fun(fun(B,A),bool),fun(B,A))),finite_fold(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A))),D),hAPP(fun(fun(B,A),bool),fun(fun(B,A),bool),hAPP(fun(B,A),fun(fun(fun(B,A),bool),fun(fun(B,A),bool)),insert(fun(B,A)),E),C)) = hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),E),hAPP(fun(fun(B,A),bool),fun(B,A),hAPP(fun(B,A),fun(fun(fun(B,A),bool),fun(B,A)),hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),fun(fun(B,A),fun(fun(fun(B,A),bool),fun(B,A))),finite_fold(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A))),D),C)). [resolve(1158,b,1188,a)].
% 2.36/2.66 Derived: -lattice(A) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,finite_finite(fun(B,A)),C)) | hBOOL(hAPP(fun(fun(B,A),bool),bool,hAPP(fun(B,A),fun(fun(fun(B,A),bool),bool),member(fun(B,A)),f106(fun(B,A),D,E,C)),C)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(fun(B,A),bool),fun(B,A),hAPP(fun(B,A),fun(fun(fun(B,A),bool),fun(B,A)),hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),fun(fun(B,A),fun(fun(fun(B,A),bool),fun(B,A))),finite_fold(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A))),D),C)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),E),D))). [resolve(1158,b,1189,a)].
% 2.36/2.66 Derived: -lattice(A) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,finite_finite(fun(B,A)),C)) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),f106(fun(B,A),D,E,C)),E)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(fun(B,A),bool),fun(B,A),hAPP(fun(B,A),fun(fun(fun(B,A),bool),fun(B,A)),hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),fun(fun(B,A),fun(fun(fun(B,A),bool),fun(B,A))),finite_fold(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A))),D),C)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),E),D))). [resolve(1158,b,1190,a)].
% 2.36/2.67 1191 semilattice_sup(bool) # label(arity_HOL_Obool___Lattices_Osemilattice__sup) # label(axiom). [assumption].
% 2.36/2.67 Derived: semilattice_sup_sup(bool) = ti(fun(bool,fun(bool,bool)),semilattice_sup_sup(bool)). [resolve(1191,a,1159,a)].
% 2.36/2.67 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),A) = ti(bool,A). [resolve(1191,a,1160,a)].
% 2.36/2.67 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),A). [resolve(1191,a,1162,a)].
% 2.36/2.67 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B)) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B). [resolve(1191,a,1164,a)].
% 2.36/2.67 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),C)) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),C)). [resolve(1191,a,1166,a)].
% 2.36/2.67 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B)),C) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),C)). [resolve(1191,a,1168,a)].
% 2.36/2.67 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B))). [resolve(1191,a,1170,a)].
% 2.36/2.67 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),A))). [resolve(1191,a,1171,a)].
% 2.36/2.67 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B) = ti(bool,B). [resolve(1191,a,1172,a)].
% 2.36/2.67 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B) != ti(bool,B). [resolve(1191,a,1173,a)].
% 2.36/2.67 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B)),C)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),C)). [resolve(1191,a,1174,a)].
% 2.36/2.67 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B)),C)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),B),C)). [resolve(1191,a,1175,a)].
% 2.36/2.67 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B)),C)) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),C)) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),B),C)). [resolve(1191,a,1176,a)].
% 2.36/2.67 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),C))). [resolve(1191,a,1177,a)].
% 2.36/2.67 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),C),B))). [resolve(1191,a,1178,a)].
% 2.50/2.73 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),A) = ti(bool,B). [resolve(1191,a,1180,a)].
% 2.50/2.73 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),C),D)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),C)),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),D))). [resolve(1191,a,1183,a)].
% 2.50/2.73 Derived: hBOOL(hAPP(fun(bool,fun(bool,bool)),bool,finite_comp_fun_idem(bool,bool),semilattice_sup_sup(bool))). [resolve(1191,a,1186,a)].
% 2.50/2.73 Derived: -hBOOL(hAPP(fun(bool,bool),bool,finite_finite(bool),A)) | -hBOOL(hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),member(bool),B),A)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),C)),hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(fun(bool,bool),bool)),finite_fold(bool,bool),semilattice_sup_sup(bool)),C),A))). [resolve(1191,a,1187,a)].
% 2.50/2.73 Derived: -hBOOL(hAPP(fun(bool,bool),bool,finite_finite(bool),A)) | hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(fun(bool,bool),bool)),finite_fold(bool,bool),semilattice_sup_sup(bool)),B),hAPP(fun(bool,bool),fun(bool,bool),hAPP(bool,fun(fun(bool,bool),fun(bool,bool)),insert(bool),C),A)) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),C),hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(fun(bool,bool),bool)),finite_fold(bool,bool),semilattice_sup_sup(bool)),B),A)). [resolve(1191,a,1188,a)].
% 2.50/2.73 Derived: -hBOOL(hAPP(fun(bool,bool),bool,finite_finite(bool),A)) | hBOOL(hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),member(bool),f106(bool,B,C,A)),A)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(fun(bool,bool),bool)),finite_fold(bool,bool),semilattice_sup_sup(bool)),B),A)),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),C),B))). [resolve(1191,a,1189,a)].
% 2.50/2.73 Derived: -hBOOL(hAPP(fun(bool,bool),bool,finite_finite(bool),A)) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),f106(bool,B,C,A)),C)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(fun(bool,bool),bool)),finite_fold(bool,bool),semilattice_sup_sup(bool)),B),A)),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),C),B))). [resolve(1191,a,1190,a)].
% 2.50/2.73 1192 -bounded_lattice(A) | bounded_lattice_bot(fun(B,A)) # label(arity_fun___Lattices_Obounded__lattice__bot) # label(axiom). [clausify(1077)].
% 2.50/2.73 1193 -bounded_lattice_bot(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) != bot_bot(A) | bot_bot(A) = ti(A,B) # label(fact_194_sup__eq__bot__iff) # label(axiom). [clausify(268)].
% 2.50/2.73 1194 -bounded_lattice_bot(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) != bot_bot(A) | bot_bot(A) = ti(A,C) # label(fact_194_sup__eq__bot__iff) # label(axiom). [clausify(268)].
% 2.50/2.73 1195 -bounded_lattice_bot(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) = bot_bot(A) | bot_bot(A) != ti(A,B) | bot_bot(A) != ti(A,C) # label(fact_194_sup__eq__bot__iff) # label(axiom). [clausify(268)].
% 2.50/2.73 1196 -bounded_lattice_bot(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),bot_bot(A)),B) = ti(A,B) # label(fact_224_sup__bot__left) # label(axiom). [clausify(298)].
% 2.50/2.73 1197 -bounded_lattice_bot(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),bot_bot(A)) = ti(A,B) # label(fact_225_sup__bot__right) # label(axiom). [clausify(299)].
% 2.50/2.73 1198 -bounded_lattice_bot(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),bot_bot(A)) = bot_bot(A) # label(fact_375_inf__bot__right) # label(axiom). [clausify(448)].
% 2.66/2.95 1199 -bounded_lattice_bot(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),bot_bot(A)),B) = bot_bot(A) # label(fact_376_inf__bot__left) # label(axiom). [clausify(449)].
% 2.66/2.95 Derived: -bounded_lattice(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) != bot_bot(fun(B,A)) | bot_bot(fun(B,A)) = ti(fun(B,A),C). [resolve(1192,b,1193,a)].
% 2.66/2.95 Derived: -bounded_lattice(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) != bot_bot(fun(B,A)) | bot_bot(fun(B,A)) = ti(fun(B,A),D). [resolve(1192,b,1194,a)].
% 2.66/2.95 Derived: -bounded_lattice(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) = bot_bot(fun(B,A)) | bot_bot(fun(B,A)) != ti(fun(B,A),C) | bot_bot(fun(B,A)) != ti(fun(B,A),D). [resolve(1192,b,1195,a)].
% 2.66/2.95 Derived: -bounded_lattice(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)),bot_bot(fun(B,A))),C) = ti(fun(B,A),C). [resolve(1192,b,1196,a)].
% 2.66/2.95 Derived: -bounded_lattice(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),bot_bot(fun(B,A))) = ti(fun(B,A),C). [resolve(1192,b,1197,a)].
% 2.66/2.95 Derived: -bounded_lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),bot_bot(fun(B,A))) = bot_bot(fun(B,A)). [resolve(1192,b,1198,a)].
% 2.66/2.95 Derived: -bounded_lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),bot_bot(fun(B,A))),C) = bot_bot(fun(B,A)). [resolve(1192,b,1199,a)].
% 2.66/2.95 1200 bounded_lattice_bot(bool) # label(arity_HOL_Obool___Lattices_Obounded__lattice__bot) # label(axiom). [assumption].
% 2.66/2.95 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B) != bot_bot(bool) | bot_bot(bool) = ti(bool,A). [resolve(1200,a,1193,a)].
% 2.66/2.95 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B) != bot_bot(bool) | bot_bot(bool) = ti(bool,B). [resolve(1200,a,1194,a)].
% 2.66/2.95 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B) = bot_bot(bool) | bot_bot(bool) != ti(bool,A) | bot_bot(bool) != ti(bool,B). [resolve(1200,a,1195,a)].
% 2.66/2.95 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),bot_bot(bool)),A) = ti(bool,A). [resolve(1200,a,1196,a)].
% 2.66/2.95 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),bot_bot(bool)) = ti(bool,A). [resolve(1200,a,1197,a)].
% 2.66/2.95 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),bot_bot(bool)) = bot_bot(bool). [resolve(1200,a,1198,a)].
% 2.66/2.95 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),bot_bot(bool)),A) = bot_bot(bool). [resolve(1200,a,1199,a)].
% 2.66/2.95 1201 -bounded_lattice(A) | bounded_lattice_top(fun(B,A)) # label(arity_fun___Lattices_Obounded__lattice__top) # label(axiom). [clausify(1076)].
% 2.66/2.95 1202 -bounded_lattice_top(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),top_top(A)) = top_top(A) # label(fact_588_sup__top__right) # label(axiom). [clausify(661)].
% 2.66/2.95 1203 -bounded_lattice_top(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),top_top(A)),B) = top_top(A) # label(fact_589_sup__top__left) # label(axiom). [clausify(662)].
% 2.66/2.95 1204 -bounded_lattice_top(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) != top_top(A) | top_top(A) = ti(A,B) # label(fact_590_inf__eq__top__iff) # label(axiom). [clausify(663)].
% 2.66/2.95 1205 -bounded_lattice_top(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) != top_top(A) | top_top(A) = ti(A,C) # label(fact_590_inf__eq__top__iff) # label(axiom). [clausify(663)].
% 2.66/2.95 1206 -bounded_lattice_top(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) = top_top(A) | top_top(A) != ti(A,B) | top_top(A) != ti(A,C) # label(fact_590_inf__eq__top__iff) # label(axiom). [clausify(663)].
% 2.66/2.95 1207 -bounded_lattice_top(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),top_top(A)) = ti(A,B) # label(fact_591_inf__top__right) # label(axiom). [clausify(664)].
% 3.54/3.83 1208 -bounded_lattice_top(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),top_top(A)),B) = ti(A,B) # label(fact_592_inf__top__left) # label(axiom). [clausify(665)].
% 3.54/3.83 Derived: -bounded_lattice(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),top_top(fun(B,A))) = top_top(fun(B,A)). [resolve(1201,b,1202,a)].
% 3.54/3.83 Derived: -bounded_lattice(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)),top_top(fun(B,A))),C) = top_top(fun(B,A)). [resolve(1201,b,1203,a)].
% 3.54/3.83 Derived: -bounded_lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D) != top_top(fun(B,A)) | top_top(fun(B,A)) = ti(fun(B,A),C). [resolve(1201,b,1204,a)].
% 3.54/3.83 Derived: -bounded_lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D) != top_top(fun(B,A)) | top_top(fun(B,A)) = ti(fun(B,A),D). [resolve(1201,b,1205,a)].
% 3.54/3.83 Derived: -bounded_lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D) = top_top(fun(B,A)) | top_top(fun(B,A)) != ti(fun(B,A),C) | top_top(fun(B,A)) != ti(fun(B,A),D). [resolve(1201,b,1206,a)].
% 3.54/3.83 Derived: -bounded_lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),top_top(fun(B,A))) = ti(fun(B,A),C). [resolve(1201,b,1207,a)].
% 3.54/3.83 Derived: -bounded_lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),top_top(fun(B,A))),C) = ti(fun(B,A),C). [resolve(1201,b,1208,a)].
% 3.54/3.83 1209 bounded_lattice_top(bool) # label(arity_HOL_Obool___Lattices_Obounded__lattice__top) # label(axiom). [assumption].
% 3.54/3.83 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),top_top(bool)) = top_top(bool). [resolve(1209,a,1202,a)].
% 3.54/3.83 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),top_top(bool)),A) = top_top(bool). [resolve(1209,a,1203,a)].
% 3.54/3.83 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B) != top_top(bool) | top_top(bool) = ti(bool,A). [resolve(1209,a,1204,a)].
% 3.54/3.83 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B) != top_top(bool) | top_top(bool) = ti(bool,B). [resolve(1209,a,1205,a)].
% 3.54/3.83 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B) = top_top(bool) | top_top(bool) != ti(bool,A) | top_top(bool) != ti(bool,B). [resolve(1209,a,1206,a)].
% 3.54/3.83 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),top_top(bool)) = ti(bool,A). [resolve(1209,a,1207,a)].
% 3.54/3.83 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),top_top(bool)),A) = ti(bool,A). [resolve(1209,a,1208,a)].
% 3.54/3.83
% 3.54/3.83 ============================== end predicate elimination =============
% 3.54/3.83
% 3.54/3.83 Auto_denials: (non-Horn, no changes).
% 3.54/3.83
% 3.54/3.83 Term ordering decisions:
% 3.54/3.83 Function symbol KB weights: bool=1. state=1. com=1. pname=1. evalc=1. fconj=1. body_1=1. while=1. body=1. wt=1. hoare_Mirabelle_MGT=1. fNot=1. semi=1. fimplies=1. fdisj=1. fTrue=1. hoare_511481251gleton=1. fFalse=1. skip=1. fa=1. wT_bodies=1. pn=1. y=1. c1=1. c2=1. fun=1. ti=1. image=1. inj_on=1. vimage=1. finite_fold=1. fun_upd=1. dom=1. restrict_map=1. combk=1. finite1357897459simple=1. finite_comp_fun_idem=1. sum_sum=1. the_inv_into=1. ran=1. big_comm_monoid_big=1. finite100568337ommute=1. override_on=1. finite908156982e_idem=1. finite_fold_image=1. fold_graph=1. option_rec=1. product_prod=1. hoare_1759541758le_rec=1. hoare_225284258e_case=1. f1=1. f2=1. f3=1. f4=1. f8=1. f17=1. f18=1. f22=1. f23=1. f49=1. f50=1. f51=1. f63=1. f100=1. f101=1. f109=1. f121=1. f122=1. f132=1. f135=1. f136=1. f154=1. f161=1. f164=1. f165=1. hoare_2118899576triple=1. option=1. ord_less_eq=1. member=1. bot_bot=1. semilattice_inf_inf=1. semilattice_sup_sup=1. insert=1. finite_finite=1. top_top=1. minus_minus=1. collect=1. uminus_uminus=1. hoare_1301688828derivs=1. hoare_759811442triple=1. complete_Sup_Sup=1. complete_Inf_Inf=1. some=1. big_lattice_Inf_fin=1. big_lattice_Sup_fin=1. fequal=1. none=1. pow=1. the_1=1. finite_fold1=1. fEx=1. finite_folding_one=1. the=1. if=1. finite2073411215e_idem=1. set=1. combi=1. finite_fold1Set=1. hoare_902341502valids=1. powp=1. fAll=1. is_none=1. ord_max=1. ord_min=1. partial_flat_lub=1. the_elem=1. big_semilattice_big=1. max=1. min=1. undefined=1. f12=1. f42=1. f150=1. combb=1. combc=1. combs=1. f13=1. f15=1. f16=1. f44=1. f45=1. f46=1. f55=1. f56=1. f57=1. f58=1. f60=1. f61=1. f62=1. f85=1. f86=1. f87=1. f88=1. f104=1. f119=1. f120=1. f123=1. f125=1. f126=1. f128=1. f133=1. f134=1. f138=1. f139=1. f140=1. f141=1. f143=1. f144=1. f145=1. f151=1. f152=1. f153=1. f155=1. f156=1. f157=1. f158=1. f159=1. f160=1. f163=1. f173=1. f174=1. f175=1. f187=1. f194=1. f195=1. hAPP=1. f6=1. f10=1. f11=1. f19=1. f20=1. f24=1. f25=1. f26=1. f27=1. f28=1. f29=1. f30=1. f41=1. f43=1. f52=1. f53=1. f59=1. f72=1. f73=1. f90=1. f91=1. f92=1. f93=1. f94=1. f95=1. f98=1. f102=1. f103=1. f105=1. f106=1. f107=1. f108=1. f117=1. f124=1. f127=1. f129=1. f130=1. f131=1. f142=1. f146=1. f147=1. f162=1. f5=1. f7=1. f9=1. f14=1. f21=1. f32=1. f33=1. f47=1. f48=1. f66=1. f67=1. f78=1. f79=1. f82=1. f83=1. f89=1. f99=1. f110=1. f111=1. f114=1. f118=1. f137=1. f148=1. f149=1. f34=1. f35=1. f36=1. f37=1. f54=1. f64=1. f65=1. f68=1. f69=1. f70=1. f71=1. f74=1. f75=1. f76=1. f77=1. f80=1. f81=1. f112=1. f113=1. f115=1. f38=1. f39=1. f40=1. f84=1. f97=1. f96=1. f31=1. f116=1.
% 7.74/7.97
% 7.74/7.97 ============================== end of process initial clauses ========
% 7.74/7.97
% 7.74/7.97 ============================== CLAUSES FOR SEARCH ====================
% 7.74/7.97
% 7.74/7.97 ============================== end of clauses for search =============
% 7.74/7.97
% 7.74/7.97 ============================== SEARCH ================================
% 7.74/7.97
% 7.74/7.97 % Starting search at 1.75 seconds.
% 7.74/7.97
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% 7.74/7.97 Low Water (keep): wt=111.000, iters=3372
% 7.74/7.97
% 7.74/7.97 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 99 (0.00 of 4.78 sec).
% 7.74/7.97
% 7.74/7.97 Low Water (keep): wt=109.000, iters=3372
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% 7.74/7.97
% 7.74/7.97 Low Water (keep): wt=75.000, iters=3404
% 7.74/7.97
% 7.74/7.97 Low Water (keep): wt=74.000, iters=3345
% 62.49/62.75
% 62.49/62.75 Low Water (keep): wt=73.000, iters=3401
% 62.49/62.75
% 62.49/62.75 Low Water (keep): wt=72.000, iters=3524
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% 62.49/62.75 Low Water (keep): wt=71.000, iters=3460
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% 62.49/62.75
% 62.49/62.75 Low Water (displace): id=5797, wt=200.000
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% 62.49/62.75 Low Water (displace): id=4930, wt=198.000
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% 62.49/62.75 Low Water (displace): id=5096, wt=197.000
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% 62.49/62.75 Low Water (displace): id=4831, wt=196.000
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% 62.49/62.75 Low Water (displace): id=5774, wt=193.000
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% 62.49/62.75 Low Water (displace): id=5793, wt=192.000
% 62.49/62.75
% 62.49/62.75 Low Water (displace): id=5035, wt=190.000
% 62.49/62.75
% 62.49/62.75 Low Water (displace): id=15223, wt=11.000
% 62.49/62.75
% 62.49/62.75 Low Water (displace): id=15225, wt=10.000
% 62.49/62.75
% 62.49/62.75 Low Water (keep): wt=44.000, iters=3404
% 62.49/62.75
% 62.49/62.75 Low Water (displace): id=15309, wt=9.000
% 62.49/62.75
% 62.49/62.75 Low Water (displace): id=15375, wt=8.000
% 62.49/62.75
% 62.49/62.75 Low Water (keep): wt=43.000, iters=3351
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% 62.49/62.75
% 62.49/62.75 Low Water (keep): wt=41.000, iters=3333
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% 62.49/62.75
% 62.49/62.75 Low Water (keep): wt=38.000, iters=3354
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% 62.49/62.75 Low Water (keep): wt=37.000, iters=3334
% 62.49/62.75
% 62.49/62.75 Low Water (keep): wt=36.000, iters=3337
% 62.49/62.75
% 62.49/62.75 Low Water (keep): wt=35.000, iters=3389
% 62.49/62.75
% 62.49/62.75 Low Water (keep): wt=33.000, iters=3715
% 62.49/62.75
% 62.49/62.75 Low Water (keep): wt=31.000, iters=3522
% 62.49/62.75
% 62.49/62.75 Low Water (keep): wt=30.000, iters=3469
% 62.49/62.75
% 62.49/62.75 Low Water (keep): wt=29.000, iters=3385
% 62.49/62.75
% 62.49/62.75 Low Water (keep): wt=27.000, iters=3333
% 62.49/62.75
% 62.49/62.75 Low Water (keep): wt=26.000, iters=3349
% 62.49/62.75
% 62.49/62.75 ============================== STATISTICS ============================
% 62.49/62.75
% 62.49/62.75 Given=5421. Generated=733564. Kept=561812. proofs=0.
% 62.49/62.75 Usable=5237. Sos=9998. Demods=706. Limbo=75, Disabled=548141. Hints=0.
% 62.49/62.75 Kept_by_rule=0, Deleted_by_rule=41197.
% 62.49/62.75 Forward_subsumed=39774. Back_subsumed=63.
% 62.49/62.75 Sos_limit_deleted=90781. Sos_displaced=544273. Sos_removed=0.
% 62.49/62.75 New_demodulators=1176 (0 lex), Back_demodulated=2131. Back_unit_deleted=35.
% 62.49/62.75 Demod_attempts=29107888. Demod_rewrites=109719.
% 62.49/62.75 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
% 62.49/62.75 Nonunit_fsub_feature_tests=740615. Nonunit_bsub_feature_tests=14860.
% 62.49/62.75 Megabytes=419.43.
% 62.49/62.75 User_CPU=60.06, System_CPU=0.61, Wall_clock=61.
% 62.49/62.75
% 62.49/62.75 Megs malloced by palloc(): 400.
% 62.49/62.75 type (bytes each) gets frees in use bytes
% 62.49/62.75 chunk ( 104) 112345 112345 0 0.0 K
% 62.49/62.75 string_buf ( 8) 101195 101195 0 0.0 K
% 62.49/62.75 token ( 20) 256937 256937 0 0.0 K
% 62.49/62.75 pterm ( 16) 183763 183763 0 0.0 K
% 62.49/62.75 hashtab ( 8) 1119 1119 0 0.0 K
% 62.49/62.75 hashnode ( 8) 4515 4515 0 0.0 K
% 62.49/62.75 term ( 20) 41500549 31962793 9537756 186284.3 K
% 62.49/62.75 term arg arrays: 37209.3 K
% 62.49/62.75 attribute ( 12) 7879 168 7711 90.4 K
% 62.49/62.75 ilist ( 8) 854780017 852529897 2250120 17579.1 K
% 62.49/62.75 plist ( 8) 9488000 8892956 595044 4648.8 K
% 62.49/62.75 i2list ( 12) 2260535 2260535 0 0.0 K
% 62.49/62.75 just ( 12) 819181 247649 571532 6697.6 K
% 62.49/62.75 parajust ( 16) 80825 70518 10307 161.0 K
% 62.49/62.75 instancejust ( 8) 0 0 0 0.0 K
% 62.49/62.75 ivyjust ( 24) 0 0 0 0.0 K
% 62.49/62.75 formula ( 28) 48352 30718 17634 482.2 K
% 62.49/62.75 formula arg arrays: 60.1 K
% 62.49/62.75 topform ( 52) 736363 171752 564611 28671.7 K
% 62.49/62.75 clist_pos ( 20) 1681166 1117009 564157 11018.7 K
% 62.49/62.75 clist ( 16) 8 1 7 0.1 K
% 62.49/62.75 context ( 808) 6217104 6217102 2 1.6 K
% 62.49/62.75 trail ( 12) 5829737 5829734 3 0.0 K
% 62.49/62.75 ac_match_pos (70044) 0 0 0 0.0 K
% 62.49/62.75 ac_match_free_vars_pos (20020)
% 62.49/62.75 0 0 0 0.0 K
% 62.49/62.75 btm_state ( 60) 0 0 0 0.0 K
% 62.49/62.75 btu_state ( 60) 0 0 0 0.0 K
% 62.49/62.75 ac_position (285432) 0 0 0 0.0 K
% 62.49/62.75 fpa_trie ( 20) 1265582 1004284 261298 5103.5 K
% 62.49/62.75 fpa_state ( 28) 1556862 1556859 3 0.1 K
% 62.49/62.75 fpa_index ( 12) 10 0 10 0.1 K
% 62.49/62.75 fpa_chunk ( 20) 2303046 2164237 138809 2711.1 K
% 62.49/62.75 fpa_list ( 16) 1080402 0 1080402 16881.3 K
% 62.49/62.75 fpa_list chunks: 11241.9 K
% 62.49/62.75 discrim ( 12) 3174135 3061770 112365 1316.8 K
% 62.49/62.75 discrim_pos ( 16) 130096 130096 0 0.0 K
% 62.49/62.75 flat2 ( 32) 18980080 18980080 0 0.0 K
% 62.49/62.75 flat ( 48) 0 0 0 0.0 K
% 62.49/62.75 flatterm ( 32) 39562730 39562730 0 0.0 K
% 62.49/62.75 mindex ( 28) 13 0 13 0.4 K
% 62.49/62.75 mindex_pos ( 56) 2895166 2895165 1 0.1 K
% 62.49/62.75 lindex ( 12) 5 0 5 0.1 K
% 62.49/62.75 clash ( 40) 0 0 0 0.0 K
% 62.49/62.75 di_tree ( 12) 15146390 8938820 6207570 72745.0 K
% 62.49/62.75 avl_node ( 20) 1121671 1101675 19996 390.5 K
% 62.49/62.75
% 62.49/62.75 Memory report, 20 @ 20 = 400 megs (400.00 megs used).
% 62.49/62.75 List 1, length 9, 0.0 K
% 62.49/62.75 List 2, length 1114, 8.7 K
% 62.49/62.75 List 3, length 77663, 910.1 K
% 62.49/62.75 List 7, length 90, 2.5 K
% 62.49/62.75 List 8, length 411, 12.8 K
% 62.49/62.75 List 10, length 2, 0.1 K
% 62.49/62.75 List 11, length 1, 0.0 K
% 62.49/62.75 List 12, length 4, 0.2 K
% 62.49/62.75 List 14, length 8, 0.4 K
% 62.49/62.75 List 16, length 281, 17.6 K
% 62.49/62.75 List 26, length 1087, 110.4 K
% 62.49/62.75 List 32, length 137, 17.1 K
% 62.49/62.75 List 64, length 208, 52.0 K
% 62.49/62.75 List 128, length 36, 18.0 K
% 62.49/62.75 List 202, length 2, 1.6 K
% 62.49/62.75 List 256, length 76, 76.0 K
% 62.49/62.75
% 62.49/62.75 ============================== SELECTOR REPORT =======================
% 62.49/62.75 Sos_deleted=90781, Sos_displaced=544273, Sos_size=9998
% 62.49/62.75 SELECTOR PART PRIORITY ORDER SIZE SELECTED
% 62.49/62.75 I 2147483647 high age 0 1234
% 62.49/62.75 H 1 high weight 0 0
% 62.49/62.75 A 1 low age 9998 466
% 62.49/62.75 F 4 low weight 176 1861
% 62.49/62.75 T 4 low weight 9822 1860
% 62.49/62.75 ============================== end of selector report ================
% 62.49/62.75
% 62.49/62.75 ============================== end of statistics =====================
% 62.49/62.75
% 62.49/62.75 Exiting with failure.
% 62.49/62.75
% 62.49/62.75 Process 7628 exit (max_megs) Sun Jun 5 12:06:06 2022
% 62.49/62.75 Prover9 interrupted
%------------------------------------------------------------------------------