TSTP Solution File: SWW470+6 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW470+6 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 01:17:05 EDT 2022
% Result : Theorem 4.29s 4.57s
% Output : Refutation 4.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW470+6 : TPTP v8.1.0. Released v5.3.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 5 02:59:17 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.59/1.84 ============================== Prover9 ===============================
% 1.59/1.84 Prover9 (32) version 2009-11A, November 2009.
% 1.59/1.84 Process 26799 was started by sandbox on n025.cluster.edu,
% 1.59/1.84 Sun Jun 5 02:59:18 2022
% 1.59/1.84 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26646_n025.cluster.edu".
% 1.59/1.84 ============================== end of head ===========================
% 1.59/1.84
% 1.59/1.84 ============================== INPUT =================================
% 1.59/1.84
% 1.59/1.84 % Reading from file /tmp/Prover9_26646_n025.cluster.edu
% 1.59/1.84
% 1.59/1.84 set(prolog_style_variables).
% 1.59/1.84 set(auto2).
% 1.59/1.84 % set(auto2) -> set(auto).
% 1.59/1.84 % set(auto) -> set(auto_inference).
% 1.59/1.84 % set(auto) -> set(auto_setup).
% 1.59/1.84 % set(auto_setup) -> set(predicate_elim).
% 1.59/1.84 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.59/1.84 % set(auto) -> set(auto_limits).
% 1.59/1.84 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.59/1.84 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.59/1.84 % set(auto) -> set(auto_denials).
% 1.59/1.84 % set(auto) -> set(auto_process).
% 1.59/1.84 % set(auto2) -> assign(new_constants, 1).
% 1.59/1.84 % set(auto2) -> assign(fold_denial_max, 3).
% 1.59/1.84 % set(auto2) -> assign(max_weight, "200.000").
% 1.59/1.84 % set(auto2) -> assign(max_hours, 1).
% 1.59/1.84 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.59/1.84 % set(auto2) -> assign(max_seconds, 0).
% 1.59/1.84 % set(auto2) -> assign(max_minutes, 5).
% 1.59/1.84 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.59/1.84 % set(auto2) -> set(sort_initial_sos).
% 1.59/1.84 % set(auto2) -> assign(sos_limit, -1).
% 1.59/1.84 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.59/1.84 % set(auto2) -> assign(max_megs, 400).
% 1.59/1.84 % set(auto2) -> assign(stats, some).
% 1.59/1.84 % set(auto2) -> clear(echo_input).
% 1.59/1.84 % set(auto2) -> set(quiet).
% 1.59/1.84 % set(auto2) -> clear(print_initial_clauses).
% 1.59/1.84 % set(auto2) -> clear(print_given).
% 1.59/1.84 assign(lrs_ticks,-1).
% 1.59/1.84 assign(sos_limit,10000).
% 1.59/1.84 assign(order,kbo).
% 1.59/1.84 set(lex_order_vars).
% 1.59/1.84 clear(print_given).
% 1.59/1.84
% 1.59/1.84 % formulas(sos). % not echoed (623 formulas)
% 1.59/1.84
% 1.59/1.84 ============================== end of input ==========================
% 1.59/1.84
% 1.59/1.84 % From the command line: assign(max_seconds, 300).
% 1.59/1.84
% 1.59/1.84 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.59/1.84
% 1.59/1.84 % Formulas that are not ordinary clauses:
% 1.59/1.84 1 (all X_b all X_c ti(fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool))),big_comm_monoid_big(X_b,X_c)) = big_comm_monoid_big(X_b,X_c)) # label(tsy_c_Big__Operators_Ocomm__monoid__big_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 2 (all X_b (lattice(X_b) -> ti(fun(fun(X_b,bool),X_b),big_lattice_Sup_fin(X_b)) = big_lattice_Sup_fin(X_b))) # label(tsy_c_Big__Operators_Olattice__class_OSup__fin_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 3 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),big_semilattice_big(X_b)) = big_semilattice_big(X_b)) # label(tsy_c_Big__Operators_Osemilattice__big_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 4 (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].
% 1.59/1.84 5 (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].
% 1.59/1.84 6 (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].
% 1.59/1.84 7 (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].
% 1.59/1.84 8 (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].
% 1.59/1.84 9 (all X_b ti(fun(fun(glb_1,X_b),fun(fun(loc_1,X_b),fun(vname,X_b))),vname_case(X_b)) = vname_case(X_b)) # label(tsy_c_Com_Ovname_Ovname__case_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 10 (all X_b ti(fun(fun(glb_1,X_b),fun(fun(loc_1,X_b),fun(vname,X_b))),vname_rec(X_b)) = vname_rec(X_b)) # label(tsy_c_Com_Ovname_Ovname__rec_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 11 (all X_b all X_c ti(fun(fun(X_b,fun(X_c,X_c)),bool),finite100568337ommute(X_b,X_c)) = finite100568337ommute(X_b,X_c)) # label(tsy_c_Finite__Set_Ocomp__fun__commute_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 12 (all X_b all X_c ti(fun(fun(X_b,fun(X_c,X_c)),bool),finite_comp_fun_idem(X_b,X_c)) = finite_comp_fun_idem(X_b,X_c)) # label(tsy_c_Finite__Set_Ocomp__fun__idem_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 13 (all X_b ti(fun(fun(X_b,bool),bool),finite_finite_1(X_b)) = finite_finite_1(X_b)) # label(tsy_c_Finite__Set_Ofinite_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 14 (all X_b all X_c ti(fun(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold(X_b,X_c)) = finite_fold(X_b,X_c)) # label(tsy_c_Finite__Set_Ofold_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 15 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b)),finite_fold1(X_b)) = finite_fold1(X_b)) # label(tsy_c_Finite__Set_Ofold1_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 16 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool))),finite_fold1Set(X_b)) = finite_fold1Set(X_b)) # label(tsy_c_Finite__Set_Ofold1Set_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 17 (all X_b all X_c ti(fun(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool)))),finite_fold_graph(X_b,X_c)) = finite_fold_graph(X_b,X_c)) # label(tsy_c_Finite__Set_Ofold__graph_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 18 (all X_b all X_c ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)))),finite_fold_image(X_b,X_c)) = finite_fold_image(X_b,X_c)) # label(tsy_c_Finite__Set_Ofold__image_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 19 (all X_b all X_c ti(fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)))),finite1357897459simple(X_b,X_c)) = finite1357897459simple(X_b,X_c)) # label(tsy_c_Finite__Set_Ofolding__image__simple_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 20 (all X_b all X_c ti(fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)))),finite908156982e_idem(X_b,X_c)) = finite908156982e_idem(X_b,X_c)) # label(tsy_c_Finite__Set_Ofolding__image__simple__idem_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 21 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),finite_folding_one(X_b)) = finite_folding_one(X_b)) # label(tsy_c_Finite__Set_Ofolding__one_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 22 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),finite2073411215e_idem(X_b)) = finite2073411215e_idem(X_b)) # label(tsy_c_Finite__Set_Ofolding__one__idem_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 23 (all X_c (minus(X_c) -> ti(fun(X_c,fun(X_c,X_c)),minus_minus(X_c)) = minus_minus(X_c))) # label(tsy_c_Groups_Ominus__class_Ominus_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 24 (all X_b (ab_semigroup_mult(X_b) -> ti(fun(X_b,fun(X_b,X_b)),times_times(X_b)) = times_times(X_b))) # label(tsy_c_Groups_Otimes__class_Otimes_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 25 (all X_b ti(fun(fun(X_b,bool),X_b),the(X_b)) = the(X_b)) # label(tsy_c_HOL_OThe_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 26 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 27 (all X_b ti(fun(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool)),hoare_279057269derivs(X_b)) = hoare_279057269derivs(X_b)) # label(tsy_c_Hoare__Mirabelle__nrugjuseim_Ohoare__derivs_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 28 (all X_b ti(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),hoare_246368825triple(X_b)) = hoare_246368825triple(X_b)) # label(tsy_c_Hoare__Mirabelle__nrugjuseim_Otriple_Otriple_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 29 (all X_c all X_b ti(fun(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_1656922687triple(X_c),X_b)),hoare_1312322281e_case(X_c,X_b)) = hoare_1312322281e_case(X_c,X_b)) # label(tsy_c_Hoare__Mirabelle__nrugjuseim_Otriple_Otriple__case_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 30 (all X_c all X_b ti(fun(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_1656922687triple(X_c),X_b)),hoare_1632998903le_rec(X_c,X_b)) = hoare_1632998903le_rec(X_c,X_b)) # label(tsy_c_Hoare__Mirabelle__nrugjuseim_Otriple_Otriple__rec_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 31 (all X_b ti(fun(nat,fun(hoare_1656922687triple(X_b),bool)),hoare_920331057_valid(X_b)) = hoare_920331057_valid(X_b)) # label(tsy_c_Hoare__Mirabelle__nrugjuseim_Otriple__valid_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 32 (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].
% 1.59/1.84 33 (all X_b (semilattice_sup(X_b) -> ti(fun(X_b,fun(X_b,X_b)),semilattice_sup_sup(X_b)) = semilattice_sup_sup(X_b))) # label(tsy_c_Lattices_Osemilattice__sup__class_Osup_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 34 (all X_b all X_c ti(fun(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool)))),fold_graph(X_b,X_c)) = fold_graph(X_b,X_c)) # label(tsy_c_Nitpick_Ofold__graph_H_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 35 (all X_b (bot(X_b) -> ti(X_b,bot_bot(X_b)) = bot_bot(X_b))) # label(tsy_c_Orderings_Obot__class_Obot_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 36 (all X_c (ord(X_c) -> ti(fun(X_c,fun(X_c,bool)),ord_less_eq(X_c)) = ord_less_eq(X_c))) # label(tsy_c_Orderings_Oord__class_Oless__eq_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 37 (all X_b ti(fun(X_b,fun(fun(X_b,bool),X_b)),partial_flat_lub(X_b)) = partial_flat_lub(X_b)) # label(tsy_c_Partial__Function_Oflat__lub_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 38 (all X_b ti(fun(fun(X_b,bool),fun(X_b,bool)),collect(X_b)) = collect(X_b)) # label(tsy_c_Set_OCollect_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 39 (all X_b all X_c ti(fun(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool))),image(X_b,X_c)) = image(X_b,X_c)) # label(tsy_c_Set_Oimage_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 40 (all X_b ti(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),insert(X_b)) = insert(X_b)) # label(tsy_c_Set_Oinsert_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 41 (all X_b ti(fun(fun(X_b,bool),X_b),the_elem(X_b)) = the_elem(X_b)) # label(tsy_c_Set_Othe__elem_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 42 (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].
% 1.59/1.84 43 (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].
% 1.59/1.84 44 (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].
% 1.59/1.84 45 (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].
% 1.59/1.84 46 (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].
% 1.59/1.84 47 (all X_b ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b)) = member(X_b)) # label(tsy_c_member_res) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 48 (all X_b all Ga hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),bot_bot(fun(hoare_1656922687triple(X_b),bool))))) # label(fact_0_empty) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 49 (all X_b all Fun1_1 all Com_1 all Fun2_1 all Fun1_2 all Com all Fun2_2 (hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Fun1_1),Com_1),Fun2_1) = hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Fun1_2),Com),Fun2_2) <-> Fun1_1 = Fun1_2 & Com_1 = Com & Fun2_1 = Fun2_2)) # label(fact_1_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 50 (all X_b all Ga all G_1 all Ts (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),G_1),Ts)) -> (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),G_1)) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),Ts))))) # label(fact_2_cut) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 51 (all X_b all Ts all Ga all T_5 (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),T_5),bot_bot(fun(hoare_1656922687triple(X_b),bool))))) -> (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),Ts)) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),T_5),Ts)))))) # label(fact_3_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 52 (all X_b all Ga all Pa all Ca all Q_1 all C ((hBOOL(C) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_1656922687triple(X_b),bool)))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),hAPP(bool,fun(X_b,fun(state,bool)),hAPP(fun(X_b,fun(bool,fun(state,bool))),fun(bool,fun(X_b,fun(state,bool))),combc(X_b,bool,fun(state,bool)),hAPP(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(bool,fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(bool,fun(state,bool))),fun(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(bool,fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X_b),combc(state,bool,bool)),hAPP(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),Pa))),C)),Ca),Q_1)),bot_bot(fun(hoare_1656922687triple(X_b),bool))))))) # label(fact_4_constant) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 53 (all X_b all Ga all Ca all Q_1 all Pa ((all Z_2 all S_2 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_2),S_2)) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),hAPP(fun(state,bool),fun(X_b,fun(state,bool)),combk(fun(state,bool),X_b),hAPP(state,fun(state,bool),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),S_2))),Ca),hAPP(fun(state,bool),fun(X_b,fun(state,bool)),combk(fun(state,bool),X_b),hAPP(X_b,fun(state,bool),Q_1,Z_2)))),bot_bot(fun(hoare_1656922687triple(X_b),bool))))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_1656922687triple(X_b),bool))))))) # label(fact_5_escape) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 54 (all X_b all Q_1 all Ga all Pa all Ca all Q_3 (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_1656922687triple(X_b),bool))))) -> ((all Z_2 all S_2 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_3,Z_2),S_2)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_2),S_2)))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_1656922687triple(X_b),bool)))))))) # label(fact_6_conseq2) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 55 (all X_b all Pa all Ga all P_2 all Ca all Q_1 (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),P_2),Ca),Q_1)),bot_bot(fun(hoare_1656922687triple(X_b),bool))))) -> ((all Z_2 all S_2 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_2),S_2)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_2,Z_2),S_2)))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_1656922687triple(X_b),bool)))))))) # label(fact_7_conseq1) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 56 (all X_b all Q_1 all Pa all Ga all P_2 all Ca all Q_3 (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),P_2),Ca),Q_3)),bot_bot(fun(hoare_1656922687triple(X_b),bool))))) -> ((all Z_2 all S_2 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_2),S_2)) -> (all S_3 ((all Z_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_2,Z_3),S_2)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_3,Z_3),S_3)))) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_2),S_3)))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_1656922687triple(X_b),bool)))))))) # label(fact_8_conseq12) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 57 (all X_b all A_3 all Ba all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),A_1))) -> (ti(X_b,A_3) != ti(X_b,Ba) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),A_1))))) # label(fact_9_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 58 (all X_b all Ba all A_3 all B ((-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),B)) -> ti(X_b,A_3) = ti(X_b,Ba)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),B))))) # label(fact_10_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 59 (all X_b all A_3 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),bot_bot(fun(X_b,bool))))) # label(fact_11_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 60 (all X_b all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),bot_bot(fun(X_b,bool)))) # label(fact_12_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 61 (all X_b all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),bot_bot(fun(X_b,bool)))) # label(fact_13_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 62 (all X_b all Pa all A_3 ((hBOOL(hAPP(X_b,bool,Pa,A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_3))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),bot_bot(fun(X_b,bool)))) & (-hBOOL(hAPP(X_b,bool,Pa,A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_3))),Pa)) = bot_bot(fun(X_b,bool))))) # label(fact_14_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 63 (all X_b all Pa all A_3 ((hBOOL(hAPP(X_b,bool,Pa,A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_3))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),bot_bot(fun(X_b,bool)))) & (-hBOOL(hAPP(X_b,bool,Pa,A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_3))),Pa)) = bot_bot(fun(X_b,bool))))) # label(fact_15_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.84 64 (all X_c all X_b all F1 all Fun1_1 all Com_1 all Fun2_1 hAPP(hoare_1656922687triple(X_c),X_b,hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_1656922687triple(X_c),X_b),hoare_1632998903le_rec(X_c,X_b),F1),hAPP(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c))),hoare_246368825triple(X_c),Fun1_1),Com_1),Fun2_1)) = hAPP(fun(X_c,fun(state,bool)),X_b,hAPP(com,fun(fun(X_c,fun(state,bool)),X_b),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b)),F1,Fun1_1),Com_1),Fun2_1)) # label(fact_16_triple_Orecs) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.85 65 (all X_b all A_3 all A_1 (ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,bool)) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),A_1)))) # label(fact_17_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.85 66 (all X_b all Pa (hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = bot_bot(fun(X_b,bool)) <-> (all X_2 -hBOOL(hAPP(X_b,bool,Pa,X_2))))) # label(fact_18_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.85 67 (all X_b all Ca -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),bot_bot(fun(X_b,bool))))) # label(fact_19_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.85 68 (all X_b all Pa (bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) <-> (all X_2 -hBOOL(hAPP(X_b,bool,Pa,X_2))))) # label(fact_20_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.85 69 (all X_b all A_1 ((exists X_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))) <-> ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)))) # label(fact_21_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.85 70 (all X_b all A_1 ((all X_2 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))) <-> ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,bool)))) # label(fact_22_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.85 71 (all X_b bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse))) # label(fact_23_empty__def) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.85 72 (all X_b all A_3 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),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),A_3),A_1) = ti(fun(X_b,bool),A_1))) # label(fact_24_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.85 73 (all X_b all Ba all A_3 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),B)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),B))))) # label(fact_25_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.85 74 (all X_b all B all X_1 all A_1 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B) <-> ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B))))) # label(fact_26_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.85 75 (all X_b all Y_1 all A_1 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),A_1),X_1)) <-> ti(X_b,Y_1) = ti(X_b,X_1) | hBOOL(hAPP(X_b,bool,A_1,X_1)))) # label(fact_27_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.85 76 (all X_b all A_3 all Ba all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),A_1))) <-> ti(X_b,A_3) = ti(X_b,Ba) | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),A_1)))) # label(fact_28_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.85 77 (all X_b all X_1 all Y_1 all 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_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_1),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_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1))) # label(fact_29_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.85 78 (all X_b all X_1 all 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_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) # label(fact_30_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.85 79 (all X_b all A_3 all Pa hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fimplies),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_3)))),Pa))) # label(fact_31_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.85 80 (all X_b all A_3 all B hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),B) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_3))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B)))) # label(fact_32_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.85 81 (all X_b all A_3 all B hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),B)))) # label(fact_33_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.85 82 (all X_b all X_2 all Xa hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),Xa) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),Xa)))) # label(fact_34_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.85 83 (all X_b all A_3 all Ba (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_3),bot_bot(fun(X_b,bool))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),bot_bot(fun(X_b,bool))) -> ti(X_b,A_3) = ti(X_b,Ba))) # label(fact_35_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.85 84 (all X_b all Ba all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),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_3),bot_bot(fun(X_b,bool))))) -> ti(X_b,Ba) = ti(X_b,A_3))) # label(fact_36_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 85 (all X_b all A_3 all Ba all Ca all D_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),bot_bot(fun(X_b,bool)))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),D_2),bot_bot(fun(X_b,bool)))) <-> ti(X_b,A_3) = ti(X_b,Ca) & ti(X_b,Ba) = ti(X_b,D_2) | ti(X_b,A_3) = ti(X_b,D_2) & ti(X_b,Ba) = ti(X_b,Ca))) # label(fact_37_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 86 (all X_b all Ba all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),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_3),bot_bot(fun(X_b,bool))))) <-> ti(X_b,Ba) = ti(X_b,A_3))) # label(fact_38_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 87 (all X_b all A_3 all 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),A_3),A_1) != bot_bot(fun(X_b,bool))) # label(fact_39_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 88 (all X_b all A_3 all A_1 bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),A_1)) # label(fact_40_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 89 (all X_b all X_1 hAPP(fun(X_b,bool),X_b,the_elem(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1)) # label(fact_41_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 90 (all X_c all X_b all F1 all Fun1_1 all Com_1 all Fun2_1 hAPP(hoare_1656922687triple(X_c),X_b,hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_1656922687triple(X_c),X_b),hoare_1312322281e_case(X_c,X_b),F1),hAPP(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c))),hoare_246368825triple(X_c),Fun1_1),Com_1),Fun2_1)) = hAPP(fun(X_c,fun(state,bool)),X_b,hAPP(com,fun(fun(X_c,fun(state,bool)),X_b),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b)),F1,Fun1_1),Com_1),Fun2_1)) # label(fact_42_triple_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 91 (all X_c all X_b (bot(X_b) -> (all X_1 hAPP(X_c,X_b,bot_bot(fun(X_c,X_b)),X_1) = bot_bot(X_b)))) # label(fact_43_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 92 (all X_b all X_c (bot(X_c) -> (all X_2 hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c)))) # label(fact_44_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 93 (all X_b all Ga all Pa hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Pa),skip),Pa)),bot_bot(fun(hoare_1656922687triple(X_b),bool)))))) # label(fact_45_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 94 (all X_b all D_2 all R_1 all Ga all Pa all Ca all Q_1 (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_1656922687triple(X_b),bool))))) -> (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Q_1),D_2),R_1)),bot_bot(fun(hoare_1656922687triple(X_b),bool))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Pa),hAPP(com,com,hAPP(com,fun(com,com),semi,Ca),D_2)),R_1)),bot_bot(fun(hoare_1656922687triple(X_b),bool)))))))) # label(fact_46_Comp) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 95 (all X_b all Y_1 -(all Fun1 all Com_2 all Fun2 Y_1 != hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Fun1),Com_2),Fun2))) # label(fact_47_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 96 (all X_b all X_1 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) -> -(all B_2 (ti(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_1),B_2) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)))))) # label(fact_48_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 97 (all X_b all A_3 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),A_1)) -> (exists B_2 (ti(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),A_3),B_2) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),B_2)))))) # label(fact_49_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 98 (all X_b all A_1 ((all Y_2 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),A_1))) -> ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,bool)))) # label(fact_50_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 99 (all X_b all Q_1 all Ga all Ca all Pa ((all Z_2 all S_2 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_2),S_2)) -> (exists P_1 exists Q_2 (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_1656922687triple(X_b),bool))))) & (all S_3 ((all Z_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_3),S_2)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_3),S_3)))) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_2),S_3)))))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_1656922687triple(X_b),bool))))))) # label(fact_51_conseq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 100 (all Com1_2 all Com2_2 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2) != skip) # label(fact_52_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 101 (all Com1_2 all Com2_2 skip != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2)) # label(fact_53_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 102 (all X_b all X_3 hAPP(fun(X_b,bool),X_b,the_elem(X_b),X_3) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),fequal(fun(X_b,bool)),X_3)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool)))))) # label(fact_54_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 103 (all Com1_1 all Com2_1 all Com1 all Com2 (hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1) = hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2) <-> Com1_1 = Com1 & Com2_1 = Com2)) # label(fact_55_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 104 (all X_b all A_1 (ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) <-> (exists X_2 exists B_2 (ti(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),B_2) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)))))) # label(fact_56_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 105 (all X_b all X_2 (hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),bot_bot(fun(X_b,bool)))))) # label(fact_57_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 106 (all X_b all Ga all Pa all X_3 all A_3 hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),hAPP(fun(state,state),fun(X_b,fun(state,bool)),hAPP(fun(X_b,fun(fun(state,state),fun(state,bool))),fun(fun(state,state),fun(X_b,fun(state,bool))),combc(X_b,fun(state,state),fun(state,bool)),hAPP(fun(X_b,fun(state,bool)),fun(X_b,fun(fun(state,state),fun(state,bool))),hAPP(fun(fun(state,bool),fun(fun(state,state),fun(state,bool))),fun(fun(X_b,fun(state,bool)),fun(X_b,fun(fun(state,state),fun(state,bool)))),combb(fun(state,bool),fun(fun(state,state),fun(state,bool)),X_b),combb(state,bool,state)),Pa)),hAPP(fun(state,nat),fun(state,state),hAPP(fun(state,fun(nat,state)),fun(fun(state,nat),fun(state,state)),combs(state,nat,state),hAPP(vname,fun(state,fun(nat,state)),hAPP(fun(state,fun(vname,fun(nat,state))),fun(vname,fun(state,fun(nat,state))),combc(state,vname,fun(nat,state)),update),X_3)),A_3))),hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,X_3),A_3)),Pa)),bot_bot(fun(hoare_1656922687triple(X_b),bool)))))) # label(fact_58_Ass) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 107 (all X_c all X_b all Ca all A_1 ((ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),Ca)),A_1) = bot_bot(fun(X_c,bool))) & (ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),Ca)),A_1) = hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),Ca),bot_bot(fun(X_c,bool)))))) # label(fact_59_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 108 (all X_c all X_b all Ca all X_1 all A_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(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),Ca)),A_1) = hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),Ca),bot_bot(fun(X_c,bool))))) # label(fact_60_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 109 (all X_b all X_c all A_1 all Ba all F all X_1 (ti(X_b,Ba) = hAPP(X_c,X_b,F,X_1) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_1)))))) # label(fact_61_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 110 (all X_b all Y_4 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),combi(X_b)),Y_4) = ti(fun(X_b,bool),Y_4)) # label(fact_62_image__ident) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 111 (all X_c all X_b all X_d all F all G all A_1 hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_d,bool),fun(X_c,bool),hAPP(fun(X_d,X_c),fun(fun(X_d,bool),fun(X_c,bool)),image(X_d,X_c),G),A_1)) = hAPP(fun(X_d,bool),fun(X_b,bool),hAPP(fun(X_d,X_b),fun(fun(X_d,bool),fun(X_b,bool)),image(X_d,X_b),hAPP(fun(X_d,X_c),fun(X_d,X_b),hAPP(fun(X_c,X_b),fun(fun(X_d,X_c),fun(X_d,X_b)),combb(X_c,X_b,X_d),F),G)),A_1)) # label(fact_63_image__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 112 (all Vname all Fun_1 all Vname_1 all Fun (hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname),Fun_1) = hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname_1),Fun) <-> ti(vname,Vname) = ti(vname,Vname_1) & Fun_1 = Fun)) # label(fact_64_com_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 113 (all X_c all X_b all Ba all F all X_1 all A_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_c,Ba) = hAPP(X_b,X_c,F,X_1) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Ba),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_1)))))) # label(fact_65_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 114 (all X_c all X_b all F all X_1 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_1))))) # label(fact_66_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 115 (all X_b all X_c all Z_1 all F all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z_1),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_1))) <-> (exists X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_1)) & ti(X_b,Z_1) = hAPP(X_c,X_b,F,X_2))))) # label(fact_67_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 116 (all Vname all Fun_1 all Com1 all Com2 hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname),Fun_1) != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2)) # label(fact_68_com_Osimps_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 117 (all Com1 all Com2 all Vname all Fun_1 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2) != hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname),Fun_1)) # label(fact_69_com_Osimps_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 118 (all Vname_1 all Fun skip != hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname_1),Fun)) # label(fact_70_com_Osimps_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 119 (all Vname_1 all Fun hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname_1),Fun) != skip) # label(fact_71_com_Osimps_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 120 (all X_c all X_b all F all A_1 (hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_1) = bot_bot(fun(X_b,bool)) <-> ti(fun(X_c,bool),A_1) = bot_bot(fun(X_c,bool)))) # label(fact_72_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 121 (all X_c all X_b all F hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),bot_bot(fun(X_c,bool))) = bot_bot(fun(X_b,bool))) # label(fact_73_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 122 (all X_b all X_c all F all A_1 (bot_bot(fun(X_b,bool)) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_1) <-> ti(fun(X_c,bool),A_1) = bot_bot(fun(X_c,bool)))) # label(fact_74_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 123 (all X_b all X_c all F all G ((all X_2 hAPP(X_b,X_c,F,X_2) = hAPP(X_b,X_c,G,X_2)) -> ti(fun(X_b,X_c),F) = ti(fun(X_b,X_c),G))) # label(fact_75_ext) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 124 (all X_b all X_1 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) <-> hBOOL(hAPP(X_b,bool,A_1,X_1)))) # label(fact_76_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 125 (all X_b all Pa hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa)) # label(fact_77_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 126 (all X_c all X_b all F all X_1 all A_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(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_1)) = hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_1))) # label(fact_78_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 127 (all X_c all X_b all F all A_3 all B hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),A_3),B)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),hAPP(X_c,X_b,F,A_3)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B))) # label(fact_79_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 128 (all X_b all X_c all Ba all F all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_1))) -> -(all X_2 (ti(X_b,Ba) = hAPP(X_c,X_b,F,X_2) -> -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_1)))))) # label(fact_80_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 129 (all X_b all X_1 hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),X_1)) = ti(X_b,X_1)) # label(fact_81_the__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 130 (all X_b all A_3 hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_3)) = ti(X_b,A_3)) # label(fact_82_the__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 131 (all X_b all X_1 all Y_1 all Pa ((hBOOL(Pa) -> ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_1)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),Y_1))))) & (-hBOOL(Pa) -> ti(X_b,Y_1) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_1)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),Y_1))))))) # label(fact_83_If__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 132 (all X_c all X_b all F all G all M_2 all N (ti(fun(X_b,bool),M_2) = ti(fun(X_b,bool),N) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),N)) -> hAPP(X_b,X_c,F,X_2) = hAPP(X_b,X_c,G,X_2))) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),M_2) = hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),G),N)))) # label(fact_84_image__cong) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 133 (all X_b all F all A_3 all Ba (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),bot_bot(fun(X_b,bool)))),Ba)) <-> ti(X_b,A_3) = ti(X_b,Ba))) # label(fact_85_fold1Set__sing) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 134 (all X_b all Pa all A_3 (hBOOL(hAPP(X_b,bool,Pa,A_3)) -> ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> ti(X_b,X_2) = ti(X_b,A_3))) -> hAPP(fun(X_b,bool),X_b,the(X_b),Pa) = ti(X_b,A_3)))) # label(fact_86_the__equality) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 135 (all X_b all X_1 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1)) -> hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1))) # label(fact_87_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 136 (all X_b all A_3 all Ga all Pa all Ca all Q_1 all X_3 all S_5 (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Pa),Ca),hAPP(fun(state,state),fun(X_b,fun(state,bool)),hAPP(fun(X_b,fun(fun(state,state),fun(state,bool))),fun(fun(state,state),fun(X_b,fun(state,bool))),combc(X_b,fun(state,state),fun(state,bool)),hAPP(fun(X_b,fun(state,bool)),fun(X_b,fun(fun(state,state),fun(state,bool))),hAPP(fun(fun(state,bool),fun(fun(state,state),fun(state,bool))),fun(fun(X_b,fun(state,bool)),fun(X_b,fun(fun(state,state),fun(state,bool)))),combb(fun(state,bool),fun(fun(state,state),fun(state,bool)),X_b),combb(state,bool,state)),Q_1)),hAPP(nat,fun(state,state),hAPP(fun(state,fun(nat,state)),fun(nat,fun(state,state)),combc(state,nat,state),hAPP(vname,fun(state,fun(nat,state)),hAPP(fun(state,fun(vname,fun(nat,state))),fun(vname,fun(state,fun(nat,state))),combc(state,vname,fun(nat,state)),update),hAPP(loc_1,vname,loc,X_3))),hAPP(loc_1,nat,hAPP(state,fun(loc_1,nat),getlocs,S_5),X_3))))),bot_bot(fun(hoare_1656922687triple(X_b),bool))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),hAPP(fun(X_b,fun(state,bool)),fun(X_b,fun(state,bool)),hAPP(fun(fun(state,bool),fun(state,bool)),fun(fun(X_b,fun(state,bool)),fun(X_b,fun(state,bool))),combb(fun(state,bool),fun(state,bool),X_b),hAPP(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),combs(state,bool,bool),hAPP(fun(state,bool),fun(state,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj),hAPP(state,fun(state,bool),fequal(state),S_5)))),hAPP(fun(state,state),fun(X_b,fun(state,bool)),hAPP(fun(X_b,fun(fun(state,state),fun(state,bool))),fun(fun(state,state),fun(X_b,fun(state,bool))),combc(X_b,fun(state,state),fun(state,bool)),hAPP(fun(X_b,fun(state,bool)),fun(X_b,fun(fun(state,state),fun(state,bool))),hAPP(fun(fun(state,bool),fun(fun(state,state),fun(state,bool))),fun(fun(X_b,fun(state,bool)),fun(X_b,fun(fun(state,state),fun(state,bool)))),combb(fun(state,bool),fun(fun(state,state),fun(state,bool)),X_b),combb(state,bool,state)),Pa)),hAPP(fun(state,nat),fun(state,state),hAPP(fun(state,fun(nat,state)),fun(fun(state,nat),fun(state,state)),combs(state,nat,state),hAPP(vname,fun(state,fun(nat,state)),hAPP(fun(state,fun(vname,fun(nat,state))),fun(vname,fun(state,fun(nat,state))),combc(state,vname,fun(nat,state)),update),hAPP(loc_1,vname,loc,X_3))),A_3)))),hAPP(com,com,hAPP(fun(state,nat),fun(com,com),hAPP(loc_1,fun(fun(state,nat),fun(com,com)),local,X_3),A_3),Ca)),Q_1)),bot_bot(fun(hoare_1656922687triple(X_b),bool))))))) # label(fact_88_hoare__derivs_OLocal) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 137 (all Loc_2 all Loc_3 (hAPP(loc_1,vname,loc,Loc_2) = hAPP(loc_1,vname,loc,Loc_3) <-> ti(loc_1,Loc_2) = ti(loc_1,Loc_3))) # label(fact_89_vname_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 138 (all Loc_2 all Fun_1 all Com_1 all Loc_3 all Fun all Com (hAPP(com,com,hAPP(fun(state,nat),fun(com,com),hAPP(loc_1,fun(fun(state,nat),fun(com,com)),local,Loc_2),Fun_1),Com_1) = hAPP(com,com,hAPP(fun(state,nat),fun(com,com),hAPP(loc_1,fun(fun(state,nat),fun(com,com)),local,Loc_3),Fun),Com) <-> ti(loc_1,Loc_2) = ti(loc_1,Loc_3) & Fun_1 = Fun & Com_1 = Com)) # label(fact_90_com_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 139 (all Loc_2 all Fun_1 all Com_1 all Com1 all Com2 hAPP(com,com,hAPP(fun(state,nat),fun(com,com),hAPP(loc_1,fun(fun(state,nat),fun(com,com)),local,Loc_2),Fun_1),Com_1) != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2)) # label(fact_91_com_Osimps_I34_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 140 (all Com1 all Com2 all Loc_2 all Fun_1 all Com_1 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2) != hAPP(com,com,hAPP(fun(state,nat),fun(com,com),hAPP(loc_1,fun(fun(state,nat),fun(com,com)),local,Loc_2),Fun_1),Com_1)) # label(fact_92_com_Osimps_I35_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 141 (all Loc_3 all Fun all Com all Vname all Fun_1 hAPP(com,com,hAPP(fun(state,nat),fun(com,com),hAPP(loc_1,fun(fun(state,nat),fun(com,com)),local,Loc_3),Fun),Com) != hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname),Fun_1)) # label(fact_93_com_Osimps_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 142 (all Vname all Fun_1 all Loc_3 all Fun all Com hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname),Fun_1) != hAPP(com,com,hAPP(fun(state,nat),fun(com,com),hAPP(loc_1,fun(fun(state,nat),fun(com,com)),local,Loc_3),Fun),Com)) # label(fact_94_com_Osimps_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 143 (all Loc_3 all Fun all Com hAPP(com,com,hAPP(fun(state,nat),fun(com,com),hAPP(loc_1,fun(fun(state,nat),fun(com,com)),local,Loc_3),Fun),Com) != skip) # label(fact_95_com_Osimps_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 144 (all Loc_3 all Fun all Com skip != hAPP(com,com,hAPP(fun(state,nat),fun(com,com),hAPP(loc_1,fun(fun(state,nat),fun(com,com)),local,Loc_3),Fun),Com)) # label(fact_96_com_Osimps_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 145 (all X_b all F all X_1 -hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),bot_bot(fun(X_b,bool))),X_1))) # label(fact_97_empty__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 146 (all X_b all F all A_1 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_1),X_1)) -> ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)))) # label(fact_98_fold1Set__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 147 (all X_b all Pa all A_3 (hBOOL(hAPP(X_b,bool,Pa,A_3)) -> ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> ti(X_b,X_2) = ti(X_b,A_3))) -> hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa)))))) # label(fact_99_theI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 148 (all X_b all A_3 all Pa ((exists X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) & (all Y_2 (hBOOL(hAPP(X_b,bool,Pa,Y_2)) -> ti(X_b,Y_2) = ti(X_b,X_2))))) -> (hBOOL(hAPP(X_b,bool,Pa,A_3)) -> hAPP(fun(X_b,bool),X_b,the(X_b),Pa) = ti(X_b,A_3)))) # label(fact_100_the1__equality) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 149 (all X_b all Pa ((exists X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) & (all Y_2 (hBOOL(hAPP(X_b,bool,Pa,Y_2)) -> ti(X_b,Y_2) = ti(X_b,X_2))))) -> hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa))))) # label(fact_101_theI_H) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 150 (all X_b all F1 all F2 all Loc_2 hAPP(vname,X_b,hAPP(fun(loc_1,X_b),fun(vname,X_b),hAPP(fun(glb_1,X_b),fun(fun(loc_1,X_b),fun(vname,X_b)),vname_rec(X_b),F1),F2),hAPP(loc_1,vname,loc,Loc_2)) = hAPP(loc_1,X_b,F2,Loc_2)) # label(fact_102_vname_Orecs_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 151 (all X_b all F1 all F2 all Loc_2 hAPP(vname,X_b,hAPP(fun(loc_1,X_b),fun(vname,X_b),hAPP(fun(glb_1,X_b),fun(fun(loc_1,X_b),fun(vname,X_b)),vname_case(X_b),F1),F2),hAPP(loc_1,vname,loc,Loc_2)) = hAPP(loc_1,X_b,F2,Loc_2)) # label(fact_103_vname_Osimps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 152 (all Ca all S0_1 all Y_4 all A_3 all S1_2 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,Ca),hAPP(nat,state,hAPP(vname,fun(nat,state),hAPP(state,fun(vname,fun(nat,state)),update,S0_1),hAPP(loc_1,vname,loc,Y_4)),hAPP(state,nat,A_3,S0_1))),S1_2)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,nat),fun(com,com),hAPP(loc_1,fun(fun(state,nat),fun(com,com)),local,Y_4),A_3),Ca)),S0_1),hAPP(nat,state,hAPP(vname,fun(nat,state),hAPP(state,fun(vname,fun(nat,state)),update,S1_2),hAPP(loc_1,vname,loc,Y_4)),hAPP(loc_1,nat,hAPP(state,fun(loc_1,nat),getlocs,S0_1),Y_4)))))) # label(fact_104_evalc_OLocal) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 153 (all Ca all S0_1 all Y_4 all A_3 all N_3 all S1_2 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,Ca),hAPP(nat,state,hAPP(vname,fun(nat,state),hAPP(state,fun(vname,fun(nat,state)),update,S0_1),hAPP(loc_1,vname,loc,Y_4)),hAPP(state,nat,A_3,S0_1))),N_3),S1_2)) -> hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,nat),fun(com,com),hAPP(loc_1,fun(fun(state,nat),fun(com,com)),local,Y_4),A_3),Ca)),S0_1),N_3),hAPP(nat,state,hAPP(vname,fun(nat,state),hAPP(state,fun(vname,fun(nat,state)),update,S1_2),hAPP(loc_1,vname,loc,Y_4)),hAPP(loc_1,nat,hAPP(state,fun(loc_1,nat),getlocs,S0_1),Y_4)))))) # label(fact_105_evaln_OLocal) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 154 (all X_b all F all A_3 all A_1 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),F),A_3),A_1),X_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),A_1)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),A_1)),X_1))))) # label(fact_106_fold1Set_Ointros) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 155 (all C1 all S2 all C0 all S0 all N_2 all S1 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C0),S0),N_2),S1)) -> (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1),S1),N_2),S2)) -> hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),semi,C0),C1)),S0),N_2),S2))))) # label(fact_107_evaln_OSemi) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 156 (all S_1 all N_2 hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,skip),S_1),N_2),S_1))) # label(fact_108_evaln_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 157 (all S_1 all N_2 all T_4 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,skip),S_1),N_2),T_4)) -> T_4 = S_1)) # label(fact_109_evaln__elim__cases_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 158 (all C1 all S2 all C0 all S0 all S1 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C0),S0),S1)) -> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1),S1),S2)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),semi,C0),C1)),S0),S2))))) # label(fact_110_evalc_OSemi) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 159 (all S_1 hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,skip),S_1),S_1))) # label(fact_111_evalc_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 160 (all S_1 all T_4 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,skip),S_1),T_4)) -> T_4 = S_1)) # label(fact_112_evalc__elim__cases_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 161 (all X_3 all A_3 all S_4 all N_3 hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,X_3),A_3)),S_4),N_3),hAPP(nat,state,hAPP(vname,fun(nat,state),hAPP(state,fun(vname,fun(nat,state)),update,S_4),X_3),hAPP(state,nat,A_3,S_4))))) # label(fact_113_evaln_OAssign) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 162 (all X_3 all A_3 all S_4 all N_3 all T_5 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,X_3),A_3)),S_4),N_3),T_5)) -> T_5 = hAPP(nat,state,hAPP(vname,fun(nat,state),hAPP(state,fun(vname,fun(nat,state)),update,S_4),X_3),hAPP(state,nat,A_3,S_4)))) # label(fact_114_evaln__elim__cases_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 163 (all X_3 all A_3 all S_4 hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,X_3),A_3)),S_4),hAPP(nat,state,hAPP(vname,fun(nat,state),hAPP(state,fun(vname,fun(nat,state)),update,S_4),X_3),hAPP(state,nat,A_3,S_4))))) # label(fact_115_evalc_OAssign) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 164 (all X_3 all A_3 all S_4 all T_5 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,X_3),A_3)),S_4),T_5)) -> T_5 = hAPP(nat,state,hAPP(vname,fun(nat,state),hAPP(state,fun(vname,fun(nat,state)),update,S_4),X_3),hAPP(state,nat,A_3,S_4)))) # label(fact_116_evalc__elim__cases_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 165 (all Ca all S_4 all T_5 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,Ca),S_4),T_5)) <-> (exists N_1 hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,Ca),S_4),N_1),T_5))))) # label(fact_117_eval__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 166 (all U_1 all C_1 all S_1 all T_4 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S_1),T_4)) -> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S_1),U_1)) -> U_1 = T_4))) # label(fact_118_com__det) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 167 (all C_1 all S_1 all N_2 all T_4 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C_1),S_1),N_2),T_4)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S_1),T_4)))) # label(fact_119_evaln__evalc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 168 (all X_c all X_b all F all Z_1 all X_1 (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_1),bot_bot(fun(X_b,bool))),X_1)) -> ti(X_c,X_1) = ti(X_c,Z_1))) # label(fact_120_empty__fold__graphE) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 169 (all X_c all X_b all F all Z_1 hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_1),bot_bot(fun(X_b,bool))),Z_1))) # label(fact_121_fold__graph_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 170 (all X_c all X_b all F all Z_1 all Y_1 all X_1 all A_1 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_1),A_1),Y_1)) -> hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Y_1)))))) # label(fact_122_fold__graph_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 171 (all Y_4 all A_3 all Ca all S_4 all T_5 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,nat),fun(com,com),hAPP(loc_1,fun(fun(state,nat),fun(com,com)),local,Y_4),A_3),Ca)),S_4),T_5)) -> -(all S1_1 (T_5 = hAPP(nat,state,hAPP(vname,fun(nat,state),hAPP(state,fun(vname,fun(nat,state)),update,S1_1),hAPP(loc_1,vname,loc,Y_4)),hAPP(loc_1,nat,hAPP(state,fun(loc_1,nat),getlocs,S_4),Y_4)) -> -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,Ca),hAPP(nat,state,hAPP(vname,fun(nat,state),hAPP(state,fun(vname,fun(nat,state)),update,S_4),hAPP(loc_1,vname,loc,Y_4)),hAPP(state,nat,A_3,S_4))),S1_1)))))) # label(fact_123_evalc__elim__cases_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 172 (all Y_4 all A_3 all Ca all S_4 all N_3 all T_5 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,nat),fun(com,com),hAPP(loc_1,fun(fun(state,nat),fun(com,com)),local,Y_4),A_3),Ca)),S_4),N_3),T_5)) -> -(all S1_1 (T_5 = hAPP(nat,state,hAPP(vname,fun(nat,state),hAPP(state,fun(vname,fun(nat,state)),update,S1_1),hAPP(loc_1,vname,loc,Y_4)),hAPP(loc_1,nat,hAPP(state,fun(loc_1,nat),getlocs,S_4),Y_4)) -> -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,Ca),hAPP(nat,state,hAPP(vname,fun(nat,state),hAPP(state,fun(vname,fun(nat,state)),update,S_4),hAPP(loc_1,vname,loc,Y_4)),hAPP(state,nat,A_3,S_4))),N_3),S1_1)))))) # label(fact_124_evaln__elim__cases_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 173 (all C1 all C2 all S_1 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_1),T_4)) -> -(all S1_1 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1),S_1),S1_1)) -> -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C2),S1_1),T_4)))))) # label(fact_125_evalc__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 174 (all C1 all C2 all S_1 all N_2 all T_4 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),semi,C1),C2)),S_1),N_2),T_4)) -> -(all S1_1 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1),S_1),N_2),S1_1)) -> -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2),S1_1),N_2),T_4)))))) # label(fact_126_evaln__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 175 (all X_b all F all A_3 all X_3 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),X_3)),X_1)) -> -(all A_4 all A_5 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),X_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),A_5) -> (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),F),A_4),A_5),X_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),A_5))))))) # label(fact_127_insert__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 176 (all Ca hAPP(com,hoare_1656922687triple(state),hoare_Mirabelle_MGT,Ca) = hAPP(fun(state,fun(state,bool)),hoare_1656922687triple(state),hAPP(com,fun(fun(state,fun(state,bool)),hoare_1656922687triple(state)),hAPP(fun(state,fun(state,bool)),fun(com,fun(fun(state,fun(state,bool)),hoare_1656922687triple(state))),hoare_246368825triple(state),fequal(state)),Ca),hAPP(com,fun(state,fun(state,bool)),evalc,Ca))) # label(fact_128_MGT__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 177 (all C_1 all S_1 all T_4 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S_1),T_4)) -> (exists N_1 hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C_1),S_1),N_1),T_4))))) # label(fact_129_evalc__evaln) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 178 (all X_b all F all A1 all A2 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A1),A2)) <-> (exists A_4 exists A_5 exists X_2 (ti(fun(X_b,bool),A1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),A_5) & ti(X_b,A2) = ti(X_b,X_2) & hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),F),A_4),A_5),X_2)) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),A_5)))))) # label(fact_130_fold1Set_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 179 (all X_c all X_b all F all Z_1 all A1 all A2 (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_1),A1),A2)) <-> ti(fun(X_b,bool),A1) = bot_bot(fun(X_b,bool)) & ti(X_c,A2) = ti(X_c,Z_1) | (exists X_2 exists A_5 exists Y_2 (ti(fun(X_b,bool),A1) = hAPP(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_5) & ti(X_c,A2) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_2),Y_2) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_5)) & hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_1),A_5),Y_2)))))) # label(fact_131_fold__graph_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.85 180 (all C2 all S2 all N2 all T2 all C1 all S1 all N1 all T1 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1),S1),N1),T1)) -> (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2),S2),N2),T2)) -> (exists N_1 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1),S1),N_1),T1)) & hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2),S2),N_1),T2))))))) # label(fact_132_evaln__max2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 181 (all X_b all F1 all F2 all Glb_3 hAPP(vname,X_b,hAPP(fun(loc_1,X_b),fun(vname,X_b),hAPP(fun(glb_1,X_b),fun(fun(loc_1,X_b),fun(vname,X_b)),vname_rec(X_b),F1),F2),hAPP(glb_1,vname,glb,Glb_3)) = hAPP(glb_1,X_b,F1,Glb_3)) # label(fact_133_vname_Orecs_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 182 (all X_b all F1 all F2 all Glb_3 hAPP(vname,X_b,hAPP(fun(loc_1,X_b),fun(vname,X_b),hAPP(fun(glb_1,X_b),fun(fun(loc_1,X_b),fun(vname,X_b)),vname_case(X_b),F1),F2),hAPP(glb_1,vname,glb,Glb_3)) = hAPP(glb_1,X_b,F1,Glb_3)) # label(fact_134_vname_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 183 (all X_b all N_3 all Pa all Ca all Q_1 (hBOOL(hAPP(hoare_1656922687triple(X_b),bool,hAPP(nat,fun(hoare_1656922687triple(X_b),bool),hoare_920331057_valid(X_b),N_3),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Pa),Ca),Q_1))) <-> (all Z_2 all S_2 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_2),S_2)) -> (all S_3 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,Ca),S_2),N_3),S_3)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_2),S_3)))))))) # label(fact_135_triple__valid__def2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 184 (all X_b all X_1 all A_1 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_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(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,A_1))))))) # label(fact_136_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 185 (all X_b all Q_1 all Pa (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) | hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),Pa)),Q_1)))))) # label(fact_137_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 186 (all X_b hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),bot_bot(fun(X_b,bool))))) # label(fact_138_finite_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 187 (all X_b all A_3 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),A_1))))) # label(fact_139_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 188 (all X_c all X_b all H all F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1)) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),H),F_1))))) # label(fact_140_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 189 (all X_b all Pa all Q_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),Pa)),Q_1)))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_1))))) # label(fact_141_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 190 (all Glb_3 all Glb_2 (hAPP(glb_1,vname,glb,Glb_3) = hAPP(glb_1,vname,glb,Glb_2) <-> ti(glb_1,Glb_3) = ti(glb_1,Glb_2))) # label(fact_142_vname_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 191 (all X_b (finite_finite(X_b) -> (all A_1 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))))) # label(fact_143_finite__code) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 192 (all X_b (finite_finite(X_b) -> (all A_1 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))))) # label(fact_144_finite) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 193 (all X_b all A_3 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),A_1))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)))) # label(fact_145_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 194 (all Loc_1 all Glb_1 hAPP(loc_1,vname,loc,Loc_1) != hAPP(glb_1,vname,glb,Glb_1)) # label(fact_146_vname_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 195 (all Glb_1 all Loc_1 hAPP(glb_1,vname,glb,Glb_1) != hAPP(loc_1,vname,loc,Loc_1)) # label(fact_147_vname_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 196 (all X_b all A_1 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) -> ((all X_2 all Y_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_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,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,F_1,A_1)),A_1))))))) # label(fact_148_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 197 (all X_b all F all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) -> (exists X1 hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_1),X1)))))) # label(fact_149_finite__nonempty__imp__fold1Set) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 198 (all X_b all Pa all F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))) -> ((all X_2 all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),F_2))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)))))) # label(fact_150_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 199 (all X_b all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) <-> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) | (exists A_5 exists A_4 (ti(fun(X_b,bool),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),A_5) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_5)))))) # label(fact_151_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 200 (all X_c all X_b all F all A_1 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_1))) -> (exists X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) & -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_1))),hAPP(X_c,fun(X_b,bool),hAPP(fun(X_b,fun(X_c,bool)),fun(X_c,fun(X_b,bool)),combc(X_b,X_c,bool),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,bool)),hAPP(fun(X_c,fun(X_c,bool)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,bool))),combb(X_c,fun(X_c,bool),X_b),fequal(X_c)),F)),hAPP(X_b,X_c,F,X_2))))))))))) # label(fact_152_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 201 (all X_c all X_b all F all Z_1 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (exists X1 hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_1),A_1),X1))))) # label(fact_153_finite__imp__fold__graph) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 202 (all X_b all X_1 all A_1 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,A_1)))))) # label(fact_154_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 203 (all X_b all Pa all F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1)) -> (ti(fun(X_b,bool),F_1) != bot_bot(fun(X_b,bool)) -> ((all X_2 hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))))) -> ((all X_2 all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> (ti(fun(X_b,bool),F_2) != bot_bot(fun(X_b,bool)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),F_2)))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1))))))) # label(fact_155_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 204 (all Y ((all Glb ti(vname,Y) != hAPP(glb_1,vname,glb,Glb)) -> -(all Loc ti(vname,Y) != hAPP(loc_1,vname,loc,Loc)))) # label(fact_156_vname_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 205 (all X_c all X_b all X_1 all A_1 all F all Z_1 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_1),G),F_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_1)) -> hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_1,A_1))))) # label(fact_157_folding__image__simple__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 206 (all X_b all X_1 all A_1 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_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(fun(X_b,bool),fun(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_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,A_1) = ti(X_b,X_1)) & (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,A_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))))))) # label(fact_158_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 207 (all X_b all X_1 all A_1 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) = ti(X_b,X_1)) & (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))))))) # label(fact_159_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 208 (all X_b all Ca all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(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))) -> -(hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B))))) # label(fact_160_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 209 (all X_b all B all Ca all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(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)))))) # label(fact_161_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 210 (all X_b all B all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),B))))) # label(fact_162_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 211 (all X_c all X_b all X_1 all F all Z_1 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_1),G),F_1)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),X_1) = ti(X_b,X_1))) # label(fact_163_folding__image__simple__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 212 (all X_b all Ca all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(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))) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B)))) # label(fact_164_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 213 (all X_b all Ca all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(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))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_1)))) # label(fact_165_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 214 (all X_b all A_1 all B hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),B)),B) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),B)) # label(fact_166_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 215 (all X_b all Ca all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(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))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_1)) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B)))) # label(fact_167_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 216 (all X_b all A_1 all B hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),B) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_1))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B))))) # label(fact_168_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 217 (all X_b all X_1 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),X_1) = ti(X_b,X_1))) # label(fact_169_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 218 (all X_b all 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)),A_1),A_1) = bot_bot(fun(X_b,bool))) # label(fact_170_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 219 (all X_b all 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)),A_1),bot_bot(fun(X_b,bool))) = ti(fun(X_b,bool),A_1)) # label(fact_171_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 220 (all X_b all 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)),bot_bot(fun(X_b,bool))),A_1) = bot_bot(fun(X_b,bool))) # label(fact_172_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 221 (all X_b all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),B))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))))) # label(fact_173_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 222 (all X_b all A_1 all X_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)),B) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),B))) # label(fact_174_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 223 (all X_b all A_1 all X_1 all B ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)),B) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),B)) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)),B) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(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))))) # label(fact_175_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 224 (all X_b all A_3 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),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),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),bot_bot(fun(X_b,bool))))) = ti(fun(X_b,bool),A_1))) # label(fact_176_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 225 (all X_b all X_1 all A_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(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = ti(fun(X_b,bool),A_1))) # label(fact_177_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 226 (all X_b all A_3 all 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),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),bot_bot(fun(X_b,bool))))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),A_1)) # label(fact_178_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 227 (all X_b all A_1 all A_3 all B hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),B)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),bot_bot(fun(X_b,bool))))),B)) # label(fact_179_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 228 (all X_b all A_1 all A_3 all B hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),B)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),B)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),bot_bot(fun(X_b,bool))))) # label(fact_180_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 229 (all X_b all A_1 all A_3 all B (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),B)))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),B))))) # label(fact_181_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 230 (all X_b all X_1 all A_1 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_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_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,A_1)) = hAPP(fun(X_b,bool),X_b,F_1,A_1))))) # label(fact_182_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 231 (all X_c all X_b all X_1 all A_1 all F all Z_1 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_1),G),F_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_1)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_1,A_1)) = hAPP(fun(X_c,bool),X_b,F_1,A_1))))) # label(fact_183_folding__image__simple__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 232 (all X_b all N all H all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1)) -> ((all X_2 all Y_2 hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),Y_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_2))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N)) -> (ti(fun(X_b,bool),N) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,F_1,N)) = hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N))))))) # label(fact_184_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 233 (all X_b all Pa all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_1)) -> ((all A_4 all A_5 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_5)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),A_5)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_5)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_5),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),bot_bot(fun(X_b,bool)))))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))))))) # label(fact_185_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 234 (all X_c all X_b all X_1 all A_1 all F all Z_1 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_1),G),F_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_1)) -> hAPP(fun(X_c,bool),X_b,F_1,A_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_1),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),bot_bot(fun(X_c,bool)))))))))) # label(fact_186_folding__image__simple_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 235 (all X_c all X_b all X_1 all A_1 all F all Z_1 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_1),G),F_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_1)) -> hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_1),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),bot_bot(fun(X_c,bool))))))))) # label(fact_187_folding__image__simple_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 236 (all X_b all X_c (minus(X_c) -> (all A_1 all B all X_2 hAPP(X_b,X_c,hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),fun(X_b,X_c)),minus_minus(fun(X_b,X_c)),A_1),B),X_2) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(X_b,X_c,A_1,X_2)),hAPP(X_b,X_c,B,X_2))))) # label(fact_188_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 237 (all X_c all X_b (minus(X_b) -> (all A_1 all B all X_1 hAPP(X_c,X_b,hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),minus_minus(fun(X_c,X_b)),A_1),B),X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_c,X_b,A_1,X_1)),hAPP(X_c,X_b,B,X_1))))) # label(fact_189_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 238 (all X_c all X_b all F all Z_1 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_1),G),F_1)) -> hAPP(fun(X_c,bool),X_b,F_1,bot_bot(fun(X_c,bool))) = ti(X_b,Z_1))) # label(fact_190_folding__image__simple_Oempty) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 239 (all X_c all X_b all X_1 all A_1 all F all Z_1 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_1),G),F_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_1)) -> (-hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_1)) -> hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_1,A_1)))))) # label(fact_191_folding__image__simple_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 240 (all X_c all X_b all A_1 all F all Z_1 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_1),G),F_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_1)) -> ((all X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_1)) -> hAPP(X_c,X_b,G,X_2) = ti(X_b,Z_1))) -> hAPP(fun(X_c,bool),X_b,F_1,A_1) = ti(X_b,Z_1))))) # label(fact_192_folding__image__simple_Oneutral) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 241 (all X_b hBOOL(hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),bool,finite_comp_fun_idem(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_b),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),combc(fun(X_b,bool),fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)))),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool))))))) # label(fact_193_comp__fun__idem__remove) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 242 (all X_b all X_c all A_3 all Z_1 all A_1 all Y_1 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_1),A_1),Y_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),A_1)) -> (exists Y_3 (ti(X_c,Y_1) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,A_3),Y_3) & hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),bot_bot(fun(X_b,bool))))),Y_3)))))))) # label(fact_194_comp__fun__commute_Ofold__graph__insertE__aux) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 243 (all X_c all X_b all F all Z_1 all Y_1 all X_1 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),fold_graph(X_b,X_c),F),Z_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),Y_1)) -> hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),fold_graph(X_b,X_c),F),Z_1),A_1),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Y_1)))))) # label(fact_195_fold__graph_H_Ointros_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 244 (all X_b (ab_semigroup_mult(X_b) -> (all A_3 all Ba all A_1 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),times_times(X_b)),Ba),A_1),X_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),A_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),A_1)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),times_times(X_b)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),hAPP(fun(X_b,bool),fun(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),A_3),bot_bot(fun(X_b,bool)))))),X_1)))))))) # label(fact_196_fold__graph__permute__diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 245 (all X_a (ab_sem1668676832m_mult(X_a) -> (all A_2 all B_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)))) # label(fact_197_mult__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 246 (all X_a (ab_sem1668676832m_mult(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X) = ti(X_a,X)))) # label(fact_198_mult__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 247 (all X_a (ab_sem1668676832m_mult(X_a) -> (all A_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),A_2) = ti(X_a,A_2)))) # label(fact_199_times_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 248 (all X_b all X_c all X_1 all Y_1 all Z_1 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,Y_1),Z_1)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,Y_1),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_1)))) # label(fact_200_comp__fun__commute_Ofun__left__comm) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 249 (all X_b all X_c all X_1 all Z_1 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite_comp_fun_idem(X_b,X_c),F)) -> hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_1)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_1))) # label(fact_201_comp__fun__idem_Ofun__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 250 (all X_b (ab_semigroup_mult(X_b) -> hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite100568337ommute(X_b,X_b),times_times(X_b))))) # label(fact_202_comp__fun__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 251 (all X_b (ab_sem1668676832m_mult(X_b) -> hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),times_times(X_b))))) # label(fact_203_comp__fun__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 252 (all X_c all X_b all F all Z_1 hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),fold_graph(X_b,X_c),F),Z_1),bot_bot(fun(X_b,bool))),Z_1))) # label(fact_204_fold__graph_H_Ointros_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 253 (all X_b hBOOL(hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),bool,finite_comp_fun_idem(X_b,fun(X_b,bool)),insert(X_b)))) # label(fact_205_comp__fun__idem__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 254 (all X_b all X_c all Y_1 all Z_1 all A_1 all X_1 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_1),A_1),X_1)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_1),A_1),Y_1)) -> ti(X_c,Y_1) = ti(X_c,X_1))))) # label(fact_206_comp__fun__commute_Ofold__graph__determ) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 255 (all X_b (ab_semigroup_mult(X_b) -> (all Z_1 all Ba all A_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),times_times(X_b)),Ba),A_1),Y_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),A_1)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),times_times(X_b)),Z_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),A_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Z_1),Y_1)))))))) # label(fact_207_fold__graph__insert__swap) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 256 (all X_b all X_c all Z_1 all X_1 all A_1 all V all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)),V)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) -> -(all Y_2 (ti(X_c,V) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Y_2) -> -hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_1),A_1),Y_2)))))))) # label(fact_208_comp__fun__commute_Ofold__graph__insertE) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 257 (all X_b all X_c all Z_1 all X_1 all A_1 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_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(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_1),A_1) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))))))) # label(fact_209_comp__fun__commute_Ofold__rec) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 258 (all X_b all X_c all Z_1 all X_1 all A_1 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))))) # label(fact_210_comp__fun__commute_Ofold__insert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 259 (all X_b (ab_semigroup_mult(X_b) -> (all X_1 all A_1 (ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_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(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_1)))))))) # label(fact_211_fold1__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 260 (all X_b (ab_sem1668676832m_mult(X_b) -> (all X_1 all A_1 (ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_1))))))) # label(fact_212_fold1__insert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 261 (all X_c all X_b all F all Z_1 hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,bool),X_b)),finite_fold(X_c,X_b),F),Z_1),bot_bot(fun(X_c,bool))) = ti(X_b,Z_1)) # label(fact_213_fold__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 262 (all X_b (ab_sem1668676832m_mult(X_b) -> (all A_3 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),A_1)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),times_times(X_b)),A_3),A_1))))) # label(fact_214_fold1__eq__fold__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 263 (all X_b (ab_semigroup_mult(X_b) -> (all A_3 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),A_1)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),A_1)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),times_times(X_b)),A_3),A_1)))))) # label(fact_215_fold1__eq__fold) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 264 (all X_b all X_c all X_1 all Z_1 all A_1 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_1),A_1)) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_1)),A_1)))) # label(fact_216_comp__fun__commute_Ofold__fun__comm) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 265 (all X_b all F all A_3 hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),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_3),bot_bot(fun(X_b,bool)))) = ti(X_b,A_3)) # label(fact_217_fold1__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 266 (all X_b all A_3 all G all F (G = hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F) -> hAPP(fun(X_b,bool),X_b,G,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),bot_bot(fun(X_b,bool)))) = ti(X_b,A_3))) # label(fact_218_fold1__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 267 (all X_b all X_c all Z_1 all A_1 all Y_1 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_1),A_1),Y_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_1),A_1) = ti(X_c,Y_1)))) # label(fact_219_comp__fun__commute_Ofold__equality) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 268 (all X_c all X_b all F all Z_1 all A_1 hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,bool),X_b)),finite_fold(X_c,X_b),F),Z_1),A_1) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_c,bool),fun(X_b,bool)),hAPP(fun(X_c,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,bool),fun(X_b,bool))),finite_fold_graph(X_c,X_b),F),Z_1),A_1))) # label(fact_220_fold__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 269 (all X_b all A_1 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> hAPP(fun(X_b,bool),X_b,F_1,A_1) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_1)))) # label(fact_221_folding__one_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 270 (all X_b all X_c all Z_1 all X_1 all A_1 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_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(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_1)),A_1))))) # label(fact_222_comp__fun__commute_Ofold__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 271 (all X_b all X_c all Z_1 all X_1 all A_1 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_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(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_1),A_1)))))) # label(fact_223_comp__fun__commute_Ofold__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 272 (all X_b all X_c all Z_1 all X_1 all A_1 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite_comp_fun_idem(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_1)),A_1)))) # label(fact_224_comp__fun__idem_Ofold__insert__idem2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 273 (all X_b all X_c all Z_1 all X_1 all A_1 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite_comp_fun_idem(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_1),A_1))))) # label(fact_225_comp__fun__idem_Ofold__insert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 274 (all X_b all X_1 all A_1 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_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(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),F),X_1),A_1))))) # label(fact_226_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 275 (all X_b all A_3 all A_1 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),A_1)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),F),A_3),A_1)))) # label(fact_227_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 276 (all X_b all X_c all Z_1 all A_1 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_1),A_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_1),A_1)))))) # label(fact_228_comp__fun__commute_Ofold__graph__fold) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 277 (all X_b all F all A_1 hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_1) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_1))) # label(fact_229_fold1__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 278 (all X_b all B all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),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)),B),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)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),finite_fold(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_b),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),combc(fun(X_b,bool),fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)))),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool))))),B),A_1))) # label(fact_230_minus__fold__remove) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 279 (all X_b (ab_sem1668676832m_mult(X_b) -> (all N all H ((all X_2 all Y_2 hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),Y_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_2))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N)) -> (ti(fun(X_b,bool),N) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),N)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N)))))))) # label(fact_231_hom__fold1__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 280 (all X_b (ab_semigroup_mult(X_b) -> (all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) -> ((all X_2 all Y_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_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,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_1)),A_1)))))))) # label(fact_232_fold1__in) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 281 (all X_b all A_1 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),big_semilattice_big(X_b),F),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> hAPP(fun(X_b,bool),X_b,F_1,A_1) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_1)))) # label(fact_233_semilattice__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 282 (all X_b (ab_sem1668676832m_mult(X_b) -> (all B all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B)) -> (ti(fun(X_b,bool),B) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_1)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),B))))))))) # label(fact_234_fold1__Un2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 283 (all X_b all B all A_1 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (ti(fun(X_b,bool),B) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),A_1)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_1,B)),hAPP(fun(X_b,bool),X_b,F_1,A_1)) = hAPP(fun(X_b,bool),X_b,F_1,A_1)))))) # label(fact_235_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.86 284 (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_236_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 285 (all X_b all A_1 all B (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)),A_1),B)) -> (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),A_1)) -> ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B)))) # label(fact_237_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 286 (all X_b all Ca all A_1 all B (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)),A_1),B)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B))))) # label(fact_238_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 287 (all X_b all A_1 all Ca all B ((-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),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))))) # label(fact_239_UnCI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 288 (all X_b all Ca all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),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))) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B))))) # label(fact_240_UnE) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 289 (all X_b all A_1 all B all X_1 ((-hBOOL(hAPP(X_b,bool,B,X_1)) -> hBOOL(hAPP(X_b,bool,A_1,X_1))) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B),X_1)))) # label(fact_241_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 290 (all X_b all A_1 all B all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B),X_1)) -> (-hBOOL(hAPP(X_b,bool,A_1,X_1)) -> hBOOL(hAPP(X_b,bool,B,X_1))))) # label(fact_242_sup1E) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 291 (all X_b all 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)),bot_bot(fun(X_b,bool))),A_1))) # label(fact_243_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 292 (all X_b all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> hBOOL(hAPP(fun(fun(X_b,bool),bool),bool,finite_finite_1(fun(X_b,bool)),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,bool),bool),collect(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),combc(fun(X_b,bool),fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool))),A_1)))))) # label(fact_244_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 293 (all X_b (semilattice_sup(X_b) -> (all Ba all A_3 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),A_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),A_3),Ba)),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),semilattice_sup_sup(X_b)),Ba),A_1)))))))) # label(fact_245_sup__le__fold__sup) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 294 (all X_b all 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)),A_1),bot_bot(fun(X_b,bool)))) <-> ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,bool)))) # label(fact_246_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 295 (all X_b all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B)) -> (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)),A_1),B)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))))) # label(fact_247_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 296 (all X_b all A_1 all B (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)),A_1),B)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))))) # label(fact_248_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 297 (all X_b all A_1 all B hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_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),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)),semilattice_sup_sup(fun(X_b,bool)),A_1),B)) # label(fact_249_Un__Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 298 (all X_b all B all 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)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B),A_1)),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)),semilattice_sup_sup(fun(X_b,bool)),B),A_1)) # label(fact_250_Un__Diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 299 (all X_b all A_1 all B all C hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B)),C) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(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),C)),hAPP(fun(X_b,bool),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),C))) # label(fact_251_Un__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 300 (all X_b all B all A_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)),B),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),B)))) # label(fact_252_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 301 (all X_b all X_1 all A_1 all B (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_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)),B)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B)) & 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)),A_1),B)))) # label(fact_253_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 302 (all X_b all B all X_1 all A_1 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_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)),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_1),B))) <-> 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)),A_1),B))))) # label(fact_254_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 303 (all X_b all Ba all A_1 all B (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)),A_1),B)) -> 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)),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),Ba),B))))) # label(fact_255_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 304 (all X_b all A_3 all C all D (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),D)) -> 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_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),C)),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_3),D))))) # label(fact_256_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 305 (all X_b all X_c all B all F all 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),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_1))) <-> (exists AA (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),AA),A_1)) & ti(fun(X_b,bool),B) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),AA))))) # label(fact_257_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 306 (all X_c all X_b all F all A_1 all B (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)),A_1),B)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_1)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),B))))) # label(fact_258_image__mono) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 307 (all X_b all A_1 all B 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_b,bool),fun(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)),A_1))) # label(fact_259_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 308 (all X_b all D all B all A_1 all C (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)),A_1),C)) -> (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)),D),B)) -> 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_b,bool),fun(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)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),C),D)))))) # label(fact_260_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 309 (all X_b all C all A_1 all B (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)),A_1),B)) -> (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),C)) -> hAPP(fun(X_b,bool),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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),C),A_1)) = ti(fun(X_b,bool),A_1)))) # label(fact_261_double__diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 310 (all X_b all A_1 all B (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)),A_1),B)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_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),A_1)) = ti(fun(X_b,bool),B))) # label(fact_262_Diff__partition) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 311 (all X_b all A_1 all B all C (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_b,bool),fun(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)),C)) <-> 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)),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)),semilattice_sup_sup(fun(X_b,bool)),B),C))))) # label(fact_263_Diff__subset__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 312 (all X_a (semilattice_sup(X_a) -> (all A_2 all B_1 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_2),B_1)),X)) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),X)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),X))))))) # label(fact_264_le__supE) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 313 (all X_a (semilattice_sup(X_a) -> (all B_1 all D_1 all A_2 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D_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_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),C_1),D_1)))))))) # label(fact_265_sup__mono) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 314 (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_266_sup__least) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 315 (all X_a (semilattice_sup(X_a) -> (all B_1 all A_2 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),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_2),B_1)),X))))))) # label(fact_267_le__supI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 316 (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_268_sup__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 317 (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_269_sup__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 318 (all X_a (semilattice_sup(X_a) -> (all A_2 all X all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_1)) -> 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_2),B_1))))))) # label(fact_270_le__supI2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 319 (all X_a (semilattice_sup(X_a) -> (all B_1 all X all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_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_2),B_1))))))) # label(fact_271_le__supI1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 320 (all X_c all X_b (lattice(X_b) -> (all F all G all X_1 hAPP(X_c,X_b,hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),semilattice_sup_sup(fun(X_c,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_c,X_b,F,X_1)),hAPP(X_c,X_b,G,X_1))))) # label(fact_272_sup__apply) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 321 (all X_b (semilattice_sup(X_b) -> (all X_1 all Y_1 all Z_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_1),Y_1)),Z_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Z_1)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),Z_1)))))) # label(fact_273_le__sup__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 322 (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_274_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 323 (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_275_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 324 (all X_a (semilattice_sup(X_a) -> (all A_2 all B_1 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_2),B_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_1),C_1))))) # label(fact_276_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 325 (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_277_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 326 (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_278_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 327 (all X_a (semilattice_sup(X_a) -> (all B_1 all A_2 all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_1),C_1))))) # label(fact_279_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 328 (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_280_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 329 (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_281_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 330 (all X_a (semilattice_sup(X_a) -> (all A_2 all B_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1)))) # label(fact_282_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 331 (all X_b (semilattice_sup(X_b) -> (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)) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_1),Y_1) = ti(X_b,Y_1))))) # label(fact_283_le__iff__sup) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 332 (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_284_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 333 (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_285_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 334 (all X_a (semilattice_sup(X_a) -> (all A_2 all B_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_1),A_2)))) # label(fact_286_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 335 (all X_b all X_c (lattice(X_c) -> (all F all G all X_2 hAPP(X_b,X_c,hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),fun(X_b,X_c)),semilattice_sup_sup(fun(X_b,X_c)),F),G),X_2) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),semilattice_sup_sup(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2))))) # label(fact_287_sup__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 336 (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_288_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 337 (all X_a (semilattice_sup(X_a) -> (all A_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),A_2) = ti(X_a,A_2)))) # label(fact_289_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 338 (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_290_sup__ge2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 339 (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_291_inf__sup__ord_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 340 (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_292_sup__ge1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 341 (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_293_inf__sup__ord_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 342 (all X_b (bounded_lattice_bot(X_b) -> (all X_1 all Y_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_1),Y_1) = bot_bot(X_b) <-> ti(X_b,X_1) = bot_bot(X_b) & ti(X_b,Y_1) = bot_bot(X_b))))) # label(fact_294_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 343 (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_295_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 344 (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_296_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 345 (all X_b all B hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),bot_bot(fun(X_b,bool))),B) = ti(fun(X_b,bool),B)) # label(fact_297_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 346 (all X_b all 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)),semilattice_sup_sup(fun(X_b,bool)),A_1),bot_bot(fun(X_b,bool))) = ti(fun(X_b,bool),A_1)) # label(fact_298_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 347 (all X_b all A_1 all B (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B) = bot_bot(fun(X_b,bool)) <-> ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,bool)) & ti(fun(X_b,bool),B) = bot_bot(fun(X_b,bool)))) # label(fact_299_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 348 (all X_b all F_1 all Ga (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),F_1),Ga))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1)) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),Ga)))) # label(fact_300_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 349 (all X_b all Ga all F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),Ga)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),F_1),Ga)))))) # label(fact_301_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 350 (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_302_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 351 (all X_b all X_c (ord(X_c) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(X_b,X_c,G,X_1))))))) # label(fact_303_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 352 (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_304_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 353 (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_305_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 354 (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_306_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 355 (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_307_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 356 (all X_a (order(X_a) -> (all C_1 all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2)) -> (ti(X_a,B_1) = 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_2))))))) # label(fact_308_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 357 (all X_a (ord(X_a) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) -> (B_1 = C_1 -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C_1))))))) # label(fact_309_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 358 (all X_a (order(X_a) -> (all C_1 all A_2 all B_1 (ti(X_a,A_2) = ti(X_a,B_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2))))))) # label(fact_310_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 359 (all X_a (ord(X_a) -> (all C_1 all A_2 all B_1 (A_2 = B_1 -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C_1))))))) # label(fact_311_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 360 (all X_b (order(X_b) -> (all Y_1 all X_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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) <-> ti(X_b,X_1) = ti(X_b,Y_1)))))) # label(fact_312_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 361 (all X_b all X_c (ord(X_c) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(X_b,X_c,G,X_1))))))) # label(fact_313_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 362 (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_314_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 363 (all X_b (order(X_b) -> (all X_1 all Y_1 (ti(X_b,X_1) = ti(X_b,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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1)))))) # label(fact_315_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 364 (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_316_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 365 (all X_b all X_c (ord(X_c) -> (all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) <-> (all X_2 hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2)))))))) # label(fact_317_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 366 (all X_b all Pa all Q_1 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),Pa)),Q_1)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_1))) # label(fact_318_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 367 (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_319_Sup__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 368 (all X_b all A_1 all B (ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B) -> -(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)),A_1),B)) -> -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),A_1))))) # label(fact_320_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 369 (all X_b all B all D all A_1 all C (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)),A_1),C)) -> (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),D)) -> 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_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)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),C),D)))))) # label(fact_321_Un__mono) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 370 (all X_b all B all A_1 all C (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)),A_1),C)) -> (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),C)) -> 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_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)),C))))) # label(fact_322_Un__least) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 371 (all X_b all C all A_1 all B (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)),A_1),B)) -> (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),C)) -> 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)),A_1),C))))) # label(fact_323_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 372 (all X_b all X_1 all A_1 all B (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)),A_1),B)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B))))) # label(fact_324_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 373 (all X_b all B all X_1 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_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)),A_1),B)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B))))) # label(fact_325_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 374 (all X_b all X_1 all A_1 all B (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)),A_1),B)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B))))) # label(fact_326_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 375 (all X_b all B all 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),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)),semilattice_sup_sup(fun(X_b,bool)),A_1),B) = ti(fun(X_b,bool),A_1))) # label(fact_327_Un__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 376 (all X_b all A_1 all B (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)),A_1),B)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B) = ti(fun(X_b,bool),B))) # label(fact_328_Un__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 377 (all X_b all A_1 all Ca all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),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))))) # label(fact_329_UnI2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 378 (all X_b all B all Ca all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),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))))) # label(fact_330_UnI1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 379 (all X_b all A_1 all B (ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B) -> 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),A_1)))) # label(fact_331_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 380 (all X_b all A_1 all B (ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B) -> 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)),A_1),B)))) # label(fact_332_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 381 (all X_b all Pa all A_1 all B ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B))) -> hBOOL(hAPP(X_b,bool,Pa,X_2)))) <-> (all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> hBOOL(hAPP(X_b,bool,Pa,X_2)))) & (all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B)) -> hBOOL(hAPP(X_b,bool,Pa,X_2)))))) # label(fact_333_ball__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 382 (all X_b all Pa all A_1 all B ((exists X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B))) & hBOOL(hAPP(X_b,bool,Pa,X_2)))) <-> (exists X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) & hBOOL(hAPP(X_b,bool,Pa,X_2)))) | (exists X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B)) & hBOOL(hAPP(X_b,bool,Pa,X_2)))))) # label(fact_334_bex__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 383 (all X_b all A_1 all B all C hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),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)),C) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B),C))) # label(fact_335_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 384 (all X_b all Ca all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),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))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_1)) | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B)))) # label(fact_336_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 385 (all X_b all A_1 all B all C hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B),C)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),C))) # label(fact_337_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 386 (all X_b all A_1 all B hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B)) # label(fact_338_Un__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 387 (all X_b all A_1 all B (ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B) <-> 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)),A_1),B)) & 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),A_1)))) # label(fact_339_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 388 (all X_b all A_1 all B (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)),A_1),B)) <-> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B) = ti(fun(X_b,bool),B))) # label(fact_340_subset__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 389 (all X_b all A_1 all B hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B),A_1)) # label(fact_341_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 390 (all X_b all A_1 all B hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),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(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)))) # label(fact_342_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 391 (all X_b all 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)),semilattice_sup_sup(fun(X_b,bool)),A_1),A_1) = ti(fun(X_b,bool),A_1)) # label(fact_343_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 392 (all X_b all B all 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),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)))) # label(fact_344_Un__upper2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 393 (all X_b all A_1 all B 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)),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)),semilattice_sup_sup(fun(X_b,bool)),A_1),B)))) # label(fact_345_Un__upper1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 394 (all X_b all 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)),A_1),A_1))) # label(fact_346_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 395 (all X_b all X_1 all Pa all Q_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)),Pa),Q_1)) -> (hBOOL(hAPP(X_b,bool,Pa,X_1)) -> hBOOL(hAPP(X_b,bool,Q_1,X_1))))) # label(fact_347_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 396 (all X_b all Q_1 all Pa all X_1 (hBOOL(hAPP(X_b,bool,Pa,X_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),Pa),Q_1)) -> hBOOL(hAPP(X_b,bool,Q_1,X_1))))) # label(fact_348_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 397 (all X_b all A_1 all B all X_1 (hBOOL(hAPP(X_b,bool,B,X_1)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B),X_1)))) # label(fact_349_sup1I2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 398 (all X_b all B all A_1 all X_1 (hBOOL(hAPP(X_b,bool,A_1,X_1)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B),X_1)))) # label(fact_350_sup1I1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 399 (all X_b all R_1 all S (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_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),R_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),R_1),S)))) # label(fact_351_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 400 (all X_b all R_1 all S all X_2 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),R_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S)),X_2)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),R_1),S))))) # label(fact_352_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 401 (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),bot_bot(X_a)),A_2))))) # label(fact_353_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 402 (all X_b (bot(X_b) -> (all A_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_3),bot_bot(X_b))) <-> ti(X_b,A_3) = bot_bot(X_b))))) # label(fact_354_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 403 (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_355_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 404 (all X_c all X_b all F all A_1 all B hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_sup_sup(fun(X_c,bool)),A_1),B)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_1)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B))) # label(fact_356_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 405 (all X_b all A_1 all A_3 all B hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),B)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B))) # label(fact_357_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 406 (all X_b all A_3 all B all C hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),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_3),B)),C) = 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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B),C))) # label(fact_358_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 407 (all X_b all Ts all Ga all Ts_1 (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),Ts_1)) -> (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),ord_less_eq(fun(hoare_1656922687triple(X_b),bool)),Ts),Ts_1)) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),Ts))))) # label(fact_359_weaken) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 408 (all X_b all Ts all Ga (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),ord_less_eq(fun(hoare_1656922687triple(X_b),bool)),Ts),Ga)) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),Ts)))) # label(fact_360_asm) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 409 (all X_b (semilattice_sup(X_b) -> hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),semilattice_sup_sup(X_b))))) # label(fact_361_comp__fun__idem__sup) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 410 (all X_b all A_3 all B hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),B) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_3))),B)) # label(fact_362_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 411 (all X_b all A_3 all 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),A_3),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)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),bot_bot(fun(X_b,bool)))),A_1)) # label(fact_363_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 412 (all X_b (semilattice_sup(X_b) -> (all Ba all A_3 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),semilattice_sup_sup(X_b)),Ba),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_3),A_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),A_3),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),semilattice_sup_sup(X_b)),Ba),A_1)))))) # label(fact_364_fold__sup__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 413 (all X_b all B all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),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)),semilattice_sup_sup(fun(X_b,bool)),A_1),B) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),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_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),finite_fold(X_b,fun(X_b,bool)),insert(X_b)),B),A_1))) # label(fact_365_union__fold__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 414 (all X_b all A_1 all X_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)),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_1),bot_bot(fun(X_b,bool))))) -> ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,bool)) | ti(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_1),bot_bot(fun(X_b,bool))))) # label(fact_366_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 415 (all X_c all X_b all B all F all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_1))) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B))))) # label(fact_367_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 416 (all X_b all X_c all F all A_1 all B 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_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_1)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B))),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_1),B))))) # label(fact_368_image__diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 417 (all X_c all X_b all B all A_1 all F all Z_1 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_1),G),F_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B)) -> hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_sup_sup(fun(X_c,bool)),A_1),B)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,A_1)),hAPP(fun(X_c,bool),X_b,F_1,B)))))) # label(fact_369_folding__image__simple__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 418 (all X_c all X_b all B all A_1 all F all Z_1 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_1),G),F_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),B),A_1)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,B)),hAPP(fun(X_c,bool),X_b,F_1,A_1)) = hAPP(fun(X_c,bool),X_b,F_1,A_1))))) # label(fact_370_folding__image__simple__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 419 (all X_b all A_1 all X_1 all B (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_b,bool),fun(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_1),bot_bot(fun(X_b,bool))))),B)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_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)),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_1),B)))))) # label(fact_371_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 420 (all X_b all A_1 all X_1 all B (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)),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_1),B))) <-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_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_b,bool),fun(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_1),bot_bot(fun(X_b,bool))))),B))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_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)),A_1),B))))) # label(fact_372_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.87 421 (all X_b all B all A_1 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B)) -> (ti(fun(X_b,bool),B) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_1,A_1)),hAPP(fun(X_b,bool),X_b,F_1,B)))))))) # label(fact_373_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 422 (all X_b (semilattice_sup(X_b) -> (all Ca all Ba all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Ba)))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),semilattice_sup_sup(X_b)),Ca),A_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),Ba),Ca)))))))) # label(fact_374_fold__sup__le__sup) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 423 (all X_b all Pa all A_1 all F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),F_1),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))) -> ((all A_4 all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),A_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),F_2)))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1))))))) # label(fact_375_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 424 (all X_b all B all A_1 ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B)))) -> 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)),A_1),B)))) # label(fact_376_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 425 (all X_c all X_b all F all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B)) -> (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),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_1))) -> (exists C_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),C_2),A_1)) & hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),C_2)) & ti(fun(X_b,bool),B) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),C_2)))))) # label(fact_377_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 426 (all M_1 all C_1 all S_1 all N_2 all T_4 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C_1),S_1),N_2),T_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),M_1)) -> hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C_1),S_1),M_1),T_4))))) # label(fact_378_evaln__nonstrict) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 427 (all X_c all X_b all F all B all A_1 ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,X_2)),B)))) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_1)),B)))) # label(fact_379_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 428 (all X_b all X_c (ord(X_c) -> (all F all G ((all X_2 hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2)))) -> hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)))))) # label(fact_380_le__funI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 429 (all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),K))))) # label(fact_381_finite__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 430 (all X_b (ordered_ab_group_add(X_b) -> (all A_3 all Ba all Ca all D_2 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_3),Ba) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ca),D_2) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_3),Ba)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),D_2))))))) # label(fact_382_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 431 (all X_b all A_1 all Ba ((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)),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),Ba),bot_bot(fun(X_b,bool))))) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),Ba),A_1) = ti(X_b,Ba)) & (-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)),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),Ba),bot_bot(fun(X_b,bool))))) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),Ba),A_1) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_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),Ba),bot_bot(fun(X_b,bool))))))))) # label(fact_383_flat__lub__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 432 (all X_a (ab_semigroup_mult(X_a) -> (all A_2 all B_1 all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1))))) # label(fact_384_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 433 (all X_b (ab_group_add(X_b) -> (all A_3 all Ba all Ca all D_2 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_3),Ba) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ca),D_2) -> (ti(X_b,A_3) = ti(X_b,Ba) <-> ti(X_b,Ca) = ti(X_b,D_2)))))) # label(fact_385_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 434 (all N (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N)) <-> (exists M all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_2),M)))))) # label(fact_386_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 435 (all X_c all X_b all F all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_1) = hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,bool)),fun(fun(X_c,bool),fun(fun(X_b,bool),fun(X_c,bool))),hAPP(fun(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool))),fun(fun(X_b,fun(X_c,bool)),fun(fun(X_c,bool),fun(fun(X_b,bool),fun(X_c,bool)))),finite_fold_image(fun(X_c,bool),X_b),semilattice_sup_sup(fun(X_c,bool))),hAPP(fun(X_c,bool),fun(X_b,fun(X_c,bool)),hAPP(fun(X_b,fun(fun(X_c,bool),fun(X_c,bool))),fun(fun(X_c,bool),fun(X_b,fun(X_c,bool))),combc(X_b,fun(X_c,bool),fun(X_c,bool)),hAPP(fun(X_b,X_c),fun(X_b,fun(fun(X_c,bool),fun(X_c,bool))),hAPP(fun(X_c,fun(fun(X_c,bool),fun(X_c,bool))),fun(fun(X_b,X_c),fun(X_b,fun(fun(X_c,bool),fun(X_c,bool)))),combb(X_c,fun(fun(X_c,bool),fun(X_c,bool)),X_b),insert(X_c)),F)),bot_bot(fun(X_c,bool)))),bot_bot(fun(X_c,bool))),A_1))) # label(fact_387_image__eq__fold__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 436 (all X_c all X_b all F all G hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),F),G) = hAPP(fun(X_c,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,bool),X_b)),finite_fold(X_c,X_b),hAPP(fun(X_c,X_b),fun(X_c,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_c),F),G))) # label(fact_388_fold__image__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 437 (all X_c all X_b all F all G all Z_1 hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),F),G),Z_1),bot_bot(fun(X_c,bool))) = ti(X_b,Z_1)) # label(fact_389_fold__image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 438 (all X_c all X_b all A_1 all F all Z_1 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_1),G),F_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_1)) -> hAPP(fun(X_c,bool),X_b,F_1,A_1) = hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),F),G),Z_1),A_1)))) # label(fact_390_folding__image__simple_Oeq__fold__g) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 439 (all X_b all X_c (ab_semigroup_mult(X_c) -> (all G all Z_1 all A_3 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),A_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),A_1)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,G,A_3)),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_1),A_1))))))) # label(fact_391_fold__image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 440 (all X_b all X_c (ab_semigroup_mult(X_c) -> (all Z_1 all G all H all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> hAPP(X_b,X_c,G,X_2) = hAPP(X_b,X_c,H,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_1),A_1) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),H),Z_1),A_1)))))) # label(fact_392_fold__image__cong) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 441 (all U all F ((all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,F,N_1)))) -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),F)),U)))))) # label(fact_393_finite__less__ub) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 442 (all X_c all X_b all X_d (comm_monoid_mult(X_d) -> (all E all G all F all H all K all T_3 all S (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S)) -> ((all Y_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Y_2),T_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_c,X_b,K,Y_2)),S)) & hAPP(X_b,X_c,H,hAPP(X_c,X_b,K,Y_2)) = ti(X_c,Y_2))) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),S)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,H,X_2)),T_3)) & hAPP(X_c,X_b,K,hAPP(X_b,X_c,H,X_2)) = ti(X_b,X_2) & hAPP(X_c,X_d,G,hAPP(X_b,X_c,H,X_2)) = hAPP(X_b,X_d,F,X_2))) -> hAPP(fun(X_b,bool),X_d,hAPP(X_d,fun(fun(X_b,bool),X_d),hAPP(fun(X_b,X_d),fun(X_d,fun(fun(X_b,bool),X_d)),hAPP(fun(X_d,fun(X_d,X_d)),fun(fun(X_b,X_d),fun(X_d,fun(fun(X_b,bool),X_d))),finite_fold_image(X_d,X_b),times_times(X_d)),F),E),S) = hAPP(fun(X_c,bool),X_d,hAPP(X_d,fun(fun(X_c,bool),X_d),hAPP(fun(X_c,X_d),fun(X_d,fun(fun(X_c,bool),X_d)),hAPP(fun(X_d,fun(X_d,X_d)),fun(fun(X_c,X_d),fun(X_d,fun(fun(X_c,bool),X_d))),finite_fold_image(X_d,X_c),times_times(X_d)),G),E),T_3))))))) # label(fact_394_fold__image__eq__general__inverses) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 443 (all X_c all X_b (comm_monoid_mult(X_b) -> (all H all G all S all R_1 all E (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,E),E)) -> ((all X1 all Y1 all X2 all Y2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,X1),X2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,Y1),Y2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X1),Y1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X2),Y2))))) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),S)) -> ((all X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),S)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_c,X_b,H,X_2)),hAPP(X_c,X_b,G,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),H),E),S)),hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),G),E),S)))))))))) # label(fact_395_fold__image__related) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 444 (all X_c all X_b all G all A_1 all F all Z_1 all F_1 (hBOOL(hAPP(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool,hAPP(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool)),big_comm_monoid_big(X_b,X_c),F),Z_1),F_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_1)) -> hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,G),A_1) = hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),F),G),Z_1),A_1)) & (-hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_1)) -> hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,G),A_1) = ti(X_b,Z_1)))) # label(fact_396_comm__monoid__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 445 (all X_b (lattice(X_b) -> (all X_1 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_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(fun(X_b,bool),fun(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_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_1) = ti(X_b,X_1)) & (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))))))))) # label(fact_397_Sup__fin_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 446 (all X_b (lattice(X_b) -> (all X_1 hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1)))) # label(fact_398_Sup__fin_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 447 (all X_b (lattice(X_b) -> (all X_1 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_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_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_1)) = hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_1)))))) # label(fact_399_Sup__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 448 (all X_c all X_b all G all A_1 all F all Z_1 all F_1 (hBOOL(hAPP(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool,hAPP(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool)),big_comm_monoid_big(X_b,X_c),F),Z_1),F_1)) -> (-hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_1)) -> hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,G),A_1) = ti(X_b,Z_1)))) # label(fact_400_comm__monoid__big_Oinfinite) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 449 (all X_b (lattice(X_b) -> (all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_1) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),semilattice_sup_sup(X_b)),A_1))))) # label(fact_401_Sup__fin_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 450 (all X_b (lattice(X_b) -> (all X_1 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_1))))))) # label(fact_402_Sup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 451 (all X_b (lattice(X_b) -> (all X_1 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_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(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_1)))))))) # label(fact_403_Sup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 452 (all X_b (lattice(X_b) -> (all B all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (ti(fun(X_b,bool),B) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),A_1)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),B)),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_1)) = hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_1))))))) # label(fact_404_Sup__fin_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 453 (all X_b (lattice(X_b) -> (all B all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B)) -> (ti(fun(X_b,bool),B) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_1)),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),B))))))))) # label(fact_405_Sup__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 454 (all X_b (lattice(X_b) -> (all A_3 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),A_1)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),semilattice_sup_sup(X_b)),A_3),A_1))))) # label(fact_406_Sup__fin_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 455 (all X_b (lattice(X_b) -> (all X_1 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_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(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),semilattice_sup_sup(X_b)),X_1),A_1)))))) # label(fact_407_Sup__fin_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 456 (all X_b (lattice(X_b) -> (all X_1 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),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)),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_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) = ti(X_b,X_1)) & (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))))))) # label(fact_408_Sup__fin_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 457 (all X_b (lattice(X_b) -> (all N all H ((all X_2 all Y_2 hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),Y_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_2))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N)) -> (ti(fun(X_b,bool),N) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),N)) = hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N)))))))) # label(fact_409_Sup__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 458 (all X_b (lattice(X_b) -> (all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) -> ((all X_2 all Y_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_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,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_1)),A_1)))))))) # label(fact_410_Sup__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 459 (all X_c all X_b all H all G all A_1 all B all F all Z_1 all F_1 (hBOOL(hAPP(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool,hAPP(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),bool)),big_comm_monoid_big(X_b,X_c),F),Z_1),F_1)) -> (ti(fun(X_c,bool),A_1) = ti(fun(X_c,bool),B) -> ((all X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),B)) -> hAPP(X_c,X_b,H,X_2) = hAPP(X_c,X_b,G,X_2))) -> hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,H),A_1) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,G),B))))) # label(fact_411_comm__monoid__big_OF__cong) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 460 (all X_b (lattice(X_b) -> (all B all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B)) -> (ti(fun(X_b,bool),B) != bot_bot(fun(X_b,bool)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_1)),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),B)))))))))) # label(fact_412_Sup__fin_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 461 (all X_b all B all A_1 all X_1 (hBOOL(hAPP(X_b,bool,A_1,X_1)) -> (hBOOL(hAPP(X_b,bool,B,X_1)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B),X_1))))) # label(fact_413_inf1I) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 462 (all X_b all A_1 all B all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B),X_1)) -> -(hBOOL(hAPP(X_b,bool,A_1,X_1)) -> -hBOOL(hAPP(X_b,bool,B,X_1))))) # label(fact_414_inf1E) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 463 (all X_b all B all Ca all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),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)))))) # label(fact_415_IntI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 464 (all X_b all Ca all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),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))) -> -(hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_1)) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B))))) # label(fact_416_IntE) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 465 (all X_b all Ga all F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1)) | hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),Ga)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),F_1),Ga))))) # label(fact_417_finite__Int) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 466 (all X_a (semilattice_inf(X_a) -> (all X all A_2 all B_1 (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_2),B_1))) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_2)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_1))))))) # label(fact_418_le__infE) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 467 (all X_a (semilattice_inf(X_a) -> (all B_1 all D_1 all A_2 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D_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),A_2),B_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),C_1),D_1)))))))) # label(fact_419_inf__mono) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 468 (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_420_inf__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 469 (all X_a (semilattice_inf(X_a) -> (all B_1 all X all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_1)) -> 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_2),B_1)))))))) # label(fact_421_le__infI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 470 (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_422_inf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 471 (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_423_inf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 472 (all X_a (semilattice_inf(X_a) -> (all A_2 all B_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),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_2),B_1)),X)))))) # label(fact_424_le__infI2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 473 (all X_a (semilattice_inf(X_a) -> (all B_1 all A_2 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_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_2),B_1)),X)))))) # label(fact_425_le__infI1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 474 (all X_b (semilattice_inf(X_b) -> (all X_1 all Y_1 all Z_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),Y_1),Z_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Z_1)))))) # label(fact_426_le__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 475 (all X_b (semilattice_inf(X_b) -> (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)) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X_1),Y_1) = ti(X_b,X_1))))) # label(fact_427_le__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 476 (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_428_inf__le2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 477 (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_429_inf__sup__ord_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 478 (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_430_inf__le1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 479 (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_431_inf__sup__ord_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 480 (all X_b all B all D all A_1 all C (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)),A_1),C)) -> (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),D)) -> 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_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)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),C),D)))))) # label(fact_432_Int__mono) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 481 (all X_b all B all C all 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)),C),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)),C),B)) -> 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),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)))))) # label(fact_433_Int__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 482 (all X_b all B all 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),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)),semilattice_inf_inf(fun(X_b,bool)),A_1),B) = ti(fun(X_b,bool),B))) # label(fact_434_Int__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 483 (all X_b all A_1 all B (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)),A_1),B)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B) = ti(fun(X_b,bool),A_1))) # label(fact_435_Int__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 484 (all X_b all A_1 all B 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_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)),B))) # label(fact_436_Int__lower2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 485 (all X_b all A_1 all B 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_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)),A_1))) # label(fact_437_Int__lower1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 486 (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_438_distrib__sup__le) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 487 (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_439_distrib__inf__le) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 488 (all X_b all X_c all F all A_1 all B 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_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_inf_inf(fun(X_c,bool)),A_1),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_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_1)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B))))) # label(fact_440_image__Int__subset) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 489 (all X_b all A_1 all B all C (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),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)),C) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B),C)) <-> 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),A_1)))) # label(fact_441_Un__Int__assoc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 490 (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_442_Inf__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 491 (all X_b (semilattice_inf(X_b) -> hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),semilattice_inf_inf(X_b))))) # label(fact_443_comp__fun__idem__inf) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 492 (all X_b all B all A_3 all C (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),C)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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_3),B)),C) = 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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B),C)))) # label(fact_444_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 493 (all X_b all B all A_3 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),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)),semilattice_inf_inf(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),A_3),B)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B)))) # label(fact_445_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 494 (all X_b all B all A_3 all C (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),C)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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_3),B)),C) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B),C))) # label(fact_446_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 495 (all X_b all B all A_3 all A_1 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),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)),semilattice_inf_inf(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),A_3),B)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B))) # label(fact_447_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 496 (all X_b all A_3 all A_1 all 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_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),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),A_3),B)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B))) # label(fact_448_insert__inter__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 497 (all X_b all B all A_3 all C ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),C)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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_3),B)),C) = 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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B),C))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),C)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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_3),B)),C) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B),C)))) # label(fact_449_Int__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 498 (all X_b all B all A_3 all A_1 ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),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)),semilattice_inf_inf(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),A_3),B)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),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)),semilattice_inf_inf(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),A_3),B)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B)))) # label(fact_450_Int__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 499 (all X_b all R_1 all S all X_2 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),R_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S)),X_2)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),R_1),S))))) # label(fact_451_inf__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 500 (all X_b all A_1 all B all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B),X_1)) -> hBOOL(hAPP(X_b,bool,A_1,X_1)))) # label(fact_452_inf1D1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 501 (all X_b all A_1 all B all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B),X_1)) -> hBOOL(hAPP(X_b,bool,B,X_1)))) # label(fact_453_inf1D2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 502 (all X_b all Pa all Q_1 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),Pa)),Q_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_b,bool),fun(X_b,bool),collect(X_b),Pa)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_1))) # label(fact_454_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 503 (all X_b all X_1 all A_1 all Pa (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),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) & hBOOL(hAPP(X_b,bool,Pa,X_1)))) # label(fact_455_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 504 (all X_b all 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)),semilattice_inf_inf(fun(X_b,bool)),A_1),A_1) = ti(fun(X_b,bool),A_1)) # label(fact_456_Int__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 505 (all X_b all A_1 all B hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_1))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B)))) # label(fact_457_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 506 (all X_b all A_1 all B hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),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)),B),A_1)) # label(fact_458_Int__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 507 (all X_b all A_1 all B hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_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)) = 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)) # label(fact_459_Int__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 508 (all X_b all A_1 all B all C hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_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)),B),C)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),C))) # label(fact_460_Int__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 509 (all X_b all Ca all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),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))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_1)) & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B)))) # label(fact_461_Int__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 510 (all X_b all A_1 all B all C hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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)),C) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_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)),B),C))) # label(fact_462_Int__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 511 (all X_b all Ca all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),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))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_1)))) # label(fact_463_IntD1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 512 (all X_b all Ca all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),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))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B)))) # label(fact_464_IntD2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 513 (all X_b all A_1 all B (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B) = bot_bot(fun(X_b,bool)) <-> (all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> (all Xa (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Xa),B)) -> ti(X_b,X_2) != ti(X_b,Xa))))))) # label(fact_465_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 514 (all X_b all 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)),semilattice_inf_inf(fun(X_b,bool)),A_1),bot_bot(fun(X_b,bool))) = bot_bot(fun(X_b,bool))) # label(fact_466_Int__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 515 (all X_b all 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)),bot_bot(fun(X_b,bool))),B) = bot_bot(fun(X_b,bool))) # label(fact_467_Int__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 516 (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_468_inf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 517 (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_469_inf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 518 (all X_a (semilattice_inf(X_a) -> (all A_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),A_2) = ti(X_a,A_2)))) # label(fact_470_inf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 519 (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_471_inf__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 520 (all X_b all X_c (lattice(X_c) -> (all F all G all X_2 hAPP(X_b,X_c,hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),fun(X_b,X_c)),semilattice_inf_inf(fun(X_b,X_c)),F),G),X_2) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),semilattice_inf_inf(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2))))) # label(fact_472_inf__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 521 (all X_a (semilattice_inf(X_a) -> (all A_2 all B_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_1),A_2)))) # label(fact_473_inf_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 522 (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_474_inf__sup__aci_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 523 (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_475_inf__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 524 (all X_a (semilattice_inf(X_a) -> (all A_2 all B_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1)))) # label(fact_476_inf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 525 (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_477_inf__sup__aci_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 526 (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_478_inf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 527 (all X_a (semilattice_inf(X_a) -> (all B_1 all A_2 all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_1),C_1))))) # label(fact_479_inf_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 528 (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_480_inf__sup__aci_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 529 (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_481_inf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 530 (all X_a (semilattice_inf(X_a) -> (all A_2 all B_1 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_2),B_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_1),C_1))))) # label(fact_482_inf_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 531 (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_483_inf__sup__aci_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 532 (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_484_inf__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 533 (all X_c all X_b (lattice(X_b) -> (all F all G all X_1 hAPP(X_c,X_b,hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),semilattice_inf_inf(fun(X_c,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_c,X_b,F,X_1)),hAPP(X_c,X_b,G,X_1))))) # label(fact_485_inf__apply) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 534 (all X_b all A_1 all C all B hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),C)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B),C)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),C)),B)) # label(fact_486_Diff__Int2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 535 (all X_b all A_1 all B all C hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(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)),C) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),C)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B),C))) # label(fact_487_Diff__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.88 536 (all X_b all A_1 all B all C hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B)),C) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_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),C))) # label(fact_488_Int__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.89 537 (all X_b all C all A_1 all 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)),C),hAPP(fun(X_b,bool),fun(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)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),C),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)),semilattice_inf_inf(fun(X_b,bool)),C),B))) # label(fact_489_Diff__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.89 538 (all X_b all A_1 all B hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(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)),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)) = ti(fun(X_b,bool),A_1)) # label(fact_490_Un__Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.89 539 (all X_b all A_1 all B all C hAPP(fun(X_b,bool),fun(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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B),C)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(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)),hAPP(fun(X_b,bool),fun(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),C))) # label(fact_491_Diff__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.89 540 (all X_b all A_1 all B all C hAPP(fun(X_b,bool),fun(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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B),C)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(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)),hAPP(fun(X_b,bool),fun(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),C))) # label(fact_492_Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.89 541 (all X_b all A_1 all B (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),B) = ti(fun(X_b,bool),A_1))) # label(fact_493_Diff__triv) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.89 542 (all X_b all A_1 all B hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_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),A_1)) = bot_bot(fun(X_b,bool))) # label(fact_494_Diff__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.89 543 (all X_b all A_1 all B all C hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B),C)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),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)),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),C))) # label(fact_495_Int__Un__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.89 544 (all X_b all A_1 all B all C hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_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)),B),C)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),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)),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),C))) # label(fact_496_Un__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.89 545 (all X_b all B all C all 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)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B),C)),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)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B),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)),semilattice_inf_inf(fun(X_b,bool)),C),A_1))) # label(fact_497_Int__Un__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.89 546 (all X_b all B all C all 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)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B),C)),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)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B),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)),semilattice_sup_sup(fun(X_b,bool)),C),A_1))) # label(fact_498_Un__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.89 547 (all X_b all A_1 all B all C hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),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)),B),C))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),C),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)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B),C))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),C),A_1))) # label(fact_499_Un__Int__crazy) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.89 548 (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].
% 1.61/1.89 549 (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].
% 1.61/1.89 550 (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].
% 1.61/1.89 551 (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].
% 1.61/1.89 552 (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].
% 1.61/1.89 553 (all T_2 all T_1 (finite_finite(T_1) & finite_finite(T_2) -> finite_finite(fun(T_2,T_1)))) # label(arity_fun___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.89 554 (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].
% 1.61/1.89 555 (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].
% 1.61/1.89 556 (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].
% 1.61/1.89 557 (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].
% 1.61/1.89 558 (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].
% 1.61/1.89 559 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.89 560 (all P (-hBOOL(hAPP(bool,bool,fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.89 561 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.89 562 (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].
% 1.61/1.89 563 (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].
% 1.61/1.89 564 (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].
% 1.61/1.89 565 (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].
% 1.61/1.89 566 (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].
% 1.61/1.89 567 (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].
% 1.61/1.89 568 (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].
% 1.61/1.89 569 (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].
% 1.61/1.89 570 (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].
% 1.61/1.89 571 (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].
% 1.67/1.91 572 (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].
% 1.67/1.91 573 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.67/1.91 574 (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].
% 1.67/1.91 575 (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].
% 1.67/1.91 576 (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].
% 1.67/1.91 577 (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].
% 1.67/1.91 578 (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].
% 1.67/1.91
% 1.67/1.91 ============================== end of process non-clausal formulas ===
% 1.67/1.91
% 1.67/1.91 ============================== PROCESS INITIAL CLAUSES ===============
% 1.67/1.91
% 1.67/1.91 ============================== PREDICATE ELIMINATION =================
% 1.67/1.91 579 ab_semigroup_mult(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.67/1.91 580 -ab_semigroup_mult(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_res) # label(axiom). [clausify(24)].
% 1.67/1.91 581 -ab_semigroup_mult(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),fun(A,bool))),finite_fold_graph(A,A),times_times(A)),B),C),D)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),E),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),fun(A,bool))),finite_fold_graph(A,A),times_times(A)),E),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),E),bot_bot(fun(A,bool)))))),D)) # label(fact_196_fold__graph__permute__diff) # label(axiom). [clausify(244)].
% 1.67/1.91 582 -ab_semigroup_mult(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite100568337ommute(A,A),times_times(A))) # label(fact_202_comp__fun__commute) # label(axiom). [clausify(250)].
% 1.67/1.91 583 -ab_semigroup_mult(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),fun(A,bool))),finite_fold_graph(A,A),times_times(A)),B),C),D)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),fun(A,bool))),finite_fold_graph(A,A),times_times(A)),E),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),D))) # label(fact_207_fold__graph__insert__swap) # label(axiom). [clausify(255)].
% 1.67/1.91 584 -ab_semigroup_mult(A) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),B)) # label(fact_211_fold1__insert) # label(axiom). [clausify(259)].
% 1.67/1.91 585 -ab_semigroup_mult(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),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),times_times(A)),C),B) # label(fact_215_fold1__eq__fold) # label(axiom). [clausify(263)].
% 1.67/1.91 586 -ab_semigroup_mult(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f74(A,B)),f75(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f74(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f75(A,B)),bot_bot(fun(A,bool)))))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),B)),B)) # label(fact_232_fold1__in) # label(axiom). [clausify(280)].
% 1.67/1.91 587 -ab_semigroup_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_384_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom). [clausify(432)].
% 1.67/1.91 588 -ab_semigroup_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),E),F),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),E),F),C)) # label(fact_391_fold__image__insert) # label(axiom). [clausify(439)].
% 1.67/1.91 589 -ab_semigroup_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f93(B,A,D,E,F,C)),C)) | hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),F),D),C) = hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),E),D),C) # label(fact_392_fold__image__cong) # label(axiom). [clausify(440)].
% 1.67/1.91 590 -ab_semigroup_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(B,A,D,f93(B,A,E,F,D,C)) != hAPP(B,A,F,f93(B,A,E,F,D,C)) | hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),D),E),C) = hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),F),E),C) # label(fact_392_fold__image__cong) # label(axiom). [clausify(440)].
% 1.67/1.91 Derived: times_times(nat) = ti(fun(nat,fun(nat,nat)),times_times(nat)). [resolve(579,a,580,a)].
% 1.67/1.91 Derived: -hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),finite_fold_graph(nat,nat),times_times(nat)),A),B),C)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),D),B)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),finite_fold_graph(nat,nat),times_times(nat)),D),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),B),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),D),bot_bot(fun(nat,bool)))))),C)). [resolve(579,a,581,a)].
% 1.67/1.91 Derived: hBOOL(hAPP(fun(nat,fun(nat,nat)),bool,finite100568337ommute(nat,nat),times_times(nat))). [resolve(579,a,582,a)].
% 1.67/1.91 Derived: -hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),finite_fold_graph(nat,nat),times_times(nat)),A),B),C)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),finite_fold_graph(nat,nat),times_times(nat)),D),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D),C))). [resolve(579,a,583,a)].
% 1.67/1.91 Derived: bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),A)). [resolve(579,a,584,a)].
% 1.67/1.91 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),times_times(nat)),B),A). [resolve(579,a,585,a)].
% 1.67/1.91 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f74(nat,A)),f75(nat,A))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f74(nat,A)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f75(nat,A)),bot_bot(fun(nat,bool)))))) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),A)),A)). [resolve(579,a,586,a)].
% 1.67/1.91 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(579,a,587,a)].
% 1.67/1.91 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),D),E),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(A,nat,D,C)),hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),D),E),B)). [resolve(579,a,588,a)].
% 1.67/1.95 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f93(A,nat,C,D,E,B)),B)) | hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),E),C),B) = hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),D),C),B). [resolve(579,a,589,a)].
% 1.67/1.95 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,nat,C,f93(A,nat,D,E,C,B)) != hAPP(A,nat,E,f93(A,nat,D,E,C,B)) | hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),C),D),B) = hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),E),D),B). [resolve(579,a,590,a)].
% 1.67/1.95 591 -lattice(A) | semilattice_inf(fun(B,A)) # label(arity_fun___Lattices_Osemilattice__inf) # label(axiom). [clausify(551)].
% 1.67/1.95 592 -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(32)].
% 1.67/1.95 593 -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_418_le__infE) # label(axiom). [clausify(466)].
% 1.67/1.95 594 -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_418_le__infE) # label(axiom). [clausify(466)].
% 1.67/1.95 595 -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_419_inf__mono) # label(axiom). [clausify(467)].
% 1.67/1.95 596 -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_420_inf__greatest) # label(axiom). [clausify(468)].
% 1.67/1.95 597 -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_421_le__infI) # label(axiom). [clausify(469)].
% 1.67/1.95 598 -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_422_inf__absorb2) # label(axiom). [clausify(470)].
% 1.67/1.95 599 -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_423_inf__absorb1) # label(axiom). [clausify(471)].
% 1.67/1.95 600 -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_424_le__infI2) # label(axiom). [clausify(472)].
% 1.67/1.95 601 -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_425_le__infI1) # label(axiom). [clausify(473)].
% 1.67/1.95 602 -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_426_le__inf__iff) # label(axiom). [clausify(474)].
% 1.67/1.95 603 -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_426_le__inf__iff) # label(axiom). [clausify(474)].
% 1.67/1.95 604 -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_426_le__inf__iff) # label(axiom). [clausify(474)].
% 1.67/1.95 605 -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_427_le__iff__inf) # label(axiom). [clausify(475)].
% 1.67/1.95 606 -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_427_le__iff__inf) # label(axiom). [clausify(475)].
% 1.67/1.95 607 -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_428_inf__le2) # label(axiom). [clausify(476)].
% 1.67/1.95 608 -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_430_inf__le1) # label(axiom). [clausify(478)].
% 1.67/1.95 609 -semilattice_inf(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite_comp_fun_idem(A,A),semilattice_inf_inf(A))) # label(fact_443_comp__fun__idem__inf) # label(axiom). [clausify(491)].
% 1.67/1.95 610 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),B) = ti(A,B) # label(fact_470_inf_Oidem) # label(axiom). [clausify(518)].
% 1.67/1.95 611 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),B) = ti(A,B) # label(fact_471_inf__idem) # label(axiom). [clausify(519)].
% 1.67/1.95 612 -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_473_inf_Ocommute) # label(axiom). [clausify(521)].
% 1.67/1.95 613 -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_475_inf__commute) # label(axiom). [clausify(523)].
% 1.67/1.95 614 -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_476_inf_Oleft__idem) # label(axiom). [clausify(524)].
% 1.67/1.95 615 -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_478_inf__left__idem) # label(axiom). [clausify(526)].
% 1.67/1.95 616 -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_479_inf_Oleft__commute) # label(axiom). [clausify(527)].
% 1.67/1.95 617 -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_481_inf__left__commute) # label(axiom). [clausify(529)].
% 1.67/1.95 618 -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_482_inf_Oassoc) # label(axiom). [clausify(530)].
% 1.67/1.95 619 -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_484_inf__assoc) # label(axiom). [clausify(532)].
% 1.67/1.95 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(591,b,592,a)].
% 1.67/1.95 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(591,b,593,a)].
% 1.67/1.95 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(591,b,594,a)].
% 1.67/1.95 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(591,b,595,a)].
% 1.67/1.95 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),E)) | 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))). [resolve(591,b,596,a)].
% 1.67/1.95 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(591,b,598,a)].
% 1.67/1.95 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(591,b,599,a)].
% 1.67/1.95 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(591,b,600,a)].
% 1.67/1.95 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(591,b,601,a)].
% 1.67/1.95 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(591,b,606,a)].
% 1.67/1.95 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(591,b,607,a)].
% 1.67/1.95 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(591,b,608,a)].
% 1.67/1.95 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(591,b,609,a)].
% 1.67/1.95 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(591,b,610,a)].
% 1.67/1.95 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(591,b,612,a)].
% 1.67/1.95 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(591,b,614,a)].
% 1.67/1.95 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(591,b,616,a)].
% 1.67/1.95 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(591,b,618,a)].
% 1.67/1.95 620 semilattice_inf(nat) # label(arity_Nat_Onat___Lattices_Osemilattice__inf) # label(axiom). [assumption].
% 1.67/1.95 Derived: semilattice_inf_inf(nat) = ti(fun(nat,fun(nat,nat)),semilattice_inf_inf(nat)). [resolve(620,a,592,a)].
% 1.67/1.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(620,a,593,a)].
% 1.67/1.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(620,a,594,a)].
% 1.67/1.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),B),D))). [resolve(620,a,595,a)].
% 1.67/1.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),B),C))). [resolve(620,a,596,a)].
% 1.67/1.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),B),A) = ti(nat,A). [resolve(620,a,598,a)].
% 1.67/1.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),B) = ti(nat,A). [resolve(620,a,599,a)].
% 1.67/1.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),C),A)),B)). [resolve(620,a,600,a)].
% 1.67/1.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),C)),B)). [resolve(620,a,601,a)].
% 1.67/1.95 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),B) != ti(nat,A). [resolve(620,a,606,a)].
% 1.67/1.95 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),B)),B)). [resolve(620,a,607,a)].
% 1.67/1.95 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),B)),A)). [resolve(620,a,608,a)].
% 1.67/1.95 Derived: hBOOL(hAPP(fun(nat,fun(nat,nat)),bool,finite_comp_fun_idem(nat,nat),semilattice_inf_inf(nat))). [resolve(620,a,609,a)].
% 1.67/1.95 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),A) = ti(nat,A). [resolve(620,a,610,a)].
% 1.67/1.95 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),B),A). [resolve(620,a,612,a)].
% 1.67/1.95 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),B). [resolve(620,a,614,a)].
% 1.67/1.95 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),C)). [resolve(620,a,616,a)].
% 1.67/1.95 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),B),C)). [resolve(620,a,618,a)].
% 1.67/1.95 621 semilattice_inf(bool) # label(arity_HOL_Obool___Lattices_Osemilattice__inf) # label(axiom). [assumption].
% 1.67/1.95 Derived: semilattice_inf_inf(bool) = ti(fun(bool,fun(bool,bool)),semilattice_inf_inf(bool)). [resolve(621,a,592,a)].
% 1.67/1.95 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(621,a,593,a)].
% 1.67/1.95 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(621,a,594,a)].
% 1.67/1.95 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(621,a,595,a)].
% 1.67/1.95 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),C)) | 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))). [resolve(621,a,596,a)].
% 1.67/1.95 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(621,a,598,a)].
% 1.67/1.95 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(621,a,599,a)].
% 1.67/1.95 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(621,a,600,a)].
% 1.67/1.95 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(621,a,601,a)].
% 1.67/1.95 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(621,a,606,a)].
% 1.67/1.95 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(621,a,607,a)].
% 1.72/1.98 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(621,a,608,a)].
% 1.72/1.98 Derived: hBOOL(hAPP(fun(bool,fun(bool,bool)),bool,finite_comp_fun_idem(bool,bool),semilattice_inf_inf(bool))). [resolve(621,a,609,a)].
% 1.72/1.98 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),A) = ti(bool,A). [resolve(621,a,610,a)].
% 1.72/1.98 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(621,a,612,a)].
% 1.72/1.98 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(621,a,614,a)].
% 1.72/1.98 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(621,a,616,a)].
% 1.72/1.98 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(621,a,618,a)].
% 1.72/1.98 622 -lattice(A) | semilattice_sup(fun(B,A)) # label(arity_fun___Lattices_Osemilattice__sup) # label(axiom). [clausify(550)].
% 1.72/1.98 623 -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(33)].
% 1.72/1.98 624 -semilattice_sup(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(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_245_sup__le__fold__sup) # label(axiom). [clausify(293)].
% 1.72/1.98 625 -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_264_le__supE) # label(axiom). [clausify(312)].
% 1.72/1.98 626 -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_264_le__supE) # label(axiom). [clausify(312)].
% 1.72/1.98 627 -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_265_sup__mono) # label(axiom). [clausify(313)].
% 1.72/1.98 628 -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_266_sup__least) # label(axiom). [clausify(314)].
% 1.72/1.98 629 -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_267_le__supI) # label(axiom). [clausify(315)].
% 1.72/1.98 630 -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_268_sup__absorb1) # label(axiom). [clausify(316)].
% 1.72/1.98 631 -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_269_sup__absorb2) # label(axiom). [clausify(317)].
% 1.72/1.98 632 -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_270_le__supI2) # label(axiom). [clausify(318)].
% 1.72/1.98 633 -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_271_le__supI1) # label(axiom). [clausify(319)].
% 1.72/1.98 634 -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_273_le__sup__iff) # label(axiom). [clausify(321)].
% 1.72/1.98 635 -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_273_le__sup__iff) # label(axiom). [clausify(321)].
% 1.72/1.98 636 -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_273_le__sup__iff) # label(axiom). [clausify(321)].
% 1.72/1.98 637 -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_274_sup__assoc) # label(axiom). [clausify(322)].
% 1.72/1.98 638 -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_276_sup_Oassoc) # label(axiom). [clausify(324)].
% 1.72/1.98 639 -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_277_sup__left__commute) # label(axiom). [clausify(325)].
% 1.72/1.98 640 -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_279_sup_Oleft__commute) # label(axiom). [clausify(327)].
% 1.72/1.98 641 -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_280_sup__left__idem) # label(axiom). [clausify(328)].
% 1.72/1.98 642 -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_282_sup_Oleft__idem) # label(axiom). [clausify(330)].
% 1.72/1.98 643 -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_283_le__iff__sup) # label(axiom). [clausify(331)].
% 1.72/1.98 644 -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_283_le__iff__sup) # label(axiom). [clausify(331)].
% 1.72/1.98 645 -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_284_sup__commute) # label(axiom). [clausify(332)].
% 1.72/1.98 646 -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_286_sup_Ocommute) # label(axiom). [clausify(334)].
% 1.72/1.98 647 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),B) = ti(A,B) # label(fact_288_sup__idem) # label(axiom). [clausify(336)].
% 1.72/1.98 648 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),B) = ti(A,B) # label(fact_289_sup_Oidem) # label(axiom). [clausify(337)].
% 1.72/1.98 649 -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_290_sup__ge2) # label(axiom). [clausify(338)].
% 1.72/1.98 650 -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_292_sup__ge1) # label(axiom). [clausify(340)].
% 1.72/1.98 651 -semilattice_sup(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite_comp_fun_idem(A,A),semilattice_sup_sup(A))) # label(fact_361_comp__fun__idem__sup) # label(axiom). [clausify(409)].
% 1.72/1.98 652 -semilattice_sup(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(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_364_fold__sup__insert) # label(axiom). [clausify(412)].
% 1.72/1.98 653 -semilattice_sup(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f84(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_374_fold__sup__le__sup) # label(axiom). [clausify(422)].
% 1.72/1.98 654 -semilattice_sup(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f84(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_374_fold__sup__le__sup) # label(axiom). [clausify(422)].
% 1.72/1.98 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(622,b,623,a)].
% 1.72/1.98 Derived: -lattice(A) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,finite_finite_1(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(622,b,624,a)].
% 1.72/1.98 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(622,b,625,a)].
% 1.72/1.98 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(622,b,626,a)].
% 1.72/1.98 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(622,b,627,a)].
% 1.72/1.98 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),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_sup_sup(fun(B,A)),C),E)),D)). [resolve(622,b,628,a)].
% 1.72/1.98 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(622,b,630,a)].
% 1.72/1.98 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(622,b,631,a)].
% 1.72/1.98 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(622,b,632,a)].
% 1.72/1.98 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(622,b,633,a)].
% 1.72/1.98 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(622,b,637,a)].
% 1.72/1.98 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(622,b,639,a)].
% 1.72/1.98 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(622,b,641,a)].
% 1.72/1.98 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(622,b,644,a)].
% 1.72/1.98 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(622,b,645,a)].
% 1.72/1.98 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(622,b,647,a)].
% 1.72/1.98 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(622,b,649,a)].
% 1.72/1.98 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(622,b,650,a)].
% 1.72/1.98 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(622,b,651,a)].
% 1.72/1.98 Derived: -lattice(A) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,finite_finite_1(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(622,b,652,a)].
% 1.72/1.98 Derived: -lattice(A) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,finite_finite_1(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)),f84(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(622,b,653,a)].
% 1.72/1.98 Derived: -lattice(A) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,finite_finite_1(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)),f84(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(622,b,654,a)].
% 1.72/1.98 655 semilattice_sup(nat) # label(arity_Nat_Onat___Lattices_Osemilattice__sup) # label(axiom). [assumption].
% 1.72/1.98 Derived: semilattice_sup_sup(nat) = ti(fun(nat,fun(nat,nat)),semilattice_sup_sup(nat)). [resolve(655,a,623,a)].
% 1.72/1.98 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),B),C)),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),semilattice_sup_sup(nat)),C),A))). [resolve(655,a,624,a)].
% 1.72/1.98 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(655,a,625,a)].
% 1.72/1.98 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(655,a,626,a)].
% 1.72/1.98 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),B),D))). [resolve(655,a,627,a)].
% 1.72/1.98 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),C)),B)). [resolve(655,a,628,a)].
% 1.72/1.99 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),B),A) = ti(nat,B). [resolve(655,a,630,a)].
% 1.72/1.99 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),B) = ti(nat,B). [resolve(655,a,631,a)].
% 1.72/1.99 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),C),B))). [resolve(655,a,632,a)].
% 1.72/1.99 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),B),C))). [resolve(655,a,633,a)].
% 1.72/1.99 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),B),C)). [resolve(655,a,637,a)].
% 1.72/1.99 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),C)). [resolve(655,a,639,a)].
% 1.72/1.99 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),B). [resolve(655,a,641,a)].
% 1.72/1.99 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),B) != ti(nat,B). [resolve(655,a,644,a)].
% 1.72/1.99 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),B),A). [resolve(655,a,645,a)].
% 1.72/1.99 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),A) = ti(nat,A). [resolve(655,a,647,a)].
% 1.72/1.99 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),B),A))). [resolve(655,a,649,a)].
% 1.72/1.99 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),B))). [resolve(655,a,650,a)].
% 1.72/1.99 Derived: hBOOL(hAPP(fun(nat,fun(nat,nat)),bool,finite_comp_fun_idem(nat,nat),semilattice_sup_sup(nat))). [resolve(655,a,651,a)].
% 1.72/1.99 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),semilattice_sup_sup(nat)),B),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),C),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),C),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),semilattice_sup_sup(nat)),B),A)). [resolve(655,a,652,a)].
% 1.72/1.99 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f84(nat,B,C,A)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),semilattice_sup_sup(nat)),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),C),B))). [resolve(655,a,653,a)].
% 1.72/1.99 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f84(nat,B,C,A)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),semilattice_sup_sup(nat)),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),C),B))). [resolve(655,a,654,a)].
% 1.72/1.99 656 semilattice_sup(bool) # label(arity_HOL_Obool___Lattices_Osemilattice__sup) # label(axiom). [assumption].
% 1.72/1.99 Derived: semilattice_sup_sup(bool) = ti(fun(bool,fun(bool,bool)),semilattice_sup_sup(bool)). [resolve(656,a,623,a)].
% 1.72/1.99 Derived: -hBOOL(hAPP(fun(bool,bool),bool,finite_finite_1(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(656,a,624,a)].
% 1.72/1.99 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(656,a,625,a)].
% 1.72/1.99 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(656,a,626,a)].
% 1.72/1.99 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(656,a,627,a)].
% 1.72/1.99 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),B)) | 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)),B)). [resolve(656,a,628,a)].
% 1.72/1.99 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(656,a,630,a)].
% 1.72/1.99 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(656,a,631,a)].
% 1.72/1.99 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(656,a,632,a)].
% 1.72/1.99 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(656,a,633,a)].
% 1.72/1.99 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(656,a,637,a)].
% 1.72/1.99 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(656,a,639,a)].
% 1.72/1.99 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(656,a,641,a)].
% 1.72/1.99 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(656,a,644,a)].
% 1.80/2.05 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(656,a,645,a)].
% 1.80/2.05 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),A) = ti(bool,A). [resolve(656,a,647,a)].
% 1.80/2.05 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(656,a,649,a)].
% 1.80/2.05 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(656,a,650,a)].
% 1.80/2.05 Derived: hBOOL(hAPP(fun(bool,fun(bool,bool)),bool,finite_comp_fun_idem(bool,bool),semilattice_sup_sup(bool))). [resolve(656,a,651,a)].
% 1.80/2.05 Derived: -hBOOL(hAPP(fun(bool,bool),bool,finite_finite_1(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(656,a,652,a)].
% 1.80/2.05 Derived: -hBOOL(hAPP(fun(bool,bool),bool,finite_finite_1(bool),A)) | hBOOL(hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),member(bool),f84(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(656,a,653,a)].
% 1.80/2.05 Derived: -hBOOL(hAPP(fun(bool,bool),bool,finite_finite_1(bool),A)) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),f84(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(656,a,654,a)].
% 1.80/2.05 657 -bounded_lattice(A) | bounded_lattice_bot(fun(B,A)) # label(arity_fun___Lattices_Obounded__lattice__bot) # label(axiom). [clausify(549)].
% 1.80/2.05 658 -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_294_sup__eq__bot__iff) # label(axiom). [clausify(342)].
% 1.80/2.05 659 -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_294_sup__eq__bot__iff) # label(axiom). [clausify(342)].
% 1.80/2.05 660 -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_294_sup__eq__bot__iff) # label(axiom). [clausify(342)].
% 1.80/2.05 661 -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_295_sup__bot__right) # label(axiom). [clausify(343)].
% 1.80/2.05 662 -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_296_sup__bot__left) # label(axiom). [clausify(344)].
% 1.80/2.05 663 -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_468_inf__bot__left) # label(axiom). [clausify(516)].
% 1.80/2.05 664 -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_469_inf__bot__right) # label(axiom). [clausify(517)].
% 1.80/2.05 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(657,b,658,a)].
% 1.80/2.05 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(657,b,659,a)].
% 1.91/2.18 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(657,b,660,a)].
% 1.91/2.18 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(657,b,661,a)].
% 1.91/2.18 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(657,b,662,a)].
% 1.91/2.18 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(657,b,663,a)].
% 1.91/2.18 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(657,b,664,a)].
% 1.91/2.18 665 bounded_lattice_bot(bool) # label(arity_HOL_Obool___Lattices_Obounded__lattice__bot) # label(axiom). [assumption].
% 1.91/2.18 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(665,a,658,a)].
% 1.91/2.18 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(665,a,659,a)].
% 1.91/2.18 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(665,a,660,a)].
% 1.91/2.18 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),bot_bot(bool)) = ti(bool,A). [resolve(665,a,661,a)].
% 1.91/2.18 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),bot_bot(bool)),A) = ti(bool,A). [resolve(665,a,662,a)].
% 1.91/2.18 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),bot_bot(bool)),A) = bot_bot(bool). [resolve(665,a,663,a)].
% 1.91/2.18 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),bot_bot(bool)) = bot_bot(bool). [resolve(665,a,664,a)].
% 1.91/2.18 666 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom). [assumption].
% 1.91/2.18 667 -linorder(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),C),B)) # label(fact_302_linorder__le__cases) # label(axiom). [clausify(350)].
% 1.91/2.18 668 -linorder(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),C),B)) # label(fact_316_linorder__linear) # label(axiom). [clausify(364)].
% 1.91/2.18 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(666,a,667,a)].
% 1.91/2.18 669 comm_monoid_mult(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.91/2.18 670 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),f95(D,B,A,E,F,V6,V7,V8,V9,C)),V9)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f96(D,B,A,E,F,V6,V7,V8,V9,C)),C)) | hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),E),V9) = hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),V6),E),C) # label(fact_394_fold__image__eq__general__inverses) # label(axiom). [clausify(442)].
% 1.91/2.18 671 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),f95(D,B,A,E,F,V6,V7,V8,V9,C)),V9)) | -hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),hAPP(B,D,V7,f96(D,B,A,E,F,V6,V7,V8,V9,C))),V9)) | hAPP(D,B,V8,hAPP(B,D,V7,f96(D,B,A,E,F,V6,V7,V8,V9,C))) != ti(B,f96(D,B,A,E,F,V6,V7,V8,V9,C)) | hAPP(D,A,F,hAPP(B,D,V7,f96(D,B,A,E,F,V6,V7,V8,V9,C))) != hAPP(B,A,V6,f96(D,B,A,E,F,V6,V7,V8,V9,C)) | hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),E),V9) = hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),V6),E),C) # label(fact_394_fold__image__eq__general__inverses) # label(axiom). [clausify(442)].
% 1.91/2.18 672 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),hAPP(D,B,E,f95(D,B,A,F,V6,V7,V8,E,V9,C))),C)) | hAPP(B,D,V8,hAPP(D,B,E,f95(D,B,A,F,V6,V7,V8,E,V9,C))) != ti(D,f95(D,B,A,F,V6,V7,V8,E,V9,C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f96(D,B,A,F,V6,V7,V8,E,V9,C)),C)) | hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),V6),F),V9) = hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),V7),F),C) # label(fact_394_fold__image__eq__general__inverses) # label(axiom). [clausify(442)].
% 1.91/2.18 673 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),hAPP(D,B,E,f95(D,B,A,F,V6,V7,V8,E,V9,C))),C)) | hAPP(B,D,V8,hAPP(D,B,E,f95(D,B,A,F,V6,V7,V8,E,V9,C))) != ti(D,f95(D,B,A,F,V6,V7,V8,E,V9,C)) | -hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),hAPP(B,D,V8,f96(D,B,A,F,V6,V7,V8,E,V9,C))),V9)) | hAPP(D,B,E,hAPP(B,D,V8,f96(D,B,A,F,V6,V7,V8,E,V9,C))) != ti(B,f96(D,B,A,F,V6,V7,V8,E,V9,C)) | hAPP(D,A,V6,hAPP(B,D,V8,f96(D,B,A,F,V6,V7,V8,E,V9,C))) != hAPP(B,A,V7,f96(D,B,A,F,V6,V7,V8,E,V9,C)) | hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),V6),F),V9) = hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),V7),F),C) # label(fact_394_fold__image__eq__general__inverses) # label(axiom). [clausify(442)].
% 1.91/2.18 674 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,C),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f97(D,A,E,F,V6,B,C)),f99(D,A,E,F,V6,B,C))) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite_1(D),V6)) | hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),f101(D,A,E,F,V6,B,C)),V6)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),E),C),V6)),hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),C),V6))) # label(fact_395_fold__image__related) # label(axiom). [clausify(443)].
% 1.91/2.18 675 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,C),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f97(D,A,E,F,V6,B,C)),f99(D,A,E,F,V6,B,C))) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite_1(D),V6)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(D,A,E,f101(D,A,E,F,V6,B,C))),hAPP(D,A,F,f101(D,A,E,F,V6,B,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),E),C),V6)),hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),C),V6))) # label(fact_395_fold__image__related) # label(axiom). [clausify(443)].
% 1.91/2.18 676 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,C),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f98(D,A,E,F,V6,B,C)),f100(D,A,E,F,V6,B,C))) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite_1(D),V6)) | hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),f101(D,A,E,F,V6,B,C)),V6)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),E),C),V6)),hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),C),V6))) # label(fact_395_fold__image__related) # label(axiom). [clausify(443)].
% 1.91/2.18 677 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,C),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f98(D,A,E,F,V6,B,C)),f100(D,A,E,F,V6,B,C))) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite_1(D),V6)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(D,A,E,f101(D,A,E,F,V6,B,C))),hAPP(D,A,F,f101(D,A,E,F,V6,B,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),E),C),V6)),hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),C),V6))) # label(fact_395_fold__image__related) # label(axiom). [clausify(443)].
% 1.91/2.18 678 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,C),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f97(D,A,E,F,V6,B,C)),f98(D,A,E,F,V6,B,C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f99(D,A,E,F,V6,B,C)),f100(D,A,E,F,V6,B,C)))) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite_1(D),V6)) | hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),f101(D,A,E,F,V6,B,C)),V6)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),E),C),V6)),hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),C),V6))) # label(fact_395_fold__image__related) # label(axiom). [clausify(443)].
% 1.91/2.18 679 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,C),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f97(D,A,E,F,V6,B,C)),f98(D,A,E,F,V6,B,C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f99(D,A,E,F,V6,B,C)),f100(D,A,E,F,V6,B,C)))) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite_1(D),V6)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(D,A,E,f101(D,A,E,F,V6,B,C))),hAPP(D,A,F,f101(D,A,E,F,V6,B,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),E),C),V6)),hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),C),V6))) # label(fact_395_fold__image__related) # label(axiom). [clausify(443)].
% 1.91/2.18 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f95(C,A,nat,D,E,F,V6,V7,V8,B)),V8)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f96(C,A,nat,D,E,F,V6,V7,V8,B)),B)) | hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),D),V8) = hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),F),D),B). [resolve(669,a,670,a)].
% 1.91/2.18 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f95(C,A,nat,D,E,F,V6,V7,V8,B)),V8)) | -hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),hAPP(A,C,V6,f96(C,A,nat,D,E,F,V6,V7,V8,B))),V8)) | hAPP(C,A,V7,hAPP(A,C,V6,f96(C,A,nat,D,E,F,V6,V7,V8,B))) != ti(A,f96(C,A,nat,D,E,F,V6,V7,V8,B)) | hAPP(C,nat,E,hAPP(A,C,V6,f96(C,A,nat,D,E,F,V6,V7,V8,B))) != hAPP(A,nat,F,f96(C,A,nat,D,E,F,V6,V7,V8,B)) | hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),D),V8) = hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),F),D),B). [resolve(669,a,671,a)].
% 1.91/2.18 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(C,A,D,f95(C,A,nat,E,F,V6,V7,D,V8,B))),B)) | hAPP(A,C,V7,hAPP(C,A,D,f95(C,A,nat,E,F,V6,V7,D,V8,B))) != ti(C,f95(C,A,nat,E,F,V6,V7,D,V8,B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f96(C,A,nat,E,F,V6,V7,D,V8,B)),B)) | hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),F),E),V8) = hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),V6),E),B). [resolve(669,a,672,a)].
% 1.91/2.18 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(C,A,D,f95(C,A,nat,E,F,V6,V7,D,V8,B))),B)) | hAPP(A,C,V7,hAPP(C,A,D,f95(C,A,nat,E,F,V6,V7,D,V8,B))) != ti(C,f95(C,A,nat,E,F,V6,V7,D,V8,B)) | -hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),hAPP(A,C,V7,f96(C,A,nat,E,F,V6,V7,D,V8,B))),V8)) | hAPP(C,A,D,hAPP(A,C,V7,f96(C,A,nat,E,F,V6,V7,D,V8,B))) != ti(A,f96(C,A,nat,E,F,V6,V7,D,V8,B)) | hAPP(C,nat,F,hAPP(A,C,V7,f96(C,A,nat,E,F,V6,V7,D,V8,B))) != hAPP(A,nat,V6,f96(C,A,nat,E,F,V6,V7,D,V8,B)) | hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),F),E),V8) = hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),V6),E),B). [resolve(669,a,673,a)].
% 1.91/2.18 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,B),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f97(C,nat,D,E,F,A,B)),f99(C,nat,D,E,F,A,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f101(C,nat,D,E,F,A,B)),F)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),D),B),F)),hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),B),F))). [resolve(669,a,674,a)].
% 1.91/2.18 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,B),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f97(C,nat,D,E,F,A,B)),f99(C,nat,D,E,F,A,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(C,nat,D,f101(C,nat,D,E,F,A,B))),hAPP(C,nat,E,f101(C,nat,D,E,F,A,B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),D),B),F)),hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),B),F))). [resolve(669,a,675,a)].
% 1.91/2.18 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,B),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f98(C,nat,D,E,F,A,B)),f100(C,nat,D,E,F,A,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f101(C,nat,D,E,F,A,B)),F)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),D),B),F)),hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),B),F))). [resolve(669,a,676,a)].
% 1.91/2.18 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,B),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f98(C,nat,D,E,F,A,B)),f100(C,nat,D,E,F,A,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(C,nat,D,f101(C,nat,D,E,F,A,B))),hAPP(C,nat,E,f101(C,nat,D,E,F,A,B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),D),B),F)),hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),B),F))). [resolve(669,a,677,a)].
% 1.91/2.18 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,B),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f97(C,nat,D,E,F,A,B)),f98(C,nat,D,E,F,A,B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f99(C,nat,D,E,F,A,B)),f100(C,nat,D,E,F,A,B)))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f101(C,nat,D,E,F,A,B)),F)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),D),B),F)),hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),B),F))). [resolve(669,a,678,a)].
% 1.91/2.18 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,B),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f97(C,nat,D,E,F,A,B)),f98(C,nat,D,E,F,A,B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f99(C,nat,D,E,F,A,B)),f100(C,nat,D,E,F,A,B)))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(C,nat,D,f101(C,nat,D,E,F,A,B))),hAPP(C,nat,E,f101(C,nat,D,E,F,A,B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),D),B),F)),hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),B),F))). [resolve(669,a,679,a)].
% 4.29/4.57
% 4.29/4.57 ============================== end predicate elimination =============
% 4.29/4.57
% 4.29/4.57 Auto_denials: (non-Horn, no changes).
% 4.29/4.57
% 4.29/4.57 Term ordering decisions:
% 4.29/4.57 Function symbol KB weights: bool=1. nat=1. state=1. com=1. vname=1. loc_1=1. evaln=1. evalc=1. fconj=1. glb_1=1. loc=1. local=1. update=1. semi=1. ass=1. fdisj=1. fimplies=1. glb=1. fNot=1. getlocs=1. skip=1. fFalse=1. fTrue=1. hoare_Mirabelle_MGT=1. b=1. c=1. g=1. p=1. x_a=1. fun=1. ti=1. image=1. finite_fold=1. finite_fold_graph=1. finite_fold_image=1. finite100568337ommute=1. finite_comp_fun_idem=1. combk=1. finite1357897459simple=1. big_comm_monoid_big=1. finite908156982e_idem=1. fold_graph=1. hoare_1312322281e_case=1. hoare_1632998903le_rec=1. f10=1. f11=1. f12=1. f13=1. f14=1. f15=1. f16=1. f19=1. f23=1. f24=1. f56=1. f57=1. f74=1. f75=1. f92=1. f94=1. f104=1. f105=1. hoare_1656922687triple=1. ord_less_eq=1. semilattice_sup_sup=1. bot_bot=1. member=1. insert=1. semilattice_inf_inf=1. finite_finite_1=1. minus_minus=1. hoare_246368825triple=1. times_times=1. collect=1. hoare_279057269derivs=1. big_lattice_Sup_fin=1. fequal=1. the=1. finite_fold1Set=1. finite_fold1=1. finite_folding_one=1. finite2073411215e_idem=1. hoare_920331057_valid=1. combi=1. partial_flat_lub=1. the_elem=1. vname_case=1. vname_rec=1. big_semilattice_big=1. undefined=1. f63=1. f64=1. f91=1. combc=1. combb=1. combs=1. f17=1. f18=1. f29=1. f30=1. f32=1. f33=1. f40=1. f53=1. f54=1. f55=1. f60=1. f61=1. f62=1. f67=1. f68=1. f87=1. f102=1. f103=1. f107=1. f108=1. hAPP=1. f26=1. f31=1. f36=1. f41=1. f42=1. f43=1. f51=1. f52=1. f58=1. f77=1. f78=1. f79=1. f80=1. f81=1. f82=1. f83=1. f84=1. f85=1. f86=1. f90=1. f1=1. f2=1. f20=1. f21=1. f25=1. f27=1. f34=1. f37=1. f38=1. f39=1. f48=1. f49=1. f50=1. f59=1. f65=1. f66=1. f76=1. f88=1. f89=1. f3=1. f4=1. f5=1. f6=1. f28=1. f35=1. f44=1. f45=1. f46=1. f93=1. f7=1. f8=1. f9=1. f22=1. f69=1. f70=1. f71=1. f97=1. f98=1. f99=1. f100=1. f101=1. f47=1. f106=1. f95=1. f96=1.
% 4.29/4.57
% 4.29/4.57 ============================== end of process initial clauses ========
% 4.29/4.57
% 4.29/4.57 ============================== CLAUSES FOR SEARCH ====================
% 4.29/4.57
% 4.29/4.57 ============================== end of clauses for search =============
% 4.29/4.57
% 4.29/4.57 ============================== SEARCH ================================
% 4.29/4.57
% 4.29/4.57 % Starting search at 0.78 seconds.
% 4.29/4.57
% 4.29/4.57 Low Water (keep): wt=187.000, iters=3661
% 4.29/4.57
% 4.29/4.57 Low Water (keep): wt=172.000, iters=3413
% 4.29/4.57
% 4.29/4.57 Low Water (keep): wt=167.000, iters=3347
% 4.29/4.57
% 4.29/4.57 Low Water (keep): wt=166.000, iters=3457
% 4.29/4.57
% 4.29/4.57 Low Water (keep): wt=164.000, iters=3432
% 4.29/4.57
% 4.29/4.57 Low Water (keep): wt=163.000, iters=3366
% 4.29/4.57
% 4.29/4.57 Low Water (keep): wt=162.000, iters=3351
% 4.29/4.57
% 4.29/4.57 Low Water (keep): wt=153.000, iters=3551
% 4.29/4.57
% 4.29/4.57 Low Water (keep): wt=145.000, iters=3472
% 4.29/4.57
% 4.29/4.57 Low Water (keep): wt=143.000, iters=3501
% 4.29/4.57
% 4.29/4.57 ============================== PROOF =================================
% 4.29/4.57 % SZS status Theorem
% 4.29/4.57 % SZS output start Refutation
% 4.29/4.57
% 4.29/4.57 % Proof 1 at 2.86 (+ 0.02) seconds.
% 4.29/4.57 % Length of proof is 27.
% 4.29/4.57 % Level of proof is 6.
% 4.29/4.57 % Maximum clause weight is 298.000.
% 4.29/4.57 % Given clauses 373.
% 4.29/4.57
% 4.29/4.57 45 (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].
% 4.29/4.57 60 (all X_b all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),bot_bot(fun(X_b,bool)))) # label(fact_12_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 4.29/4.57 89 (all X_b all X_1 hAPP(fun(X_b,bool),X_b,the_elem(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1)) # label(fact_41_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 4.29/4.57 99 (all X_b all Q_1 all Ga all Ca all Pa ((all Z_2 all S_2 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_2),S_2)) -> (exists P_1 exists Q_2 (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_1656922687triple(X_b),bool))))) & (all S_3 ((all Z_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_3),S_2)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_3),S_3)))) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_2),S_3)))))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),Ga),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_1656922687triple(X_b),bool))))))) # label(fact_51_conseq) # label(axiom) # label(non_clause). [assumption].
% 4.29/4.57 129 (all X_b all X_1 hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),X_1)) = ti(X_b,X_1)) # label(fact_81_the__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 4.29/4.57 564 (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].
% 4.29/4.57 565 (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].
% 4.29/4.57 766 ti(bool,fFalse) = fFalse # label(tsy_c_fFalse_res) # label(hypothesis). [assumption].
% 4.29/4.57 776 hAPP(A,B,C,D) = ti(B,hAPP(A,B,C,D)) # label(tsy_c_hAPP_res) # label(axiom). [clausify(45)].
% 4.29/4.57 777 ti(A,hAPP(B,A,C,D)) = hAPP(B,A,C,D). [copy(776),flip(a)].
% 4.29/4.57 808 hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),bot_bot(fun(A,bool))) = hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(A,fun(A,bool),fequal(A),B)) # label(fact_12_singleton__conv2) # label(axiom). [clausify(60)].
% 4.29/4.57 864 hAPP(fun(A,bool),A,the_elem(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),bot_bot(fun(A,bool)))) = ti(A,B) # label(fact_41_the__elem__eq) # label(axiom). [clausify(89)].
% 4.29/4.57 865 ti(A,B) = hAPP(fun(A,bool),A,the_elem(A),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(A,fun(A,bool),fequal(A),B))). [copy(864),rewrite([808(18)]),flip(a)].
% 4.29/4.57 881 hBOOL(hAPP(state,bool,hAPP(A,fun(state,bool),B,f20(A,C,D,E,B)),f21(A,C,D,E,B))) | hBOOL(hAPP(fun(hoare_1656922687triple(A),bool),bool,hAPP(fun(hoare_1656922687triple(A),bool),fun(fun(hoare_1656922687triple(A),bool),bool),hoare_279057269derivs(A),D),hAPP(fun(hoare_1656922687triple(A),bool),fun(hoare_1656922687triple(A),bool),hAPP(hoare_1656922687triple(A),fun(fun(hoare_1656922687triple(A),bool),fun(hoare_1656922687triple(A),bool)),insert(hoare_1656922687triple(A)),hAPP(fun(A,fun(state,bool)),hoare_1656922687triple(A),hAPP(com,fun(fun(A,fun(state,bool)),hoare_1656922687triple(A)),hAPP(fun(A,fun(state,bool)),fun(com,fun(fun(A,fun(state,bool)),hoare_1656922687triple(A))),hoare_246368825triple(A),B),E),C)),bot_bot(fun(hoare_1656922687triple(A),bool))))) # label(fact_51_conseq) # label(axiom). [clausify(99)].
% 4.29/4.58 882 hBOOL(hAPP(state,bool,hAPP(A,fun(state,bool),B,f20(A,C,D,E,B)),f21(A,C,D,E,B))) | hBOOL(hAPP(fun(hoare_1656922687triple(A),bool),bool,hAPP(fun(hoare_1656922687triple(A),bool),fun(fun(hoare_1656922687triple(A),bool),bool),hoare_279057269derivs(A),D),hAPP(fun(hoare_1656922687triple(A),bool),fun(hoare_1656922687triple(A),bool),collect(hoare_1656922687triple(A)),hAPP(hoare_1656922687triple(A),fun(hoare_1656922687triple(A),bool),fequal(hoare_1656922687triple(A)),hAPP(fun(A,fun(state,bool)),hoare_1656922687triple(A),hAPP(com,fun(fun(A,fun(state,bool)),hoare_1656922687triple(A)),hAPP(fun(A,fun(state,bool)),fun(com,fun(fun(A,fun(state,bool)),hoare_1656922687triple(A))),hoare_246368825triple(A),B),E),C))))). [copy(881),rewrite([808(74)])].
% 4.29/4.58 946 hAPP(fun(A,bool),A,the(A),hAPP(A,fun(A,bool),fequal(A),B)) = ti(A,B) # label(fact_81_the__sym__eq__trivial) # label(axiom). [clausify(129)].
% 4.29/4.58 947 hAPP(fun(A,bool),A,the_elem(A),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(A,fun(A,bool),fequal(A),B))) = hAPP(fun(A,bool),A,the(A),hAPP(A,fun(A,bool),fequal(A),B)). [copy(946),rewrite([865(9)]),flip(a)].
% 4.29/4.58 1569 hAPP(A,A,combi(A),B) = ti(A,B) # label(help_COMBI_1_1_U) # label(axiom). [clausify(564)].
% 4.29/4.58 1570 hAPP(fun(A,bool),A,the(A),hAPP(A,fun(A,bool),fequal(A),B)) = hAPP(A,A,combi(A),B). [copy(1569),rewrite([865(3),947(16)]),flip(a)].
% 4.29/4.58 1571 hAPP(A,B,hAPP(B,fun(A,B),combk(B,A),C),D) = ti(B,C) # label(help_COMBK_1_1_U) # label(axiom). [clausify(565)].
% 4.29/4.58 1572 hAPP(A,B,hAPP(B,fun(A,B),combk(B,A),C),D) = hAPP(B,B,combi(B),C). [copy(1571),rewrite([865(5),947(18),1570(12)])].
% 4.29/4.58 1580 -hBOOL(fFalse) # label(help_fFalse_1_1_U) # label(axiom). [assumption].
% 4.29/4.58 1590 -hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),g),hAPP(fun(hoare_1656922687triple(x_a),bool),fun(hoare_1656922687triple(x_a),bool),hAPP(hoare_1656922687triple(x_a),fun(fun(hoare_1656922687triple(x_a),bool),fun(hoare_1656922687triple(x_a),bool)),insert(hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),hoare_246368825triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),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))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_1656922687triple(x_a),bool))))) # label(conj_0) # label(negated_conjecture). [assumption].
% 4.29/4.58 1591 -hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),bool),hoare_279057269derivs(x_a),g),hAPP(fun(hoare_1656922687triple(x_a),bool),fun(hoare_1656922687triple(x_a),bool),collect(hoare_1656922687triple(x_a)),hAPP(hoare_1656922687triple(x_a),fun(hoare_1656922687triple(x_a),bool),fequal(hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),hoare_246368825triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),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))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b))))))). [copy(1590),rewrite([808(303)])].
% 4.29/4.58 1840 hAPP(A,A,combi(A),hAPP(B,A,C,D)) = hAPP(B,A,C,D). [back_rewrite(777),rewrite([865(2),947(15),1570(9)])].
% 4.29/4.58 1849 hAPP(bool,bool,combi(bool),fFalse) = fFalse. [back_rewrite(766),rewrite([865(3),947(24),1570(15)])].
% 4.29/4.58 6354 $F. [resolve(1591,a,882,b),rewrite([1572(252),1840(22),1572(234),1849(6)]),unit_del(a,1580)].
% 4.29/4.58
% 4.29/4.58 % SZS output end Refutation
% 4.29/4.58 ============================== end of proof ==========================
% 4.29/4.58
% 4.29/4.58 ============================== STATISTICS ============================
% 4.29/4.58
% 4.29/4.58 Given=373. Generated=8346. Kept=5347. proofs=1.
% 4.29/4.58 Usable=348. Sos=4339. Demods=433. Limbo=0, Disabled=1645. Hints=0.
% 4.29/4.58 Megabytes=49.62.
% 4.29/4.58 User_CPU=2.86, System_CPU=0.02, Wall_clock=3.
% 4.29/4.58
% 4.29/4.58 ============================== end of statistics =====================
% 4.29/4.58
% 4.29/4.58 ============================== end of search =========================
% 4.29/4.58
% 4.29/4.58 THEOREM PROVED
% 4.29/4.58 % SZS status Theorem
% 4.29/4.58
% 4.29/4.58 Exiting with 1 proof.
% 4.29/4.58
% 4.29/4.58 Process 26799 exit (max_proofs) Sun Jun 5 02:59:21 2022
% 4.29/4.58 Prover9 interrupted
%------------------------------------------------------------------------------