TSTP Solution File: SWW471+6 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW471+6 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 01:17:07 EDT 2022
% Result : Unknown 185.47s 185.76s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWW471+6 : TPTP v8.1.0. Released v5.3.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jun 5 00:28:37 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.63/1.85 ============================== Prover9 ===============================
% 1.63/1.85 Prover9 (32) version 2009-11A, November 2009.
% 1.63/1.85 Process 32742 was started by sandbox on n027.cluster.edu,
% 1.63/1.85 Sun Jun 5 00:28:39 2022
% 1.63/1.85 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32588_n027.cluster.edu".
% 1.63/1.85 ============================== end of head ===========================
% 1.63/1.85
% 1.63/1.85 ============================== INPUT =================================
% 1.63/1.85
% 1.63/1.85 % Reading from file /tmp/Prover9_32588_n027.cluster.edu
% 1.63/1.85
% 1.63/1.85 set(prolog_style_variables).
% 1.63/1.85 set(auto2).
% 1.63/1.85 % set(auto2) -> set(auto).
% 1.63/1.85 % set(auto) -> set(auto_inference).
% 1.63/1.85 % set(auto) -> set(auto_setup).
% 1.63/1.85 % set(auto_setup) -> set(predicate_elim).
% 1.63/1.85 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.63/1.85 % set(auto) -> set(auto_limits).
% 1.63/1.85 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.63/1.85 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.63/1.85 % set(auto) -> set(auto_denials).
% 1.63/1.85 % set(auto) -> set(auto_process).
% 1.63/1.85 % set(auto2) -> assign(new_constants, 1).
% 1.63/1.85 % set(auto2) -> assign(fold_denial_max, 3).
% 1.63/1.85 % set(auto2) -> assign(max_weight, "200.000").
% 1.63/1.85 % set(auto2) -> assign(max_hours, 1).
% 1.63/1.85 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.63/1.85 % set(auto2) -> assign(max_seconds, 0).
% 1.63/1.85 % set(auto2) -> assign(max_minutes, 5).
% 1.63/1.85 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.63/1.85 % set(auto2) -> set(sort_initial_sos).
% 1.63/1.85 % set(auto2) -> assign(sos_limit, -1).
% 1.63/1.85 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.63/1.85 % set(auto2) -> assign(max_megs, 400).
% 1.63/1.85 % set(auto2) -> assign(stats, some).
% 1.63/1.85 % set(auto2) -> clear(echo_input).
% 1.63/1.85 % set(auto2) -> set(quiet).
% 1.63/1.85 % set(auto2) -> clear(print_initial_clauses).
% 1.63/1.85 % set(auto2) -> clear(print_given).
% 1.63/1.85 assign(lrs_ticks,-1).
% 1.63/1.85 assign(sos_limit,10000).
% 1.63/1.85 assign(order,kbo).
% 1.63/1.85 set(lex_order_vars).
% 1.63/1.85 clear(print_given).
% 1.63/1.85
% 1.63/1.85 % formulas(sos). % not echoed (633 formulas)
% 1.63/1.85
% 1.63/1.85 ============================== end of input ==========================
% 1.63/1.85
% 1.63/1.85 % From the command line: assign(max_seconds, 300).
% 1.63/1.85
% 1.63/1.85 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.63/1.85
% 1.63/1.85 % Formulas that are not ordinary clauses:
% 1.63/1.85 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].
% 1.63/1.85 2 (all X_b (lattice(X_b) -> ti(fun(fun(X_b,bool),X_b),big_lattice_Inf_fin(X_b)) = big_lattice_Inf_fin(X_b))) # label(tsy_c_Big__Operators_Olattice__class_OInf__fin_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 3 (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].
% 1.63/1.85 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].
% 1.63/1.85 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].
% 1.63/1.85 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].
% 1.63/1.85 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].
% 1.63/1.85 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].
% 1.63/1.85 9 (all X_b ti(fun(fun(X_b,bool),nat),finite_card(X_b)) = finite_card(X_b)) # label(tsy_c_Finite__Set_Ocard_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 10 (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].
% 1.63/1.85 11 (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].
% 1.63/1.85 12 (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].
% 1.63/1.85 13 (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].
% 1.63/1.85 14 (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].
% 1.63/1.85 15 (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].
% 1.63/1.85 16 (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].
% 1.63/1.85 17 (all X_b (minus(X_b) -> ti(fun(X_b,fun(X_b,X_b)),minus_minus(X_b)) = minus_minus(X_b))) # label(tsy_c_Groups_Ominus__class_Ominus_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 18 (all X_b (one(X_b) -> ti(X_b,one_one(X_b)) = one_one(X_b))) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 19 (all X_b (cancel_semigroup_add(X_b) -> ti(fun(X_b,fun(X_b,X_b)),plus_plus(X_b)) = plus_plus(X_b))) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 20 (all X_a (ab_semigroup_add(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 21 (all X_a (monoid_add(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_2_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 22 (all X_c (ab_semigroup_mult(X_c) -> ti(fun(X_c,fun(X_c,X_c)),times_times(X_c)) = times_times(X_c))) # label(tsy_c_Groups_Otimes__class_Otimes_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 23 (all X_b (zero(X_b) -> ti(X_b,zero_zero(X_b)) = zero_zero(X_b))) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 24 (all X_b ti(fun(fun(X_b,bool),X_b),the_1(X_b)) = the_1(X_b)) # label(tsy_c_HOL_OThe_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 25 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 26 (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].
% 1.63/1.85 27 (all X_b ti(fun(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool)),hoare_2027193591valids(X_b)) = hoare_2027193591valids(X_b)) # label(tsy_c_Hoare__Mirabelle__nrugjuseim_Ohoare__valids_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 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].
% 1.63/1.85 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].
% 1.63/1.85 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].
% 1.63/1.85 31 (all X_b ti(fun(fun(X_b,nat),fun(hoare_1656922687triple(X_b),nat)),hoare_983366810e_size(X_b)) = hoare_983366810e_size(X_b)) # label(tsy_c_Hoare__Mirabelle__nrugjuseim_Otriple_Otriple__size_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 32 (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].
% 1.63/1.85 33 (all X_a ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a)) = if(X_a)) # label(tsy_c_If_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 34 (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].
% 1.63/1.85 35 (all X_a (semilattice_sup(X_a) -> ti(fun(X_a,fun(X_a,X_a)),semilattice_sup_sup(X_a)) = semilattice_sup_sup(X_a))) # label(tsy_c_Lattices_Osemilattice__sup__class_Osup_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 36 (all X_b ti(fun(X_b,fun(fun(nat,X_b),fun(nat,X_b))),nat_case(X_b)) = nat_case(X_b)) # label(tsy_c_Nat_Onat_Onat__case_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 37 (all X_b ti(fun(hoare_1656922687triple(X_b),nat),size_size(hoare_1656922687triple(X_b))) = size_size(hoare_1656922687triple(X_b))) # label(tsy_c_Nat_Osize__class_Osize_1_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 38 (all X_c (bot(X_c) -> ti(X_c,bot_bot(X_c)) = bot_bot(X_c))) # label(tsy_c_Orderings_Obot__class_Obot_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 39 (all X_b ti(fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),powp(X_b)) = powp(X_b)) # label(tsy_c_Predicate_OPowp_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 40 (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].
% 1.63/1.85 41 (all X_c all X_b ti(fun(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool))),image(X_c,X_b)) = image(X_c,X_b)) # label(tsy_c_Set_Oimage_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 42 (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].
% 1.63/1.85 43 (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].
% 1.63/1.85 44 (all X_b all X_c ti(fun(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool))),sum_Plus(X_b,X_c)) = sum_Plus(X_b,X_c)) # label(tsy_c_Sum__Type_OPlus_res) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 45 (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].
% 1.63/1.85 46 (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].
% 1.63/1.85 47 (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].
% 1.63/1.85 48 (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].
% 1.63/1.85 49 (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].
% 1.63/1.85 50 (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].
% 1.63/1.85 51 (all X_b all Fun1 all Com all Fun2 all Fun1_2 all Com_1 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),Com),Fun2) = 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_1),Fun2_2) <-> Fun1 = Fun1_2 & Com = Com_1 & Fun2 = Fun2_2)) # label(fact_0_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 52 (all X_b all Ga 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_2027193591valids(X_b),Ga),Ts)) <-> (all N ((all X (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),bool),member(hoare_1656922687triple(X_b)),X),Ga)) -> hBOOL(hAPP(hoare_1656922687triple(X_b),bool,hAPP(nat,fun(hoare_1656922687triple(X_b),bool),hoare_920331057_valid(X_b),N),X)))) -> (all X (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),bool),member(hoare_1656922687triple(X_b)),X),Ts)) -> hBOOL(hAPP(hoare_1656922687triple(X_b),bool,hAPP(nat,fun(hoare_1656922687triple(X_b),bool),hoare_920331057_valid(X_b),N),X)))))))) # label(fact_1_hoare__valids__def) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 53 (all X_b all Ga all Pa all Qa all Procsa (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),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),semilattice_sup_sup(fun(hoare_1656922687triple(X_b),bool)),Ga),hAPP(fun(pname,bool),fun(hoare_1656922687triple(X_b),bool),hAPP(fun(pname,hoare_1656922687triple(X_b)),fun(fun(pname,bool),fun(hoare_1656922687triple(X_b),bool)),image(pname,hoare_1656922687triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_1656922687triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_1656922687triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),pname),hoare_246368825triple(X_b)),Pa)),body)),Qa)),Procsa))),hAPP(fun(pname,bool),fun(hoare_1656922687triple(X_b),bool),hAPP(fun(pname,hoare_1656922687triple(X_b)),fun(fun(pname,bool),fun(hoare_1656922687triple(X_b),bool)),image(pname,hoare_1656922687triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_1656922687triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_1656922687triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),pname),hoare_246368825triple(X_b)),Pa)),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body_1))),Qa)),Procsa))) -> hBOOL(hAPP(fun(hoare_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(pname,bool),fun(hoare_1656922687triple(X_b),bool),hAPP(fun(pname,hoare_1656922687triple(X_b)),fun(fun(pname,bool),fun(hoare_1656922687triple(X_b),bool)),image(pname,hoare_1656922687triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_1656922687triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_1656922687triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),pname),hoare_246368825triple(X_b)),Pa)),body)),Qa)),Procsa))))) # label(fact_2_hoare__derivs_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 54 (all X_b all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))))) # label(fact_3_UnE) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 55 (all X_b all A_3 all B_2 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)),A_3),B_2),X_2)) -> (-hBOOL(hAPP(X_b,bool,A_3,X_2)) -> hBOOL(hAPP(X_b,bool,B_2,X_2))))) # label(fact_4_sup1E) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 56 (all X_b all A_3 all B_2 all X_2 ((-hBOOL(hAPP(X_b,bool,B_2,X_2)) -> hBOOL(hAPP(X_b,bool,A_3,X_2))) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2),X_2)))) # label(fact_5_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 57 (all X_b all A_3 all C_1 all B_2 ((-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))))) # label(fact_6_UnCI) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 58 (all X_b all X_c all A_3 all B_1 all F all X_2 (ti(X_b,B_1) = hAPP(X_c,X_b,F,X_2) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_1),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))))) # label(fact_7_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 59 (all X_c all X_b all F1 all Fun1 all Com all Fun2 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),Com),Fun2)) = hAPP(fun(X_c,fun(state,bool)),X_b,hAPP(com,fun(fun(X_c,fun(state,bool)),X_b),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b)),F1,Fun1),Com),Fun2)) # label(fact_8_triple_Orecs) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 60 (all X_c all X_b all F1 all Fun1 all Com all Fun2 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),Com),Fun2)) = hAPP(fun(X_c,fun(state,bool)),X_b,hAPP(com,fun(fun(X_c,fun(state,bool)),X_b),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b)),F1,Fun1),Com),Fun2)) # label(fact_9_triple_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 61 (all X_c all X_b all F all A_3 all B_2 hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_sup_sup(fun(X_c,bool)),A_3),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B_2))) # label(fact_10_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 62 (all X_b all X_c (lattice(X_c) -> (all F all G all X hAPP(X_b,X_c,hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),fun(X_b,X_c)),semilattice_sup_sup(fun(X_b,X_c)),F),G),X) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),semilattice_sup_sup(X_c),hAPP(X_b,X_c,F,X)),hAPP(X_b,X_c,G,X))))) # label(fact_11_sup__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 63 (all X_c all X_b (lattice(X_b) -> (all F all G all X_2 hAPP(X_c,X_b,hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),semilattice_sup_sup(fun(X_c,X_b)),F),G),X_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,G,X_2))))) # label(fact_12_sup__apply) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 64 (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_13_cut) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 65 (all X_a (semilattice_sup(X_a) -> (all X_1 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_1),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z))))) # label(fact_14_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 66 (all X_a (lattice(X_a) -> (all X_1 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_1),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z))))) # label(fact_15_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 67 (all X_a (semilattice_sup(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B),C))))) # label(fact_16_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 68 (all X_a (semilattice_sup(X_a) -> (all X_1 all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Z))))) # label(fact_17_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 69 (all X_a (lattice(X_a) -> (all X_1 all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Z))))) # label(fact_18_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 70 (all X_a (semilattice_sup(X_a) -> (all B all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B),C))))) # label(fact_19_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 71 (all X_a (semilattice_sup(X_a) -> (all X_1 all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)))) # label(fact_20_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 72 (all X_a (lattice(X_a) -> (all X_1 all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)))) # label(fact_21_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 73 (all X_a (semilattice_sup(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B)))) # label(fact_22_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 74 (all X_a (semilattice_sup(X_a) -> (all X_1 all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X_1)))) # label(fact_23_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 75 (all X_a (lattice(X_a) -> (all X_1 all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X_1)))) # label(fact_24_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 76 (all X_a (semilattice_sup(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B),A_1)))) # label(fact_25_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 77 (all X_a (semilattice_sup(X_a) -> (all X_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),X_1) = ti(X_a,X_1)))) # label(fact_26_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 78 (all X_a (semilattice_sup(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),A_1) = ti(X_a,A_1)))) # label(fact_27_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 79 (all X_c all X_b all B_1 all F all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> (ti(X_c,B_1) = hAPP(X_b,X_c,F,X_2) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B_1),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))))) # label(fact_28_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 80 (all X_c all X_b all F all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))))) # label(fact_29_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 81 (all X_b all X_c all Z_1 all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z_1),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) <-> (exists X (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X),A_3)) & ti(X_b,Z_1) = hAPP(X_c,X_b,F,X))))) # label(fact_30_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 82 (all X_b all A_3 all C_1 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))))) # label(fact_31_UnI2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 83 (all X_b all B_2 all C_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))))) # label(fact_32_UnI1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 84 (all X_b all A_3 all B_2 all X_2 (hBOOL(hAPP(X_b,bool,B_2,X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2),X_2)))) # label(fact_33_sup1I2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 85 (all X_b all B_2 all A_3 all X_2 (hBOOL(hAPP(X_b,bool,A_3,X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2),X_2)))) # label(fact_34_sup1I1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 86 (all X_b all Pa all A_3 all B_2 ((all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))) -> hBOOL(hAPP(X_b,bool,Pa,X)))) <-> (all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3)) -> hBOOL(hAPP(X_b,bool,Pa,X)))) & (all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),B_2)) -> hBOOL(hAPP(X_b,bool,Pa,X)))))) # label(fact_35_ball__Un) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 87 (all X_b all Pa all A_3 all B_2 ((exists X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))) & hBOOL(hAPP(X_b,bool,Pa,X)))) <-> (exists X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3)) & hBOOL(hAPP(X_b,bool,Pa,X)))) | (exists X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),B_2)) & hBOOL(hAPP(X_b,bool,Pa,X)))))) # label(fact_36_bex__Un) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 88 (all X_b all A_3 all B_2 all C_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),C_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_2))) # label(fact_37_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 89 (all X_b all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)))) # label(fact_38_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 90 (all X_b all A_3 all B_2 all C_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),C_2))) # label(fact_39_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 91 (all X_b all A_3 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)) # label(fact_40_Un__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 92 (all X_b all A_3 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),A_3)) # label(fact_41_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 93 (all X_b all A_3 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2)))) # label(fact_42_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 94 (all X_b all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),A_3) = ti(fun(X_b,bool),A_3)) # label(fact_43_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 95 (all X_b all Y_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),combi(X_b)),Y_3) = ti(fun(X_b,bool),Y_3)) # label(fact_44_image__ident) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 96 (all X_c all X_b all X_d all F all G all A_3 hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_d,bool),fun(X_c,bool),hAPP(fun(X_d,X_c),fun(fun(X_d,bool),fun(X_c,bool)),image(X_d,X_c),G),A_3)) = hAPP(fun(X_d,bool),fun(X_b,bool),hAPP(fun(X_d,X_b),fun(fun(X_d,bool),fun(X_b,bool)),image(X_d,X_b),hAPP(fun(X_d,X_c),fun(X_d,X_b),hAPP(fun(X_c,X_b),fun(fun(X_d,X_c),fun(X_d,X_b)),combb(X_c,X_b,X_d),F),G)),A_3)) # label(fact_45_image__image) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 97 (all X_b all R_2 all S_1 all X (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),R_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)),S_1)),X)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),R_2),S_1))))) # label(fact_46_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 98 (all X_b all Pa all Qa hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),Pa)),Qa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Qa))) # label(fact_47_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 99 (all X_b all X_c all B_1 all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_1),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) -> -(all X (ti(X_b,B_1) = hAPP(X_c,X_b,F,X) -> -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X),A_3)))))) # label(fact_48_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 100 (all X_b all N_1 all Pa all Pn_1 all Qa (hBOOL(hAPP(hoare_1656922687triple(X_b),bool,hAPP(nat,fun(hoare_1656922687triple(X_b),bool),hoare_920331057_valid(X_b),N_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),Pa),hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn_1))),Qa))) <-> hBOOL(hAPP(hoare_1656922687triple(X_b),bool,hAPP(nat,fun(hoare_1656922687triple(X_b),bool),hoare_920331057_valid(X_b),hAPP(nat,nat,suc,N_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),Pa),hAPP(pname,com,body,Pn_1)),Qa))))) # label(fact_49_Body__triple__valid__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 101 (all X_b all Y_1 -(all Fun1_1 all Com_2 all Fun2_1 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_1),Com_2),Fun2_1))) # label(fact_50_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 102 (all X_b all Pn_1 all Ga all Pa all Qa all Procsa (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),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),semilattice_sup_sup(fun(hoare_1656922687triple(X_b),bool)),Ga),hAPP(fun(pname,bool),fun(hoare_1656922687triple(X_b),bool),hAPP(fun(pname,hoare_1656922687triple(X_b)),fun(fun(pname,bool),fun(hoare_1656922687triple(X_b),bool)),image(pname,hoare_1656922687triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_1656922687triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_1656922687triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),pname),hoare_246368825triple(X_b)),Pa)),body)),Qa)),Procsa))),hAPP(fun(pname,bool),fun(hoare_1656922687triple(X_b),bool),hAPP(fun(pname,hoare_1656922687triple(X_b)),fun(fun(pname,bool),fun(hoare_1656922687triple(X_b),bool)),image(pname,hoare_1656922687triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_1656922687triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_1656922687triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),pname),hoare_246368825triple(X_b)),Pa)),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body_1))),Qa)),Procsa))) -> (hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),Pn_1),Procsa)) -> hBOOL(hAPP(fun(hoare_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(pname,fun(X_b,fun(state,bool)),Pa,Pn_1)),hAPP(pname,com,body,Pn_1)),hAPP(pname,fun(X_b,fun(state,bool)),Qa,Pn_1))),bot_bot(fun(hoare_1656922687triple(X_b),bool)))))))) # label(fact_51_Body1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 103 (all X_c all X_b all F all G all M_3 all N_3 (ti(fun(X_b,bool),M_3) = ti(fun(X_b,bool),N_3) -> ((all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),N_3)) -> hAPP(X_b,X_c,F,X) = hAPP(X_b,X_c,G,X))) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),M_3) = hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),G),N_3)))) # label(fact_52_image__cong) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 104 (all X_b all A_3 all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),powp(X_b),A_3),X)) <-> (all Xa (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Xa),X)) -> hBOOL(hAPP(X_b,bool,A_3,Xa)))))) # label(fact_53_Powp__def) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 105 (all X_b all Pa all Pn_1 all Qa hBOOL(hAPP(hoare_1656922687triple(X_b),bool,hAPP(nat,fun(hoare_1656922687triple(X_b),bool),hoare_920331057_valid(X_b),zero_zero(nat)),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(pname,com,body,Pn_1)),Qa)))) # label(fact_54_Body__triple__valid__0) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 106 (all Pname_3 all Pname_2 (hAPP(pname,com,body,Pname_3) = hAPP(pname,com,body,Pname_2) <-> ti(pname,Pname_3) = ti(pname,Pname_2))) # label(fact_55_com_Osimps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 107 (all Pn all S0 all S1_1 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn))),S0),S1_1)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(pname,com,body,Pn)),S0),S1_1)))) # label(fact_56_evalc_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 108 (all P all S_2 all S1_1 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(pname,com,body,P)),S_2),S1_1)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,P))),S_2),S1_1)))) # label(fact_57_evalc__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 109 (all X_a (lattice(X_a) -> (all X_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),X_1) = ti(X_a,X_1)))) # label(fact_58_Sup__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 110 (all X_b all A_2 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),bot_bot(fun(X_b,bool))))) # label(fact_59_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 111 (all X_b all A_2 all B_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_1),A_3))) -> (ti(X_b,A_2) != ti(X_b,B_1) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))))) # label(fact_60_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.85 112 (all X_b all B_1 all A_2 all B_2 ((-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2)) -> ti(X_b,A_2) = ti(X_b,B_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_1),B_2))))) # label(fact_61_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 113 (all X_b all A_2 all A_3 bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) # label(fact_62_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 114 (all X_b all A_2 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3) != bot_bot(fun(X_b,bool))) # label(fact_63_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 115 (all X_b all X (hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),bot_bot(fun(X_b,bool)))))) # label(fact_64_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 116 (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_65_empty__def) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 117 (all X_b all A_2 all B_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)))) # label(fact_66_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 118 (all X_b all A_3 ((all X -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3))) <-> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)))) # label(fact_67_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 119 (all X_b all A_2 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) # label(fact_68_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 120 (all X_b all A_3 ((exists X hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3))) <-> ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)))) # label(fact_69_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 121 (all X_b all A_2 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) # label(fact_70_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 122 (all X_b all Pa all A_2 ((hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) & (-hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Pa)) = bot_bot(fun(X_b,bool))))) # label(fact_71_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 123 (all X_b all Pa all A_2 ((hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) & (-hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Pa)) = bot_bot(fun(X_b,bool))))) # label(fact_72_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 124 (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 -hBOOL(hAPP(X_b,bool,Pa,X))))) # label(fact_73_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 125 (all X_b all X_c all F all G ((all X hAPP(X_b,X_c,F,X) = hAPP(X_b,X_c,G,X)) -> ti(fun(X_b,X_c),F) = ti(fun(X_b,X_c),G))) # label(fact_74_ext) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 126 (all X_b all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) <-> hBOOL(hAPP(X_b,bool,A_3,X_2)))) # label(fact_75_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 127 (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_76_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 128 (all X_b all C_1 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),bot_bot(fun(X_b,bool))))) # label(fact_77_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 129 (all X_b all A_2 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2)))) # label(fact_78_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 130 (all X_b all A_2 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_2),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fimplies),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)))),Pa))) # label(fact_79_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 131 (all X_b all B_1 all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) <-> ti(X_b,B_1) = ti(X_b,A_2))) # label(fact_80_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 132 (all X_b all X_2 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) # label(fact_81_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 133 (all X_b all X_2 all Y_1 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),A_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3))) # label(fact_82_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 134 (all X_b all A_2 all B_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_1),A_3))) <-> ti(X_b,A_2) = ti(X_b,B_1) | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)))) # label(fact_83_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 135 (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 -hBOOL(hAPP(X_b,bool,Pa,X))))) # label(fact_84_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 136 (all X_b all A_2 all B_1 all C_1 all D_1 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_1),bot_bot(fun(X_b,bool)))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),D_1),bot_bot(fun(X_b,bool)))) <-> ti(X_b,A_2) = ti(X_b,C_1) & ti(X_b,B_1) = ti(X_b,D_1) | ti(X_b,A_2) = ti(X_b,D_1) & ti(X_b,B_1) = ti(X_b,C_1))) # label(fact_85_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 137 (all X_b all Y_1 all A_3 all X_2 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),A_3),X_2)) <-> ti(X_b,Y_1) = ti(X_b,X_2) | hBOOL(hAPP(X_b,bool,A_3,X_2)))) # label(fact_86_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 138 (all X_b all B_2 all X_2 all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),B_2) <-> ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2))))) # label(fact_87_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 139 (all X_b all A_2 all A_3 (ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)))) # label(fact_88_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 140 (all X_b all B_1 all A_2 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_1),B_2))))) # label(fact_89_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 141 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3) = ti(fun(X_b,bool),A_3))) # label(fact_90_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 142 (all X_b all B_1 all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) -> ti(X_b,B_1) = ti(X_b,A_2))) # label(fact_91_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 143 (all X_b all A_2 all B_1 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_1),bot_bot(fun(X_b,bool))) -> ti(X_b,A_2) = ti(X_b,B_1))) # label(fact_92_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 144 (all U_1 all C all S_2 all T_4 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C),S_2),T_4)) -> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C),S_2),U_1)) -> U_1 = T_4))) # label(fact_93_com__det) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 145 (all X_b all A_2 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))),A_3)) # label(fact_94_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 146 (all X_b all X 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),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))),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_95_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 147 (all X_b all Ga all T_3 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),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_3),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_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),Ts)))) # label(fact_96_derivs__insertD) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 148 (all X_b all Ts all Ga all T_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)),T_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),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_3),Ts)))))) # label(fact_97_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 149 (all X_c all X_b all C_1 all A_3 ((ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C_1)),A_3) = bot_bot(fun(X_c,bool))) & (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C_1)),A_3) = hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),C_1),bot_bot(fun(X_c,bool)))))) # label(fact_98_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 150 (all X_c all X_b all C_1 all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C_1)),A_3) = hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),C_1),bot_bot(fun(X_c,bool))))) # label(fact_99_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 151 (all X_c all X_b all F all A_2 all B_2 hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),A_2),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),hAPP(X_c,X_b,F,A_2)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B_2))) # label(fact_100_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 152 (all X_c all X_b all F all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)) = hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) # label(fact_101_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 153 (all X_b all A_3 all A_2 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))) # label(fact_102_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 154 (all X_b all A_2 all B_2 all C_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)),C_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_2))) # label(fact_103_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 155 (all X_b all X_c all F all A_3 (bot_bot(fun(X_b,bool)) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3) <-> ti(fun(X_c,bool),A_3) = bot_bot(fun(X_c,bool)))) # label(fact_104_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 156 (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_105_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 157 (all X_c all X_b all F all A_3 (hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3) = bot_bot(fun(X_b,bool)) <-> ti(fun(X_c,bool),A_3) = bot_bot(fun(X_c,bool)))) # label(fact_106_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 158 (all X_b all Pa all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),bot_bot(fun(X_b,bool)))) -> hBOOL(hAPP(X_b,bool,Pa,X)))) # label(fact_107_ball__empty) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 159 (all X_b all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),bot_bot(fun(X_b,bool))),B_2) = ti(fun(X_b,bool),B_2)) # label(fact_108_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 160 (all X_b all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool))) = ti(fun(X_b,bool),A_3)) # label(fact_109_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 161 (all X_b all A_3 all B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2) = bot_bot(fun(X_b,bool)) <-> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) & ti(fun(X_b,bool),B_2) = bot_bot(fun(X_b,bool)))) # label(fact_110_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 162 (all X_b all Ga all Pa all C_1 all Qa all C_2 ((hBOOL(C_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),C_1),Qa)),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_2)),C_1),Qa)),bot_bot(fun(hoare_1656922687triple(X_b),bool))))))) # label(fact_111_constant) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 163 (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_112_empty) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 164 (all X_a (bounded_lattice_bot(X_a) -> (all X_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),bot_bot(X_a)),X_1) = ti(X_a,X_1)))) # label(fact_113_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 165 (all X_a (bounded_lattice_bot(X_a) -> (all X_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),bot_bot(X_a)) = ti(X_a,X_1)))) # label(fact_114_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 166 (all X_b (bounded_lattice_bot(X_b) -> (all X_2 all Y_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),Y_1) = bot_bot(X_b) <-> ti(X_b,X_2) = bot_bot(X_b) & ti(X_b,Y_1) = bot_bot(X_b))))) # label(fact_115_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 167 (all X_a all N_2 all T_4 (hBOOL(hAPP(hoare_1656922687triple(X_a),bool,hAPP(nat,fun(hoare_1656922687triple(X_a),bool),hoare_920331057_valid(X_a),hAPP(nat,nat,suc,N_2)),T_4)) -> hBOOL(hAPP(hoare_1656922687triple(X_a),bool,hAPP(nat,fun(hoare_1656922687triple(X_a),bool),hoare_920331057_valid(X_a),N_2),T_4)))) # label(fact_116_triple__valid__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 168 (all X_b all A_2 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),B_2)) # label(fact_117_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 169 (all X_b all Ga all Pa all Pn_1 all Qa (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(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn_1))),Qa)),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(pname,com,body,Pn_1)),Qa)),bot_bot(fun(hoare_1656922687triple(X_b),bool))))))) # label(fact_118_weak__Body) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 170 (all X_b all Pa all Pn_1 all Qa 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),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(pname,com,body,Pn_1)),Qa)),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(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn_1))),Qa)),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(pname,com,body,Pn_1)),Qa)),bot_bot(fun(hoare_1656922687triple(X_b),bool))))))) # label(fact_119_BodyN) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 171 (all X_b all N_1 all Ts ((all X (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),bool),member(hoare_1656922687triple(X_b)),X),Ts)) -> hBOOL(hAPP(hoare_1656922687triple(X_b),bool,hAPP(nat,fun(hoare_1656922687triple(X_b),bool),hoare_920331057_valid(X_b),hAPP(nat,nat,suc,N_1)),X)))) -> (all X (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),bool),member(hoare_1656922687triple(X_b)),X),Ts)) -> hBOOL(hAPP(hoare_1656922687triple(X_b),bool,hAPP(nat,fun(hoare_1656922687triple(X_b),bool),hoare_920331057_valid(X_b),N_1),X)))))) # label(fact_120_triples__valid__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 172 (all X_b all Ga all C_1 all Qa all Pa ((all Z_3 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_3),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),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_3))),C_1),hAPP(fun(state,bool),fun(X_b,fun(state,bool)),combk(fun(state,bool),X_b),hAPP(X_b,fun(state,bool),Qa,Z_3)))),bot_bot(fun(hoare_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),C_1),Qa)),bot_bot(fun(hoare_1656922687triple(X_b),bool))))))) # label(fact_121_escape) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 173 (all X_b all Pa all Ga all P_1 all C_1 all Qa (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),C_1),Qa)),bot_bot(fun(hoare_1656922687triple(X_b),bool))))) -> ((all Z_3 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_3),S_3)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_3),S_3)))) -> hBOOL(hAPP(fun(hoare_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),C_1),Qa)),bot_bot(fun(hoare_1656922687triple(X_b),bool)))))))) # label(fact_122_conseq1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 174 (all X_b all Qa all Ga all Pa all C_1 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),C_1),Q_1)),bot_bot(fun(hoare_1656922687triple(X_b),bool))))) -> ((all Z_3 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_3),S_3)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Qa,Z_3),S_3)))) -> hBOOL(hAPP(fun(hoare_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),C_1),Qa)),bot_bot(fun(hoare_1656922687triple(X_b),bool)))))))) # label(fact_123_conseq2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 175 (all X_b all Fa all Fun1 all Com all Fun2 hAPP(hoare_1656922687triple(X_b),nat,hAPP(fun(X_b,nat),fun(hoare_1656922687triple(X_b),nat),hoare_983366810e_size(X_b),Fa),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),Fun2)) = zero_zero(nat)) # label(fact_124_triple_Osize_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 176 (all C_1 hAPP(com,hoare_1656922687triple(state),hoare_Mirabelle_MGT,C_1) = 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)),C_1),hAPP(com,fun(state,fun(state,bool)),evalc,C_1))) # label(fact_125_MGT__def) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 177 (all X_b all Fun1 all Com all Fun2 hAPP(hoare_1656922687triple(X_b),nat,size_size(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),Fun1),Com),Fun2)) = zero_zero(nat)) # label(fact_126_triple_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 178 (all X_b all Qa all Pa all Ga all P_1 all C_1 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_1),C_1),Q_1)),bot_bot(fun(hoare_1656922687triple(X_b),bool))))) -> ((all Z_3 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_3),S_3)) -> (all S_4 ((all Z_4 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_4),S_3)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_4),S_4)))) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Qa,Z_3),S_4)))))) -> hBOOL(hAPP(fun(hoare_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),C_1),Qa)),bot_bot(fun(hoare_1656922687triple(X_b),bool)))))))) # label(fact_127_conseq12) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 179 (all X_b all X_2 hAPP(fun(X_b,bool),X_b,the_elem(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))) = ti(X_b,X_2)) # label(fact_128_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 180 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_129_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 181 (all Nat_4 zero_zero(nat) != hAPP(nat,nat,suc,Nat_4)) # label(fact_130_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 182 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_131_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 183 (all Nat_3 hAPP(nat,nat,suc,Nat_3) != zero_zero(nat)) # label(fact_132_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 184 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_133_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 185 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_134_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 186 (all X_b all X_c (bot(X_c) -> (all X hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X) = bot_bot(X_c)))) # label(fact_135_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 187 (all X_1 all Y (hAPP(nat,nat,suc,X_1) = hAPP(nat,nat,suc,Y) -> X_1 = Y)) # label(fact_137_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 188 (all Nat all Nat_2 (hAPP(nat,nat,suc,Nat) = hAPP(nat,nat,suc,Nat_2) <-> Nat = Nat_2)) # label(fact_138_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 189 (all N_2 hAPP(nat,nat,suc,N_2) != N_2) # label(fact_139_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 190 (all N_2 N_2 != hAPP(nat,nat,suc,N_2)) # label(fact_140_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 191 (all X_c all X_b (bot(X_b) -> (all X_2 hAPP(X_c,X_b,bot_bot(fun(X_c,X_b)),X_2) = bot_bot(X_b)))) # label(fact_141_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 192 (all Y (Y != zero_zero(nat) -> -(all Nat_1 Y != hAPP(nat,nat,suc,Nat_1)))) # label(fact_142_nat_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 193 (all Pa all K (hBOOL(hAPP(nat,bool,Pa,K)) -> ((all N (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N))) -> hBOOL(hAPP(nat,bool,Pa,N)))) -> hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))))) # label(fact_143_zero__induct) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 194 (all N_1 all Pa (hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))) -> ((all N (hBOOL(hAPP(nat,bool,Pa,N)) -> hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N))))) -> hBOOL(hAPP(nat,bool,Pa,N_1))))) # label(fact_144_nat__induct) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 195 (all N_2 (N_2 != zero_zero(nat) -> (exists M_2 N_2 = hAPP(nat,nat,suc,M_2)))) # label(fact_145_not0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 196 (all Pn all S0 all N_2 all S1_1 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn))),S0),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,hAPP(pname,com,body,Pn)),S0),hAPP(nat,nat,suc,N_2)),S1_1)))) # label(fact_146_evaln_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 197 (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_147_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 198 (all S_2 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_2),N_2),T_4)) -> T_4 = S_2)) # label(fact_148_evaln__elim__cases_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 199 (all S_2 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_2),N_2),S_2))) # label(fact_149_evaln_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 200 (all S_2 hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,skip),S_2),S_2))) # label(fact_150_evalc_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 201 (all S_2 all T_4 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,skip),S_2),T_4)) -> T_4 = S_2)) # label(fact_151_evalc__elim__cases_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 202 (all C all S_2 all N_2 all S_5 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C),S_2),N_2),S_5)) -> hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C),S_2),hAPP(nat,nat,suc,N_2)),S_5)))) # label(fact_152_evaln__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 203 (all C_1 all S all T_3 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S),T_3)) <-> (exists N hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C_1),S),N),T_3))))) # label(fact_153_eval__eq) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 204 (all C all S_2 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),S_2),N_2),T_4)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C),S_2),T_4)))) # label(fact_154_evaln__evalc) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 205 (all Pname_1 hAPP(pname,com,body,Pname_1) != skip) # label(fact_155_com_Osimps_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 206 (all Pname_1 skip != hAPP(pname,com,body,Pname_1)) # label(fact_156_com_Osimps_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 207 (all X_b all N_1 all Pa all C_1 all Qa (hBOOL(hAPP(hoare_1656922687triple(X_b),bool,hAPP(nat,fun(hoare_1656922687triple(X_b),bool),hoare_920331057_valid(X_b),N_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),Pa),C_1),Qa))) <-> (all Z_3 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_3),S_3)) -> (all S_4 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C_1),S_3),N_1),S_4)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Qa,Z_3),S_4)))))))) # label(fact_157_triple__valid__def2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 208 (all P all S_2 all N_2 all S1_1 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(pname,com,body,P)),S_2),N_2),S1_1)) -> -(all N (N_2 = hAPP(nat,nat,suc,N) -> -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,P))),S_2),N),S1_1)))))) # label(fact_158_evaln__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 209 (all C all S_2 all T_4 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C),S_2),T_4)) -> (exists N hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C),S_2),N),T_4))))) # label(fact_159_evalc__evaln) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 210 (all X_b all Ga all Pa all B_1 all C_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),hAPP(fun(state,bool),fun(X_b,fun(state,bool)),hAPP(fun(X_b,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(X_b,fun(state,bool))),combc(X_b,fun(state,bool),fun(state,bool)),hAPP(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),X_b),combs(state,bool,bool)),hAPP(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),Pa))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),B_1))),hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),Pa)),bot_bot(fun(hoare_1656922687triple(X_b),bool)))))) # label(fact_160_LoopF) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 211 (all X_b all D_1 all R_2 all Ga all Pa all C_1 all Qa (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),C_1),Qa)),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),Qa),D_1),R_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),hAPP(com,com,hAPP(com,fun(com,com),semi,C_1),D_1)),R_2)),bot_bot(fun(hoare_1656922687triple(X_b),bool)))))))) # label(fact_161_Comp) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 212 (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_1(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),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_162_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 213 (all X_c all X_b all Pa all Qa all Ga all P_1 all C0 all Q_1 all U (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),U)) -> ((all P_2 (hBOOL(hAPP(fun(hoare_1656922687triple(X_c),bool),bool,hAPP(fun(hoare_1656922687triple(X_c),bool),fun(fun(hoare_1656922687triple(X_c),bool),bool),hoare_279057269derivs(X_c),Ga),hAPP(fun(hoare_1656922687triple(X_c),bool),fun(hoare_1656922687triple(X_c),bool),hAPP(hoare_1656922687triple(X_c),fun(fun(hoare_1656922687triple(X_c),bool),fun(hoare_1656922687triple(X_c),bool)),insert(hoare_1656922687triple(X_c)),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),hAPP(X_b,fun(X_c,fun(state,bool)),P_1,P_2)),hAPP(X_b,com,C0,P_2)),hAPP(X_b,fun(X_c,fun(state,bool)),Q_1,P_2))),bot_bot(fun(hoare_1656922687triple(X_c),bool))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_c),bool),bool,hAPP(fun(hoare_1656922687triple(X_c),bool),fun(fun(hoare_1656922687triple(X_c),bool),bool),hoare_279057269derivs(X_c),Ga),hAPP(fun(hoare_1656922687triple(X_c),bool),fun(hoare_1656922687triple(X_c),bool),hAPP(hoare_1656922687triple(X_c),fun(fun(hoare_1656922687triple(X_c),bool),fun(hoare_1656922687triple(X_c),bool)),insert(hoare_1656922687triple(X_c)),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),hAPP(X_b,fun(X_c,fun(state,bool)),Pa,P_2)),hAPP(X_b,com,C0,P_2)),hAPP(X_b,fun(X_c,fun(state,bool)),Qa,P_2))),bot_bot(fun(hoare_1656922687triple(X_c),bool))))))) -> (hBOOL(hAPP(fun(hoare_1656922687triple(X_c),bool),bool,hAPP(fun(hoare_1656922687triple(X_c),bool),fun(fun(hoare_1656922687triple(X_c),bool),bool),hoare_279057269derivs(X_c),Ga),hAPP(fun(X_b,bool),fun(hoare_1656922687triple(X_c),bool),hAPP(fun(X_b,hoare_1656922687triple(X_c)),fun(fun(X_b,bool),fun(hoare_1656922687triple(X_c),bool)),image(X_b,hoare_1656922687triple(X_c)),hAPP(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,hoare_1656922687triple(X_c)),hAPP(fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c))),fun(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,hoare_1656922687triple(X_c))),combs(X_b,fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c)),hAPP(fun(X_b,com),fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c))),hAPP(fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c)))),fun(fun(X_b,com),fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c)))),combs(X_b,com,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c))),hAPP(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c)))),hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c)))),fun(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c))))),combb(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c))),X_b),hoare_246368825triple(X_c)),P_1)),C0)),Q_1)),U))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_c),bool),bool,hAPP(fun(hoare_1656922687triple(X_c),bool),fun(fun(hoare_1656922687triple(X_c),bool),bool),hoare_279057269derivs(X_c),Ga),hAPP(fun(X_b,bool),fun(hoare_1656922687triple(X_c),bool),hAPP(fun(X_b,hoare_1656922687triple(X_c)),fun(fun(X_b,bool),fun(hoare_1656922687triple(X_c),bool)),image(X_b,hoare_1656922687triple(X_c)),hAPP(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,hoare_1656922687triple(X_c)),hAPP(fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c))),fun(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,hoare_1656922687triple(X_c))),combs(X_b,fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c)),hAPP(fun(X_b,com),fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c))),hAPP(fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c)))),fun(fun(X_b,com),fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c)))),combs(X_b,com,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c))),hAPP(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c)))),hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c)))),fun(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c))))),combb(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_1656922687triple(X_c))),X_b),hoare_246368825triple(X_c)),Pa)),C0)),Qa)),U))))))) # label(fact_163_finite__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 214 (all C_1 all N_1 all B_1 all S (-hBOOL(hAPP(state,bool,B_1,S)) -> hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S),N_1),S)))) # label(fact_164_evaln_OWhileFalse) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 215 (all S2_1 all C_1 all N_1 all S1 all B_1 all S0_1 (hBOOL(hAPP(state,bool,B_1,S0_1)) -> (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C_1),S0_1),N_1),S1)) -> (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S1),N_1),S2_1)) -> hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S0_1),N_1),S2_1)))))) # label(fact_165_evaln_OWhileTrue) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 216 (all S2_1 all C_1 all S1 all B_1 all S0_1 (hBOOL(hAPP(state,bool,B_1,S0_1)) -> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S0_1),S1)) -> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S1),S2_1)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S0_1),S2_1)))))) # label(fact_166_evalc_OWhileTrue) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 217 (all C_1 all B_1 all S (-hBOOL(hAPP(state,bool,B_1,S)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S),S)))) # label(fact_167_evalc_OWhileFalse) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 218 (all C1_1 all S2 all C0_1 all S0 all N_2 all S1_1 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C0_1),S0),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,C1_1),S1_1),N_2),S2)) -> hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),semi,C0_1),C1_1)),S0),N_2),S2))))) # label(fact_168_evaln_OSemi) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 219 (all C1_1 all S2 all C0_1 all S0 all S1_1 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C0_1),S0),S1_1)) -> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1_1),S1_1),S2)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),semi,C0_1),C1_1)),S0),S2))))) # label(fact_169_evalc_OSemi) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.86 220 (all Com1 all Com2 all Fun_1 all Com_1 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2) != hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1)) # label(fact_170_com_Osimps_I46_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 221 (all Fun_1 all Com_1 all Com1 all Com2 hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1) != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2)) # label(fact_171_com_Osimps_I47_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 222 (all Com1 all Com2 all Com1_3 all Com2_3 (hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2) = hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_3),Com2_3) <-> Com1 = Com1_3 & Com2 = Com2_3)) # label(fact_172_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 223 (all Fun all Com all Fun_1 all Com_1 (hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com) = hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1) <-> Fun = Fun_1 & Com = Com_1)) # label(fact_173_com_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 224 (all Pname_2 all Fun all Com hAPP(pname,com,body,Pname_2) != hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com)) # label(fact_174_com_Osimps_I59_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 225 (all Fun all Com all Pname_2 hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com) != hAPP(pname,com,body,Pname_2)) # label(fact_175_com_Osimps_I58_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 226 (all Fun_1 all Com_1 skip != hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1)) # label(fact_176_com_Osimps_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 227 (all Fun_1 all Com_1 hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1) != skip) # label(fact_177_com_Osimps_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 228 (all Pname_1 all Com1_1 all Com2_1 hAPP(pname,com,body,Pname_1) != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1)) # label(fact_178_com_Osimps_I49_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 229 (all Com1_1 all Com2_1 all Pname_1 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1) != hAPP(pname,com,body,Pname_1)) # label(fact_179_com_Osimps_I48_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 230 (all Com1_2 all Com2_2 skip != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2)) # label(fact_180_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 231 (all Com1_2 all Com2_2 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2) != skip) # label(fact_181_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 232 (all C1_1 all C2_1 all S_2 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_1),C2_1)),S_2),T_4)) -> -(all S1_2 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1_1),S_2),S1_2)) -> -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C2_1),S1_2),T_4)))))) # label(fact_182_evalc__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 233 (all C1_1 all C2_1 all S_2 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_1),C2_1)),S_2),N_2),T_4)) -> -(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,C1_1),S_2),N_2),S1_2)) -> -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2_1),S1_2),N_2),T_4)))))) # label(fact_183_evaln__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 234 (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_184_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 235 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3))))) # label(fact_185_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 236 (all X_b hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),bot_bot(fun(X_b,bool))))) # label(fact_186_finite_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 237 (all X_b all Qa 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),Qa))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),Pa)),Qa)))))) # label(fact_187_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 238 (all X_b (finite_finite(X_b) -> (all A_3 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))))) # label(fact_188_finite) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 239 (all X_b (finite_finite(X_b) -> (all A_3 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))))) # label(fact_189_finite__code) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 240 (all X_b all Pa all Qa (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),Pa)),Qa)))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Qa))))) # label(fact_190_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 241 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)))) # label(fact_191_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 242 (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_192_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 243 (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_193_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 244 (all X_b all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_2)) <-> ti(fun(X_b,bool),A_2) = bot_bot(fun(X_b,bool)) | (exists A_4 exists A_5 (ti(fun(X_b,bool),A_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_5),A_4) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_4)))))) # label(fact_194_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 245 (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 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),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X),F_2))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)))))) # label(fact_195_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 246 (all X_c all X_b all F all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) -> (exists X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3)) & -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))),hAPP(X_c,fun(X_b,bool),hAPP(fun(X_b,fun(X_c,bool)),fun(X_c,fun(X_b,bool)),combc(X_b,X_c,bool),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,bool)),hAPP(fun(X_c,fun(X_c,bool)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,bool))),combb(X_c,fun(X_c,bool),X_b),fequal(X_c)),F)),hAPP(X_b,X_c,F,X))))))))))) # label(fact_196_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 247 (all B_1 all C_1 all S all T_3 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S),T_3)) -> ((T_3 = S -> hBOOL(hAPP(state,bool,B_1,S))) -> -(hBOOL(hAPP(state,bool,B_1,S)) -> (all S1_2 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S),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,bool),fun(com,com),while,B_1),C_1)),S1_2),T_3)))))))) # label(fact_197_evalc__WHILE__case) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 248 (all B_1 all C_1 all S all N_1 all T_3 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S),N_1),T_3)) -> ((T_3 = S -> hBOOL(hAPP(state,bool,B_1,S))) -> -(hBOOL(hAPP(state,bool,B_1,S)) -> (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,C_1),S),N_1),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,bool),fun(com,com),while,B_1),C_1)),S1_2),N_1),T_3)))))))) # label(fact_198_evaln__WHILE__case) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 249 (all X_b all A_3 (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) <-> (exists X exists B_3 (ti(fun(X_b,bool),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X),B_3) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),B_3)))))) # label(fact_199_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 250 (all X_b all B_2 all A_3 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_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (ti(fun(X_b,bool),B_2) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_1,A_3)),hAPP(fun(X_b,bool),X_b,F_1,B_2)))))))) # label(fact_200_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 251 (all X_b all X_2 all A_3 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_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),hAPP(fun(X_b,bool),X_b,F_1,A_3)))))) # label(fact_201_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 252 (all X_c all X_b all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3) = hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,bool)),fun(fun(X_c,bool),fun(fun(X_b,bool),fun(X_c,bool))),hAPP(fun(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool))),fun(fun(X_b,fun(X_c,bool)),fun(fun(X_c,bool),fun(fun(X_b,bool),fun(X_c,bool)))),finite_fold_image(fun(X_c,bool),X_b),semilattice_sup_sup(fun(X_c,bool))),hAPP(fun(X_c,bool),fun(X_b,fun(X_c,bool)),hAPP(fun(X_b,fun(fun(X_c,bool),fun(X_c,bool))),fun(fun(X_c,bool),fun(X_b,fun(X_c,bool))),combc(X_b,fun(X_c,bool),fun(X_c,bool)),hAPP(fun(X_b,X_c),fun(X_b,fun(fun(X_c,bool),fun(X_c,bool))),hAPP(fun(X_c,fun(fun(X_c,bool),fun(X_c,bool))),fun(fun(X_b,X_c),fun(X_b,fun(fun(X_c,bool),fun(X_c,bool)))),combb(X_c,fun(fun(X_c,bool),fun(X_c,bool)),X_b),insert(X_c)),F)),bot_bot(fun(X_c,bool)))),bot_bot(fun(X_c,bool))),A_3))) # label(fact_202_image__eq__fold__image) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 253 (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 hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X),bot_bot(fun(X_b,bool)))))) -> ((all X 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),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X),F_2)))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1))))))) # label(fact_203_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 254 (all X_b all X_2 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_2),X_2) = ti(X_b,X_2))) # label(fact_204_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 255 (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_205_fold__image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 256 (all X_b all X_2 all A_3 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_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),hAPP(fun(X_b,bool),X_b,F_1,A_3)) = hAPP(fun(X_b,bool),X_b,F_1,A_3))))) # label(fact_206_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 257 (all X_b all N_3 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 all Y_2 hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X),Y_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_b,X_b,H,X)),hAPP(X_b,X_b,H,Y_2))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (ti(fun(X_b,bool),N_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,F_1,N_3)) = hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_3))))))) # label(fact_207_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 258 (all X_c all X_b all G all A_3 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_3)) -> hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,G),A_3) = hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),F),G),Z_1),A_3)) & (-hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,G),A_3) = ti(X_b,Z_1)))) # label(fact_208_comm__monoid__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 259 (all X_b all X_2 all A_3 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_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),hAPP(fun(X_b,bool),X_b,F_1,A_3))))))) # label(fact_209_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 260 (all X_b all X_2 hAPP(fun(X_b,bool),X_b,the_1(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),X_2)) = ti(X_b,X_2)) # label(fact_210_the__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 261 (all X_b all A_2 hAPP(fun(X_b,bool),X_b,the_1(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)) = ti(X_b,A_2)) # label(fact_211_the__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 262 (all X_c all X_b all G all A_3 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_3)) -> hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,G),A_3) = ti(X_b,Z_1)))) # label(fact_212_comm__monoid__big_Oinfinite) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 263 (all X_b all X_2 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_2),bot_bot(fun(X_b,bool)))) = ti(X_b,X_2))) # label(fact_213_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 264 (all X_b all X_2 all Y_1 all Pa ((hBOOL(Pa) -> ti(X_b,X_2) = hAPP(fun(X_b,bool),X_b,the_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_2)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),Y_1))))) & (-hBOOL(Pa) -> ti(X_b,Y_1) = hAPP(fun(X_b,bool),X_b,the_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_2)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),Y_1))))))) # label(fact_214_If__def) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 265 (all X_b all Pa all A_2 (hBOOL(hAPP(X_b,bool,Pa,A_2)) -> ((all X (hBOOL(hAPP(X_b,bool,Pa,X)) -> ti(X_b,X) = ti(X_b,A_2))) -> hAPP(fun(X_b,bool),X_b,the_1(X_b),Pa) = ti(X_b,A_2)))) # label(fact_215_the__equality) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 266 (all X_b all A_3 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_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> ((all X 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),Y_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,F_1,A_3)),A_3))))))) # label(fact_216_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 267 (all X_c all X_b all H all G all A_3 all B_2 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_3) = ti(fun(X_c,bool),B_2) -> ((all X (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X),B_2)) -> hAPP(X_c,X_b,H,X) = hAPP(X_c,X_b,G,X))) -> hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,H),A_3) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),F_1,G),B_2))))) # label(fact_217_comm__monoid__big_OF__cong) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 268 (all X_b all Pa all A_2 (hBOOL(hAPP(X_b,bool,Pa,A_2)) -> ((all X (hBOOL(hAPP(X_b,bool,Pa,X)) -> ti(X_b,X) = ti(X_b,A_2))) -> hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the_1(X_b),Pa)))))) # label(fact_218_theI) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 269 (all X_b all A_2 all Pa ((exists X (hBOOL(hAPP(X_b,bool,Pa,X)) & (all Y_2 (hBOOL(hAPP(X_b,bool,Pa,Y_2)) -> ti(X_b,Y_2) = ti(X_b,X))))) -> (hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),X_b,the_1(X_b),Pa) = ti(X_b,A_2)))) # label(fact_219_the1__equality) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 270 (all X_b all Pa ((exists X (hBOOL(hAPP(X_b,bool,Pa,X)) & (all Y_2 (hBOOL(hAPP(X_b,bool,Pa,Y_2)) -> ti(X_b,Y_2) = ti(X_b,X))))) -> hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the_1(X_b),Pa))))) # label(fact_220_theI_H) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 271 (all C2_1 all S2 all N2 all T2 all C1_1 all S1_1 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_1),S1_1),N1),T1)) -> (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2_1),S2),N2),T2)) -> (exists N (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1_1),S1_1),N),T1)) & hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2_1),S2),N),T2))))))) # label(fact_221_evaln__max2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 272 (all X_c all X_b all B_2 all A_3 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_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2)) -> hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_sup_sup(fun(X_c,bool)),A_3),B_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,A_3)),hAPP(fun(X_c,bool),X_b,F_1,B_2)))))) # label(fact_222_folding__image__simple__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 273 (all X_c all X_b all X_2 all A_3 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_3)) -> hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_2),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_2)),hAPP(fun(X_c,bool),X_b,F_1,A_3))))) # label(fact_223_folding__image__simple__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 274 (all X_c all X_b all X_2 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_2),X_2) = ti(X_b,X_2))) # label(fact_224_folding__image__simple__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 275 (all X_c all X_b all X_2 all A_3 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_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_2)),hAPP(fun(X_c,bool),X_b,F_1,A_3)) = hAPP(fun(X_c,bool),X_b,F_1,A_3))))) # label(fact_225_folding__image__simple__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 276 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> (exists B_3 (ti(fun(X_b,bool),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_3) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_3)))))) # label(fact_226_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 277 (all X_b all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> -(all B_3 (ti(fun(X_b,bool),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),B_3) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_3)))))) # label(fact_227_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 278 (all X_b all A_3 ((all Y_2 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),A_3))) -> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)))) # label(fact_228_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 279 (all X_b (lattice(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (ti(fun(X_b,bool),B_2) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),B_2))))))))) # label(fact_229_Sup__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 280 (all X_b (lattice(X_b) -> (all X_2 hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))) = ti(X_b,X_2)))) # label(fact_230_Sup__fin_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 281 (all X_b (lattice(X_b) -> (all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)) = hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)))))) # label(fact_231_Sup__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 282 (all X_b (lattice(X_b) -> (all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)))))))) # label(fact_232_Sup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 283 (all X_b (lattice(X_b) -> (all X_2 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)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3))))))) # label(fact_233_Sup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 284 (all X_b (lattice(X_b) -> (all N_3 all H ((all X 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),Y_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(X_b,X_b,H,X)),hAPP(X_b,X_b,H,Y_2))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (ti(fun(X_b,bool),N_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),N_3)) = hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_3)))))))) # label(fact_234_Sup__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 285 (all X_b (lattice(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> ((all X 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),Y_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)),A_3)))))))) # label(fact_235_Sup__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 286 (all X_b (lattice(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),B_2)))))))) # label(fact_236_Sup__fin_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 287 (all X_b (lattice(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (ti(fun(X_b,bool),B_2) != bot_bot(fun(X_b,bool)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),B_2)))))))))) # label(fact_237_Sup__fin_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 288 (all X_b all B_2 all A_3 all X_2 (hBOOL(hAPP(X_b,bool,A_3,X_2)) -> (hBOOL(hAPP(X_b,bool,B_2,X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2),X_2))))) # label(fact_238_inf1I) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 289 (all X_b all B_2 all C_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))))) # label(fact_239_IntI) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 290 (all X_b all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))) -> -(hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))))) # label(fact_240_IntE) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 291 (all X_b all A_3 all B_2 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)),A_3),B_2),X_2)) -> -(hBOOL(hAPP(X_b,bool,A_3,X_2)) -> -hBOOL(hAPP(X_b,bool,B_2,X_2))))) # label(fact_241_inf1E) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 292 (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_242_finite__Int) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 293 (all X_a (bounded_lattice_bot(X_a) -> (all X_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),bot_bot(X_a)) = bot_bot(X_a)))) # label(fact_243_inf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 294 (all X_a (bounded_lattice_bot(X_a) -> (all X_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),bot_bot(X_a)),X_1) = bot_bot(X_a)))) # label(fact_244_inf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 295 (all X_a (distrib_lattice(X_a) -> (all Y all Z all X_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)),X_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Z),X_1))))) # label(fact_245_sup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 296 (all X_a (distrib_lattice(X_a) -> (all Y all Z all X_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)),X_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Z),X_1))))) # label(fact_246_inf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 297 (all X_a (distrib_lattice(X_a) -> (all X_1 all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Z))))) # label(fact_247_sup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 298 (all X_a (distrib_lattice(X_a) -> (all X_1 all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Z))))) # label(fact_248_inf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 299 (all X_a (lattice(X_a) -> (all X_1 all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)) = ti(X_a,X_1)))) # label(fact_249_sup__inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 300 (all X_a (lattice(X_a) -> (all X_1 all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)) = ti(X_a,X_1)))) # label(fact_250_inf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 301 (all X_b all A_3 all B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2) = bot_bot(fun(X_b,bool)) <-> (all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3)) -> (all Xa (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Xa),B_2)) -> ti(X_b,X) != ti(X_b,Xa))))))) # label(fact_251_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 302 (all X_b all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool))) = bot_bot(fun(X_b,bool))) # label(fact_252_Int__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 303 (all X_b all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),bot_bot(fun(X_b,bool))),B_2) = bot_bot(fun(X_b,bool))) # label(fact_253_Int__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 304 (all X_b all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),A_3) = ti(fun(X_b,bool),A_3)) # label(fact_254_Int__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 305 (all X_a (semilattice_inf(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),A_1) = ti(X_a,A_1)))) # label(fact_255_inf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 306 (all X_a (semilattice_inf(X_a) -> (all X_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),X_1) = ti(X_a,X_1)))) # label(fact_256_inf__idem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 307 (all X_b all X_c (lattice(X_c) -> (all F all G all X hAPP(X_b,X_c,hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),fun(X_b,X_c)),semilattice_inf_inf(fun(X_b,X_c)),F),G),X) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),semilattice_inf_inf(X_c),hAPP(X_b,X_c,F,X)),hAPP(X_b,X_c,G,X))))) # label(fact_257_inf__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 308 (all X_b all A_3 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2)))) # label(fact_258_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 309 (all X_b all A_3 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),A_3)) # label(fact_259_Int__commute) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 310 (all X_a (semilattice_inf(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B),A_1)))) # label(fact_260_inf_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 311 (all X_a (lattice(X_a) -> (all X_1 all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),X_1)))) # label(fact_261_inf__sup__aci_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 312 (all X_a (semilattice_inf(X_a) -> (all X_1 all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),X_1)))) # label(fact_262_inf__commute) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 313 (all X_b all A_3 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)) # label(fact_263_Int__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 314 (all X_a (semilattice_inf(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)))) # label(fact_264_inf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 315 (all X_a (lattice(X_a) -> (all X_1 all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)))) # label(fact_265_inf__sup__aci_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 316 (all X_a (semilattice_inf(X_a) -> (all X_1 all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)))) # label(fact_266_inf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 317 (all X_b all A_3 all B_2 all C_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),C_2))) # label(fact_267_Int__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 318 (all X_a (semilattice_inf(X_a) -> (all B all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B),C))))) # label(fact_268_inf_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 319 (all X_a (lattice(X_a) -> (all X_1 all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Z))))) # label(fact_269_inf__sup__aci_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 320 (all X_a (semilattice_inf(X_a) -> (all X_1 all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Z))))) # label(fact_270_inf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 321 (all X_b all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)))) # label(fact_271_Int__iff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 322 (all X_b all A_3 all B_2 all C_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),C_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_2))) # label(fact_272_Int__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 323 (all X_a (semilattice_inf(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B),C))))) # label(fact_273_inf_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 324 (all X_a (lattice(X_a) -> (all X_1 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_1),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))))) # label(fact_274_inf__sup__aci_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 325 (all X_a (semilattice_inf(X_a) -> (all X_1 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_1),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))))) # label(fact_275_inf__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 326 (all X_c all X_b (lattice(X_b) -> (all F all G all X_2 hAPP(X_c,X_b,hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),semilattice_inf_inf(fun(X_c,X_b)),F),G),X_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,G,X_2))))) # label(fact_276_inf__apply) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 327 (all X_b all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)))) # label(fact_277_IntD1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 328 (all X_b all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)))) # label(fact_278_IntD2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 329 (all X_b all A_3 all B_2 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)),A_3),B_2),X_2)) -> hBOOL(hAPP(X_b,bool,A_3,X_2)))) # label(fact_279_inf1D1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 330 (all X_b all A_3 all B_2 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)),A_3),B_2),X_2)) -> hBOOL(hAPP(X_b,bool,B_2,X_2)))) # label(fact_280_inf1D2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 331 (all X_b all Pa all Qa hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),Pa)),Qa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Qa))) # label(fact_281_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 332 (all X_b all X_2 all A_3 all Pa (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) & hBOOL(hAPP(X_b,bool,Pa,X_2)))) # label(fact_282_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 333 (all X_b all R_2 all S_1 all X (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),R_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)),S_1)),X)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),R_2),S_1))))) # label(fact_283_inf__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 334 (all X_a (lattice(X_a) -> (all X_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),X_1) = ti(X_a,X_1)))) # label(fact_284_Inf__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 335 (all X_b all A_3 all B_2 all C_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),C_2),A_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),C_2),A_3))) # label(fact_285_Un__Int__crazy) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 336 (all X_b all B_2 all C_2 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_2)),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),A_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),C_2),A_3))) # label(fact_286_Un__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.87 337 (all X_b all B_2 all C_2 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_2)),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),A_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),C_2),A_3))) # label(fact_287_Int__Un__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 338 (all X_b all A_3 all B_2 all C_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),C_2))) # label(fact_288_Un__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 339 (all X_b all A_3 all B_2 all C_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),C_2))) # label(fact_289_Int__Un__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 340 (all X_b all B_2 all A_2 all C_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),C_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)),C_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_2)))) # label(fact_290_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 341 (all X_b all B_2 all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))) # label(fact_291_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 342 (all X_b all B_2 all A_2 all C_2 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),C_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)),C_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_2))) # label(fact_292_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 343 (all X_b all B_2 all A_2 all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))) # label(fact_293_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 344 (all X_b all A_2 all A_3 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))) # label(fact_294_insert__inter__insert) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 345 (all X_b all B_2 all A_2 all C_2 ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),C_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)),C_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_2))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),C_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)),C_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_2)))) # label(fact_295_Int__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 346 (all X_b all B_2 all A_2 all A_3 ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))) # label(fact_296_Int__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 347 (all X_b (lattice(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),A_2),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)) = ti(X_b,A_2)))))) # label(fact_297_inf__Sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 348 (all X_c all X_b all Pa all F all G all S_1 hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,X_b)),combs(X_c,X_b,X_b),hAPP(fun(X_c,X_b),fun(X_c,fun(X_b,X_b)),hAPP(fun(X_c,fun(X_b,fun(X_b,X_b))),fun(fun(X_c,X_b),fun(X_c,fun(X_b,X_b))),combs(X_c,X_b,fun(X_b,X_b)),hAPP(fun(X_c,bool),fun(X_c,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_c,bool),fun(X_c,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_c),if(X_b)),Pa)),F)),G)),S_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_inf_inf(fun(X_c,bool)),S_1),hAPP(fun(X_c,bool),fun(X_c,bool),collect(X_c),Pa)))),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),G),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_inf_inf(fun(X_c,bool)),S_1),hAPP(fun(X_c,bool),fun(X_c,bool),collect(X_c),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(bool,bool),fun(fun(X_c,bool),fun(X_c,bool)),combb(bool,bool,X_c),fNot),Pa)))))) # label(fact_298_if__image__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 349 (all X_b all B_2 all A_3 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_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))),hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_1,A_3)),hAPP(fun(X_b,bool),X_b,F_1,B_2))))))) # label(fact_299_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 350 (all X_b all B_2 all A_3 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_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (ti(fun(X_b,bool),B_2) != bot_bot(fun(X_b,bool)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_1,A_3)),hAPP(fun(X_b,bool),X_b,F_1,B_2))))))))) # label(fact_300_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 351 (all X_a (lattice(X_a) -> (all X_1 all Y all Z ((all X all Y_2 all Z_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y_2),Z_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Z_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Z)))))) # label(fact_301_distrib__imp2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 352 (all X_a (lattice(X_a) -> (all X_1 all Y all Z ((all X all Y_2 all Z_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y_2),Z_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Z_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Z)))))) # label(fact_302_distrib__imp1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 353 (all X_c all X_b all B_2 all A_3 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_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2)) -> (hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_inf_inf(fun(X_c,bool)),A_3),B_2) = bot_bot(fun(X_c,bool)) -> hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_sup_sup(fun(X_c,bool)),A_3),B_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,A_3)),hAPP(fun(X_c,bool),X_b,F_1,B_2))))))) # label(fact_303_folding__image__simple_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 354 (all X_b (lattice(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (ti(fun(X_b,bool),B_2) != bot_bot(fun(X_b,bool)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),B_2)))))))))) # label(fact_304_Inf__fin_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 355 (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_305_folding__image__simple_Oempty) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 356 (all X_b (lattice(X_b) -> (all X_2 hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))) = ti(X_b,X_2)))) # label(fact_306_Inf__fin_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 357 (all X_b (lattice(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),A_2),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)) = ti(X_b,A_2)))))) # label(fact_307_sup__Inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 358 (all X_b (lattice(X_b) -> (all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)) = hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)))))) # label(fact_308_Inf__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 359 (all X_c all X_b all X_2 all A_3 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_3)) -> (-hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)) -> hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_2),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_2)),hAPP(fun(X_c,bool),X_b,F_1,A_3)))))) # label(fact_309_folding__image__simple_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 360 (all X_c all X_b all A_3 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_3)) -> hAPP(fun(X_c,bool),X_b,F_1,A_3) = hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),F),G),Z_1),A_3)))) # label(fact_310_folding__image__simple_Oeq__fold__g) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 361 (all X_b (lattice(X_b) -> (all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)))))))) # label(fact_311_Inf__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 362 (all X_b (lattice(X_b) -> (all X_2 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)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3))))))) # label(fact_312_Inf__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 363 (all X_b (lattice(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (ti(fun(X_b,bool),B_2) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),B_2))))))))) # label(fact_313_Inf__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 364 (all X_c all X_b all B_2 all A_3 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_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_sup_sup(fun(X_c,bool)),A_3),B_2))),hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_inf_inf(fun(X_c,bool)),A_3),B_2))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,A_3)),hAPP(fun(X_c,bool),X_b,F_1,B_2)))))) # label(fact_314_folding__image__simple_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 365 (all X_b (lattice(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),B_2)))))))) # label(fact_315_Inf__fin_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 366 (all X_b (lattice(X_b) -> (all N_3 all H ((all X all Y_2 hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X),Y_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(X_b,X_b,H,X)),hAPP(X_b,X_b,H,Y_2))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (ti(fun(X_b,bool),N_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),N_3)) = hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_3)))))))) # label(fact_316_Inf__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 367 (all X_b (lattice(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> ((all X 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_inf_inf(X_b),X),Y_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)),A_3)))))))) # label(fact_317_Inf__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 368 (all X_c all X_b all B_2 all A_3 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_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2)) -> ((all X (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_inf_inf(fun(X_c,bool)),A_3),B_2))) -> hAPP(X_c,X_b,G,X) = ti(X_b,Z_1))) -> hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_sup_sup(fun(X_c,bool)),A_3),B_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,A_3)),hAPP(fun(X_c,bool),X_b,F_1,B_2))))))) # label(fact_318_folding__image__simple_Ounion__inter__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 369 (all X_c all X_b all A_3 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_3)) -> ((all X (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X),A_3)) -> hAPP(X_c,X_b,G,X) = ti(X_b,Z_1))) -> hAPP(fun(X_c,bool),X_b,F_1,A_3) = ti(X_b,Z_1))))) # label(fact_319_folding__image__simple_Oneutral) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 370 (all X_b (lattice(X_b) -> (all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = ti(X_b,X_2)) & (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool))))))))))) # label(fact_320_Inf__fin_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 371 (all X_b (lattice(X_b) -> (all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3) = ti(X_b,X_2)) & (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))))))))))) # label(fact_321_Inf__fin_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 372 (all X_b all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) -> -(hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))))) # label(fact_322_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 373 (all X_b all B_2 all C_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)))))) # label(fact_323_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 374 (all X_b all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))))) # label(fact_324_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 375 (all X_b all A_3 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_2),A_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)) # label(fact_325_Un__Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 376 (all X_b all B_2 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_2),A_3)),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),A_3)) # label(fact_326_Un__Diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 377 (all X_b all A_3 all B_2 all C_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),C_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),C_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_2),C_2))) # label(fact_327_Un__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 378 (all X_b all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)))) # label(fact_328_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 379 (all X_b all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)))) # label(fact_329_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 380 (all X_c all X_b (minus(X_b) -> (all A_3 all B_2 all X_2 hAPP(X_c,X_b,hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),minus_minus(fun(X_c,X_b)),A_3),B_2),X_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_c,X_b,A_3,X_2)),hAPP(X_c,X_b,B_2,X_2))))) # label(fact_330_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 381 (all X_b all A_3 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)) # label(fact_331_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 382 (all X_b all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)))) # label(fact_332_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 383 (all X_b all A_3 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2))))) # label(fact_333_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 384 (all X_b all X_c (minus(X_c) -> (all A_3 all B_2 all X hAPP(X_b,X_c,hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),fun(X_b,X_c)),minus_minus(fun(X_b,X_c)),A_3),B_2),X) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(X_b,X_c,A_3,X)),hAPP(X_b,X_c,B_2,X))))) # label(fact_334_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 385 (all X_b all A_3 all X_2 all B_2 ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))))) # label(fact_335_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 386 (all X_b all A_3 all X_2 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) # label(fact_336_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 387 (all X_b all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),bot_bot(fun(X_b,bool))),A_3) = bot_bot(fun(X_b,bool))) # label(fact_337_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 388 (all X_b all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool))) = ti(fun(X_b,bool),A_3)) # label(fact_338_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 389 (all X_b all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),A_3) = bot_bot(fun(X_b,bool))) # label(fact_339_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 390 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))))) # label(fact_340_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 391 (all X_b all A_3 all C_2 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),C_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),C_2)),B_2)) # label(fact_341_Diff__Int2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 392 (all X_b all A_3 all B_2 all C_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),C_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),C_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_2))) # label(fact_342_Diff__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 393 (all X_b all A_3 all B_2 all C_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),C_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_2),C_2))) # label(fact_343_Int__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 394 (all X_b all C_2 all A_3 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),C_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),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_2),A_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),C_2),B_2))) # label(fact_344_Diff__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 395 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = ti(fun(X_b,bool),A_3))) # label(fact_345_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 396 (all X_b all X_2 all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))) = ti(fun(X_b,bool),A_3))) # label(fact_346_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 397 (all X_b all A_2 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) # label(fact_347_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 398 (all X_b all A_3 all A_2 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))),B_2)) # label(fact_348_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 399 (all X_b all A_3 all A_2 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) # label(fact_349_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 400 (all X_b all A_3 all A_2 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))))) # label(fact_350_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 401 (all X_b all A_3 all B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2) = ti(fun(X_b,bool),A_3))) # label(fact_351_Diff__triv) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 402 (all X_b all A_3 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_2),A_3)) = bot_bot(fun(X_b,bool))) # label(fact_352_Diff__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 403 (all X_b all A_3 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)) = ti(fun(X_b,bool),A_3)) # label(fact_353_Un__Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 404 (all X_b all A_3 all B_2 all C_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),C_2))) # label(fact_354_Diff__Un) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 405 (all X_b all A_3 all B_2 all C_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),C_2))) # label(fact_355_Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 406 (all X_c all X_b all X_2 all A_3 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_3)) -> hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_2),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_2)),hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_2),bot_bot(fun(X_c,bool))))))))) # label(fact_356_folding__image__simple_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 407 (all X_c all X_b all X_2 all A_3 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_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)) -> hAPP(fun(X_c,bool),X_b,F_1,A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_2)),hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_2),bot_bot(fun(X_c,bool)))))))))) # label(fact_357_folding__image__simple_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 408 (all X_b all X_2 all A_3 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_3)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = ti(X_b,X_2)) & (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))))))))) # label(fact_358_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 409 (all X_b all X_2 all A_3 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_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,A_3) = ti(X_b,X_2)) & (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool))))))))))) # label(fact_359_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 410 (all X_b (lattice(X_b) -> (all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3) = ti(X_b,X_2)) & (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))))))))))) # label(fact_360_Sup__fin_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 411 (all X_b (lattice(X_b) -> (all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = ti(X_b,X_2)) & (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool))))))))))) # label(fact_361_Sup__fin_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 412 (all X_b all Pa all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3)) -> ((all A_5 all A_4 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_4)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),A_4)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_4)) -> 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_4),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_5),bot_bot(fun(X_b,bool)))))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))))))) # label(fact_362_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 413 (all X_b (group_add(X_b) -> (all A_2 all B_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1) = zero_zero(X_b) <-> ti(X_b,A_2) = ti(X_b,B_1))))) # label(fact_363_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 414 (all X_b (ab_group_add(X_b) -> (all A_2 all B_1 (ti(X_b,A_2) = ti(X_b,B_1) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1) = zero_zero(X_b))))) # label(fact_364_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 415 (all M all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)) # label(fact_365_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 416 (all M all N_2 all K_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N_2)),hAPP(nat,nat,suc,K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)),K_1)) # label(fact_366_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 417 (all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N_2) = zero_zero(nat)) # label(fact_367_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 418 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat)) = M) # label(fact_368_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 419 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M) = zero_zero(nat)) # label(fact_369_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 420 (all M all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2) = zero_zero(nat) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),M) = zero_zero(nat) -> M = N_2))) # label(fact_370_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 421 (all X_b (zero(X_b) -> (all X_2 (zero_zero(X_b) = ti(X_b,X_2) <-> ti(X_b,X_2) = zero_zero(X_b))))) # label(fact_371_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 422 (all X_b (ab_group_add(X_b) -> (all A_2 all B_1 all C_1 all D_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1) -> (ti(X_b,A_2) = ti(X_b,B_1) <-> ti(X_b,C_1) = ti(X_b,D_1)))))) # label(fact_372_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 423 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_373_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 424 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_1) = zero_zero(X_a)))) # label(fact_374_diff__self) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 425 (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_375_comp__fun__idem__remove) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 426 (all I_1 all Pa all K (hBOOL(hAPP(nat,bool,Pa,K)) -> ((all N (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N))) -> hBOOL(hAPP(nat,bool,Pa,N)))) -> hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K),I_1)))))) # label(fact_376_zero__induct__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 427 (all I all J all K_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),K_1)),J)) # label(fact_377_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 428 (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_378_comp__fun__idem__sup) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 429 (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_379_comp__fun__idem__inf) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 430 (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_380_comp__fun__idem__insert) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 431 (all X_b all X_c all X_2 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_2),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_2),Z_1)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_2),Z_1))) # label(fact_381_comp__fun__idem_Ofun__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 432 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),combi(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1))) # label(fact_382_diff__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 433 (all X_b all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))))))) # label(fact_383_card__insert) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 434 (all X_b all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = zero_zero(nat))) # label(fact_384_card__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 435 (all X_b hAPP(fun(X_b,bool),nat,finite_card(X_b),bot_bot(fun(X_b,bool))) = zero_zero(nat)) # label(fact_385_card_Oempty) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 436 (all X_b all F1 all F2 hAPP(nat,X_b,hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(X_b,fun(fun(nat,X_b),fun(nat,X_b)),nat_case(X_b),F1),F2),zero_zero(nat)) = ti(X_b,F1)) # label(fact_386_nat__case__0) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 437 (all X_b all F1 all F2 all Nat hAPP(nat,X_b,hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(X_b,fun(fun(nat,X_b),fun(nat,X_b)),nat_case(X_b),F1),F2),hAPP(nat,nat,suc,Nat)) = hAPP(nat,X_b,F2,Nat)) # label(fact_387_nat__case__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 438 (all X_b all A_3 (hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = zero_zero(nat) <-> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) | -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)))) # label(fact_388_card__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 439 (all X_b all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))) # label(fact_389_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 440 (all X_b all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))) # label(fact_390_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.88 441 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))))) # label(fact_391_card__Diff__subset__Int) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 442 (all X_b all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))) # label(fact_392_card__Suc__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 443 (all X_b all A_3 all K (hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(nat,nat,suc,K) <-> (exists B_4 exists B_3 (ti(fun(X_b,bool),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_4),B_3) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_4),B_3)) & hAPP(fun(X_b,bool),nat,finite_card(X_b),B_3) = K & (K = zero_zero(nat) -> ti(fun(X_b,bool),B_3) = bot_bot(fun(X_b,bool))))))) # label(fact_393_card__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 444 (all X_b all A_3 all K (hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(nat,nat,suc,K) -> (exists B_4 exists B_3 (ti(fun(X_b,bool),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_4),B_3) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_4),B_3)) & hAPP(fun(X_b,bool),nat,finite_card(X_b),B_3) = K & (K = zero_zero(nat) -> ti(fun(X_b,bool),B_3) = bot_bot(fun(X_b,bool))))))) # label(fact_394_card__eq__SucD) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 445 (all X_b all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),one_one(nat))))) # label(fact_395_card__Diff__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 446 (all X_b all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),one_one(nat))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool))))) = hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))) # label(fact_396_card__Diff__singleton__if) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 447 (all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N_2)),one_one(nat)) = N_2) # label(fact_397_diff__Suc__1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 448 (all M all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,N_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N_2)) # label(fact_398_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 449 (all X_b (one(X_b) -> (all X_2 (one_one(X_b) = ti(X_b,X_2) <-> ti(X_b,X_2) = one_one(X_b))))) # label(fact_400_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 450 (all X_b all B_2 all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))),one_one(nat)))))) # label(fact_401_card__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 451 (all X_b all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (((exists X hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3))) -> one_one(nat) = zero_zero(nat)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = zero_zero(nat)))) # label(fact_402_card_Oneutral) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 452 (all X_a (zero_neq_one(X_a) -> zero_zero(X_a) != one_one(X_a))) # label(fact_403_zero__neq__one) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 453 (all X_a (zero_neq_one(X_a) -> one_one(X_a) != zero_zero(X_a))) # label(fact_404_one__neq__zero) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 454 (all X_b all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))))))) # label(fact_405_card_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 455 (all X_b all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool))))))))) # label(fact_406_card_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 456 (all N_2 hAPP(nat,nat,suc,N_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),one_one(nat))) # label(fact_407_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 457 (all N_2 hAPP(nat,nat,suc,N_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N_2)) # label(fact_408_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 458 (all M all K_1 all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)) # label(fact_409_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 459 (all K_1 all M all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)) # label(fact_410_diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 460 (all I all J all K_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K_1))) # label(fact_411_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 461 (all N_2 all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),M)),N_2) = M) # label(fact_412_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 462 (all M all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)),N_2) = M) # label(fact_413_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 463 (all N_2 all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),M)) = zero_zero(nat)) # label(fact_414_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 464 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),B) = ti(X_a,A_1)))) # label(fact_415_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 465 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),B) = ti(X_a,A_1)))) # label(fact_416_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 466 (all M all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),M)) # label(fact_417_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 467 (all X_1 all Y all Z hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X_1),Z))) # label(fact_418_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 468 (all M all N_2 all K_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K_1))) # label(fact_419_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 469 (all K all M_1 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1) <-> M_1 = N_1)) # label(fact_420_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 470 (all M_1 all K all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K) <-> M_1 = N_1)) # label(fact_421_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 471 (all M all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N_2))) # label(fact_422_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 472 (all M all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N_2) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2))) # label(fact_423_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 473 (all M all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N_2)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2))) # label(fact_424_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 474 (all M_1 all N_1 (hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1) <-> M_1 = hAPP(nat,nat,suc,zero_zero(nat)) & N_1 = zero_zero(nat) | M_1 = zero_zero(nat) & N_1 = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_425_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 475 (all M_1 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1) = hAPP(nat,nat,suc,zero_zero(nat)) <-> M_1 = hAPP(nat,nat,suc,zero_zero(nat)) & N_1 = zero_zero(nat) | M_1 = zero_zero(nat) & N_1 = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_426_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 476 (all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N_2) = N_2) # label(fact_427_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 477 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),zero_zero(nat)) = M) # label(fact_428_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 478 (all M_1 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1) = zero_zero(nat) <-> M_1 = zero_zero(nat) & N_1 = zero_zero(nat))) # label(fact_429_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 479 (all M all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2) = M -> N_2 = zero_zero(nat))) # label(fact_430_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 480 (all X_a (comm_monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_431_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 481 (all X_a (monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_432_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 482 (all X_b (linord219039673up_add(X_b) -> (all A_2 (zero_zero(X_b) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2) <-> ti(X_b,A_2) = zero_zero(X_b))))) # label(fact_433_double__zero__sym) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 483 (all X_a (comm_monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_434_add__0) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 484 (all X_a (monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_435_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 485 (all X_a (ab_semigroup_add(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))) # label(fact_436_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 486 (all X_b (cancel_semigroup_add(X_b) -> (all A_2 all B_1 all C_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),B_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1) <-> ti(X_b,B_1) = ti(X_b,C_1))))) # label(fact_437_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 487 (all X_b (cancel_semigroup_add(X_b) -> (all B_1 all A_2 all C_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_1),A_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2) <-> ti(X_b,B_1) = ti(X_b,C_1))))) # label(fact_438_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 488 (all X_a (cancel_semigroup_add(X_a) -> (all A_1 all B all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) -> ti(X_a,B) = ti(X_a,C))))) # label(fact_439_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 489 (all X_a (cancel146912293up_add(X_a) -> (all A_1 all B all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) -> ti(X_a,B) = ti(X_a,C))))) # label(fact_440_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 490 (all X_a (cancel_semigroup_add(X_a) -> (all B all A_1 all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1) -> ti(X_a,B) = ti(X_a,C))))) # label(fact_441_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 491 (all X_b all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2))))) # label(fact_442_card_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 492 (all X_b all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))))) # label(fact_443_card__Un__Int) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 493 (all N_2 all M ((M = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2) = N_2) & (M != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N_2))))) # label(fact_444_add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 494 (all X_b all X_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))) # label(fact_445_card_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 495 (all X_b all A_3 ((hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(fun(X_b,bool),nat,hAPP(nat,fun(fun(X_b,bool),nat),hAPP(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat))),finite_fold_image(nat,X_b),plus_plus(nat)),hAPP(nat,fun(X_b,nat),combk(nat,X_b),one_one(nat))),zero_zero(nat)),A_3)) & (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = zero_zero(nat)))) # label(fact_446_card__def) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 496 (all X_b all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(fun(X_b,bool),nat,hAPP(nat,fun(fun(X_b,bool),nat),hAPP(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat))),finite_fold_image(nat,X_b),plus_plus(nat)),hAPP(nat,fun(X_b,nat),combk(nat,X_b),one_one(nat))),zero_zero(nat)),A_3))) # label(fact_447_card_Oeq__fold__g) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 497 (all X_b all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)))))) # label(fact_448_card__Un__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 498 (all X_b all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (((exists X hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))) -> one_one(nat) = zero_zero(nat)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)))))) # label(fact_449_card_Ounion__inter__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 499 (all Com1_1 all Com2_1 hAPP(com,nat,com_size,hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,com_size,Com1_1)),hAPP(com,nat,com_size,Com2_1))),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_450_com_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 500 (all Pname hAPP(com,nat,com_size,hAPP(pname,com,body,Pname)) = zero_zero(nat)) # label(fact_451_com_Osize_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 501 (all Fun all Com hAPP(com,nat,com_size,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,com_size,Com)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_453_com_Osize_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 502 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_454_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 503 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_455_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 504 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C all D hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D))))) # label(fact_456_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 505 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),B)))) # label(fact_457_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 506 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))) # label(fact_458_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 507 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),D)))) # label(fact_459_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 508 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),D))))) # label(fact_460_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 509 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)))) # label(fact_461_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 510 (all X_b (semiri456707255roduct(X_b) -> (all B_1 all A_2 (ti(X_b,B_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_1),A_2) <-> ti(X_b,A_2) = zero_zero(X_b))))) # label(fact_462_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 511 (all X_b (linord219039673up_add(X_b) -> (all A_2 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2) = zero_zero(X_b) <-> ti(X_b,A_2) = zero_zero(X_b))))) # label(fact_463_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 512 (all X_c all X_b all B_2 all A_3 ((hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) & hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2)) -> hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_c,bool),nat,finite_card(X_c),B_2))) & (-(hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) & hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))) -> hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2)) = zero_zero(nat)))) # label(fact_464_card__Plus__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 513 (all X_b all X_c all A_3 all B_2 (hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite_1(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) & hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2)))) # label(fact_465_finite__Plus__iff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 514 (all X_c all X_b all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2)) -> hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite_1(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2)))))) # label(fact_466_finite__Plus) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 515 (all X_b all X_c all A_3 all B_2 (hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite_1(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)))) # label(fact_467_finite__PlusD_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 516 (all X_b all X_c all A_3 all B_2 (hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite_1(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2))) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2)))) # label(fact_468_finite__PlusD_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 517 (all X_c all X_b all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2)) -> hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_c,bool),nat,finite_card(X_c),B_2))))) # label(fact_469_card__Plus) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 518 (all X_c all X_b all A_3 all B_2 (hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2) = bot_bot(fun(sum_sum(X_b,X_c),bool)) <-> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) & ti(fun(X_c,bool),B_2) = bot_bot(fun(X_c,bool)))) # label(fact_470_Plus__eq__empty__conv) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 519 (all Com1_1 all Com2_1 hAPP(com,nat,size_size(com),hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,size_size(com),Com1_1)),hAPP(com,nat,size_size(com),Com2_1))),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_471_com_Osize_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 520 (all Pname hAPP(com,nat,size_size(com),hAPP(pname,com,body,Pname)) = zero_zero(nat)) # label(fact_472_com_Osize_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 521 (all Fun all Com hAPP(com,nat,size_size(com),hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,size_size(com),Com)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_474_com_Osize_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 522 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),one_one(X_c)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),one_one(X_c)),A_3)),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),one_one(X_c)),B_2)))))))) # label(fact_475_fold__Un__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 523 (all Fun all Com1 all Com2 hAPP(com,nat,size_size(com),hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun),Com1),Com2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,size_size(com),Com1)),hAPP(com,nat,size_size(com),Com2))),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_476_com_Osize_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 524 (all C0 all C1 all N_1 all S1 all B_1 all S (-hBOOL(hAPP(state,bool,B_1,S)) -> (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),N_1),S1)) -> hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C0),C1)),S),N_1),S1))))) # label(fact_477_evaln_OIfFalse) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 525 (all C1 all C0 all N_1 all S1 all B_1 all S (hBOOL(hAPP(state,bool,B_1,S)) -> (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C0),S),N_1),S1)) -> hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C0),C1)),S),N_1),S1))))) # label(fact_478_evaln_OIfTrue) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 526 (all B_1 all C1 all C2 all S all N_1 all T_3 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C1),C2)),S),N_1),T_3)) -> ((hBOOL(hAPP(state,bool,B_1,S)) -> -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),N_1),T_3))) -> -(-hBOOL(hAPP(state,bool,B_1,S)) -> -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2),S),N_1),T_3)))))) # label(fact_479_evaln__elim__cases_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 527 (all B_1 all C1 all C2 all S all T_3 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C1),C2)),S),T_3)) -> ((hBOOL(hAPP(state,bool,B_1,S)) -> -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1),S),T_3))) -> -(-hBOOL(hAPP(state,bool,B_1,S)) -> -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C2),S),T_3)))))) # label(fact_480_evalc__elim__cases_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 528 (all C1 all C0 all S1 all B_1 all S (hBOOL(hAPP(state,bool,B_1,S)) -> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C0),S),S1)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C0),C1)),S),S1))))) # label(fact_481_evalc_OIfTrue) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 529 (all C0 all C1 all S1 all B_1 all S (-hBOOL(hAPP(state,bool,B_1,S)) -> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1),S),S1)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C0),C1)),S),S1))))) # label(fact_482_evalc_OIfFalse) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 530 (all X_b all X_c (ab_semigroup_mult(X_c) -> (all G all Z_1 all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,G,A_2)),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_1),A_3))))))) # label(fact_483_fold__image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 531 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),M) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M)))) # label(fact_484_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 532 (all X_a (comm_semiring_1(X_a) -> (all M all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M)))) # label(fact_485_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 533 (all X_a (comm_semiring_1(X_a) -> (all M hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),M) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),M)))) # label(fact_486_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 534 (all X_b (semiri456707255roduct(X_b) -> (all W all Y_1 all X_2 all Z_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),Z_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W),Z_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),Y_1)) <-> ti(X_b,W) = ti(X_b,X_2) | ti(X_b,Y_1) = ti(X_b,Z_1))))) # label(fact_487_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 535 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),M)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),M)))) # label(fact_488_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 536 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))) # label(fact_489_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 537 (all X_b (semiri456707255roduct(X_b) -> (all C_1 all D_1 all A_2 all B_1 (ti(X_b,A_2) != ti(X_b,B_1) & ti(X_b,C_1) != ti(X_b,D_1) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_1),D_1)) != hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),D_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_1),C_1)))))) # label(fact_490_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 538 (all X_a (comm_semiring_1(X_a) -> (all X_1 all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Z))))) # label(fact_491_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 539 (all X_a (semiri456707255roduct(X_a) -> (all C all D all A_1 all B all R_1 (ti(X_a,R_1) != zero_zero(X_a) -> (ti(X_a,A_1) = ti(X_a,B) & ti(X_a,C) != ti(X_a,D) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_1),C)) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_1),D))))))) # label(fact_492_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 540 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)))) # label(fact_493_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 541 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_494_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 542 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Ry))))) # label(fact_495_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 543 (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].
% 1.63/1.89 544 (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].
% 1.63/1.89 545 (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].
% 1.63/1.89 546 (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].
% 1.63/1.89 547 (all T_2 all T_1 (distrib_lattice(T_1) -> distrib_lattice(fun(T_2,T_1)))) # label(arity_fun___Lattices_Odistrib__lattice) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 548 (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].
% 1.63/1.89 549 (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].
% 1.63/1.89 550 (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].
% 1.63/1.89 551 (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].
% 1.63/1.89 552 (all T_2 all T_1 (finite_finite(T_1) & finite_finite(T_2) -> finite_finite(sum_sum(T_2,T_1)))) # label(arity_sum___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 553 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 554 (all X_a all X_1 all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X_1),Y) = ti(X_a,X_1)) # label(help_If_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 555 (all X_a all X_1 all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X_1),Y) = ti(X_a,Y)) # label(help_If_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 556 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_If_3_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 557 (all P (-hBOOL(hAPP(bool,bool,fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 558 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 559 (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].
% 1.63/1.89 560 (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].
% 1.63/1.89 561 (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].
% 1.63/1.89 562 (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].
% 1.63/1.89 563 (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].
% 1.63/1.89 564 (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].
% 1.63/1.89 565 (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].
% 1.63/1.89 566 (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].
% 1.63/1.89 567 (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].
% 1.63/1.89 568 (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].
% 1.63/1.89 569 (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].
% 1.63/1.89 570 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 571 (all X_a all X_1 all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X_1),Y)) | ti(X_a,X_1) = ti(X_a,Y))) # label(help_fequal_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 572 (all X_a all X_1 all Y (ti(X_a,X_1) != ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X_1),Y)))) # label(help_fequal_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.89 573 (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].
% 1.63/1.89 574 (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].
% 1.63/1.89 575 (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].
% 1.63/1.89 576 (all N ((all X (hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,hAPP(hoare_1656922687triple(x_a),fun(fun(hoare_1656922687triple(x_a),bool),bool),member(hoare_1656922687triple(x_a)),X),hAPP(fun(hoare_1656922687triple(x_a),bool),fun(hoare_1656922687triple(x_a),bool),hAPP(fun(hoare_1656922687triple(x_a),bool),fun(fun(hoare_1656922687triple(x_a),bool),fun(hoare_1656922687triple(x_a),bool)),semilattice_sup_sup(fun(hoare_1656922687triple(x_a),bool)),g),hAPP(fun(pname,bool),fun(hoare_1656922687triple(x_a),bool),hAPP(fun(pname,hoare_1656922687triple(x_a)),fun(fun(pname,bool),fun(hoare_1656922687triple(x_a),bool)),image(pname,hoare_1656922687triple(x_a)),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_1656922687triple(x_a)),hAPP(fun(pname,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_1656922687triple(x_a))),combs(pname,fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)),hAPP(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),hAPP(fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)))),fun(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)))),combs(pname,com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)))),hAPP(fun(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))))),combb(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),pname),hoare_246368825triple(x_a)),p)),body)),q)),procs)))) -> hBOOL(hAPP(hoare_1656922687triple(x_a),bool,hAPP(nat,fun(hoare_1656922687triple(x_a),bool),hoare_920331057_valid(x_a),N),X)))) -> (all X (hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,hAPP(hoare_1656922687triple(x_a),fun(fun(hoare_1656922687triple(x_a),bool),bool),member(hoare_1656922687triple(x_a)),X),hAPP(fun(pname,bool),fun(hoare_1656922687triple(x_a),bool),hAPP(fun(pname,hoare_1656922687triple(x_a)),fun(fun(pname,bool),fun(hoare_1656922687triple(x_a),bool)),image(pname,hoare_1656922687triple(x_a)),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_1656922687triple(x_a)),hAPP(fun(pname,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_1656922687triple(x_a))),combs(pname,fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)),hAPP(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),hAPP(fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)))),fun(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)))),combs(pname,com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)))),hAPP(fun(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))))),combb(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),pname),hoare_246368825triple(x_a)),p)),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body_1))),q)),procs))) -> hBOOL(hAPP(hoare_1656922687triple(x_a),bool,hAPP(nat,fun(hoare_1656922687triple(x_a),bool),hoare_920331057_valid(x_a),N),X)))))) # label(conj_0) # label(hypothesis) # label(non_clause). [assumption].
% 1.70/1.95 577 -((all X (hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,hAPP(hoare_1656922687triple(x_a),fun(fun(hoare_1656922687triple(x_a),bool),bool),member(hoare_1656922687triple(x_a)),X),g)) -> hBOOL(hAPP(hoare_1656922687triple(x_a),bool,hAPP(nat,fun(hoare_1656922687triple(x_a),bool),hoare_920331057_valid(x_a),n),X)))) -> (all X (hBOOL(hAPP(fun(hoare_1656922687triple(x_a),bool),bool,hAPP(hoare_1656922687triple(x_a),fun(fun(hoare_1656922687triple(x_a),bool),bool),member(hoare_1656922687triple(x_a)),X),hAPP(fun(pname,bool),fun(hoare_1656922687triple(x_a),bool),hAPP(fun(pname,hoare_1656922687triple(x_a)),fun(fun(pname,bool),fun(hoare_1656922687triple(x_a),bool)),image(pname,hoare_1656922687triple(x_a)),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_1656922687triple(x_a)),hAPP(fun(pname,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_1656922687triple(x_a))),combs(pname,fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)),hAPP(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),hAPP(fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)))),fun(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)))),combs(pname,com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)))),hAPP(fun(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a)))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))))),combb(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_1656922687triple(x_a))),pname),hoare_246368825triple(x_a)),p)),body)),q)),procs))) -> hBOOL(hAPP(hoare_1656922687triple(x_a),bool,hAPP(nat,fun(hoare_1656922687triple(x_a),bool),hoare_920331057_valid(x_a),n),X))))) # label(conj_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.70/1.95
% 1.70/1.95 ============================== end of process non-clausal formulas ===
% 1.70/1.95
% 1.70/1.95 ============================== PROCESS INITIAL CLAUSES ===============
% 1.70/1.95
% 1.70/1.95 ============================== PREDICATE ELIMINATION =================
% 1.70/1.95 578 one(nat) # label(arity_Nat_Onat___Groups_Oone) # label(axiom). [assumption].
% 1.70/1.95 579 -one(A) | one_one(A) = ti(A,one_one(A)) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom). [clausify(18)].
% 1.70/1.95 Derived: one_one(nat) = ti(nat,one_one(nat)). [resolve(578,a,579,a)].
% 1.70/1.95 580 cancel_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.70/1.95 581 -cancel_semigroup_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom). [clausify(19)].
% 1.70/1.95 582 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) = ti(A,D) # label(fact_437_add__left__cancel) # label(axiom). [clausify(486)].
% 1.75/2.04 583 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) != ti(A,D) # label(fact_437_add__left__cancel) # label(axiom). [clausify(486)].
% 1.75/2.04 584 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C) | ti(A,B) = ti(A,D) # label(fact_438_add__right__cancel) # label(axiom). [clausify(487)].
% 1.75/2.04 585 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C) | ti(A,B) != ti(A,D) # label(fact_438_add__right__cancel) # label(axiom). [clausify(487)].
% 1.75/2.04 586 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) = ti(A,D) # label(fact_439_add__left__imp__eq) # label(axiom). [clausify(488)].
% 1.75/2.04 587 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C) | ti(A,B) = ti(A,D) # label(fact_441_add__right__imp__eq) # label(axiom). [clausify(490)].
% 1.75/2.04 Derived: plus_plus(nat) = ti(fun(nat,fun(nat,nat)),plus_plus(nat)). [resolve(580,a,581,a)].
% 1.75/2.04 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C) | ti(nat,B) = ti(nat,C). [resolve(580,a,582,a)].
% 1.75/2.04 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C) | ti(nat,B) != ti(nat,C). [resolve(580,a,583,a)].
% 1.75/2.04 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B) | ti(nat,A) = ti(nat,C). [resolve(580,a,584,a)].
% 1.75/2.04 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B) | ti(nat,A) != ti(nat,C). [resolve(580,a,585,a)].
% 1.75/2.04 588 ab_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 1.75/2.04 589 -ab_semigroup_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom). [clausify(20)].
% 1.75/2.04 590 -ab_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_436_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom). [clausify(485)].
% 1.75/2.04 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)). [resolve(588,a,590,a)].
% 1.75/2.04 591 monoid_add(nat) # label(arity_Nat_Onat___Groups_Omonoid__add) # label(axiom). [assumption].
% 1.75/2.04 592 -monoid_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_2_res) # label(axiom). [clausify(21)].
% 1.75/2.04 593 -monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_432_add__0__right) # label(axiom). [clausify(481)].
% 1.75/2.04 594 -monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_435_add__0__left) # label(axiom). [clausify(484)].
% 1.75/2.04 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),zero_zero(nat)) = ti(nat,A). [resolve(591,a,593,a)].
% 1.75/2.04 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),A) = ti(nat,A). [resolve(591,a,594,a)].
% 1.75/2.04 595 ab_semigroup_mult(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.75/2.04 596 -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(22)].
% 1.75/2.04 597 -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_483_fold__image__insert) # label(axiom). [clausify(530)].
% 1.86/2.11 Derived: times_times(nat) = ti(fun(nat,fun(nat,nat)),times_times(nat)). [resolve(595,a,596,a)].
% 1.86/2.11 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(595,a,597,a)].
% 1.86/2.11 598 zero(nat) # label(arity_Nat_Onat___Groups_Ozero) # label(axiom). [assumption].
% 1.86/2.11 599 -zero(A) | zero_zero(A) = ti(A,zero_zero(A)) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom). [clausify(23)].
% 1.86/2.11 Derived: zero_zero(nat) = ti(nat,zero_zero(nat)). [resolve(598,a,599,a)].
% 1.86/2.11 600 -lattice(A) | semilattice_inf(fun(B,A)) # label(arity_fun___Lattices_Osemilattice__inf) # label(axiom). [clausify(546)].
% 1.86/2.11 601 -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(34)].
% 1.86/2.11 602 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),B) = ti(A,B) # label(fact_255_inf_Oidem) # label(axiom). [clausify(305)].
% 1.86/2.11 603 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),B) = ti(A,B) # label(fact_256_inf__idem) # label(axiom). [clausify(306)].
% 1.86/2.11 604 -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_260_inf_Ocommute) # label(axiom). [clausify(310)].
% 1.86/2.11 605 -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_262_inf__commute) # label(axiom). [clausify(312)].
% 1.86/2.11 606 -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_264_inf_Oleft__idem) # label(axiom). [clausify(314)].
% 1.86/2.11 607 -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_266_inf__left__idem) # label(axiom). [clausify(316)].
% 1.86/2.11 608 -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_268_inf_Oleft__commute) # label(axiom). [clausify(318)].
% 1.86/2.11 609 -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_270_inf__left__commute) # label(axiom). [clausify(320)].
% 1.86/2.11 610 -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_273_inf_Oassoc) # label(axiom). [clausify(323)].
% 1.86/2.11 611 -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_275_inf__assoc) # label(axiom). [clausify(325)].
% 1.86/2.11 612 -semilattice_inf(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite_comp_fun_idem(A,A),semilattice_inf_inf(A))) # label(fact_379_comp__fun__idem__inf) # label(axiom). [clausify(429)].
% 1.86/2.11 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(600,b,601,a)].
% 1.86/2.11 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(600,b,602,a)].
% 1.86/2.11 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(600,b,604,a)].
% 1.86/2.11 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(600,b,606,a)].
% 1.86/2.11 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(600,b,608,a)].
% 1.86/2.11 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(600,b,610,a)].
% 1.86/2.11 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(600,b,612,a)].
% 1.86/2.11 613 semilattice_inf(nat) # label(arity_Nat_Onat___Lattices_Osemilattice__inf) # label(axiom). [assumption].
% 1.86/2.11 Derived: semilattice_inf_inf(nat) = ti(fun(nat,fun(nat,nat)),semilattice_inf_inf(nat)). [resolve(613,a,601,a)].
% 1.86/2.11 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),A) = ti(nat,A). [resolve(613,a,602,a)].
% 1.86/2.11 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(613,a,604,a)].
% 1.86/2.11 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(613,a,606,a)].
% 1.86/2.11 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(613,a,608,a)].
% 1.86/2.11 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(613,a,610,a)].
% 1.86/2.11 Derived: hBOOL(hAPP(fun(nat,fun(nat,nat)),bool,finite_comp_fun_idem(nat,nat),semilattice_inf_inf(nat))). [resolve(613,a,612,a)].
% 1.86/2.11 614 semilattice_inf(bool) # label(arity_HOL_Obool___Lattices_Osemilattice__inf) # label(axiom). [assumption].
% 1.86/2.11 Derived: semilattice_inf_inf(bool) = ti(fun(bool,fun(bool,bool)),semilattice_inf_inf(bool)). [resolve(614,a,601,a)].
% 1.91/2.14 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),A) = ti(bool,A). [resolve(614,a,602,a)].
% 1.91/2.14 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(614,a,604,a)].
% 1.91/2.14 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(614,a,606,a)].
% 1.91/2.14 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(614,a,608,a)].
% 1.91/2.14 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(614,a,610,a)].
% 1.91/2.14 Derived: hBOOL(hAPP(fun(bool,fun(bool,bool)),bool,finite_comp_fun_idem(bool,bool),semilattice_inf_inf(bool))). [resolve(614,a,612,a)].
% 1.91/2.14 615 -lattice(A) | semilattice_sup(fun(B,A)) # label(arity_fun___Lattices_Osemilattice__sup) # label(axiom). [clausify(545)].
% 1.91/2.14 616 -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(35)].
% 1.91/2.14 617 -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_14_sup__assoc) # label(axiom). [clausify(65)].
% 1.91/2.14 618 -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_16_sup_Oassoc) # label(axiom). [clausify(67)].
% 1.91/2.14 619 -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_17_sup__left__commute) # label(axiom). [clausify(68)].
% 1.91/2.14 620 -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_19_sup_Oleft__commute) # label(axiom). [clausify(70)].
% 1.91/2.14 621 -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_20_sup__left__idem) # label(axiom). [clausify(71)].
% 1.91/2.14 622 -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_22_sup_Oleft__idem) # label(axiom). [clausify(73)].
% 1.91/2.14 623 -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_23_sup__commute) # label(axiom). [clausify(74)].
% 1.91/2.14 624 -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_25_sup_Ocommute) # label(axiom). [clausify(76)].
% 1.91/2.14 625 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),B) = ti(A,B) # label(fact_26_sup__idem) # label(axiom). [clausify(77)].
% 1.91/2.14 626 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),B) = ti(A,B) # label(fact_27_sup_Oidem) # label(axiom). [clausify(78)].
% 1.91/2.14 627 -semilattice_sup(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite_comp_fun_idem(A,A),semilattice_sup_sup(A))) # label(fact_378_comp__fun__idem__sup) # label(axiom). [clausify(428)].
% 1.91/2.14 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(615,b,616,a)].
% 1.91/2.14 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(615,b,617,a)].
% 1.91/2.14 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(615,b,619,a)].
% 1.91/2.14 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(615,b,621,a)].
% 1.91/2.14 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(615,b,623,a)].
% 1.91/2.14 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(615,b,625,a)].
% 1.91/2.14 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(615,b,627,a)].
% 1.91/2.14 628 semilattice_sup(nat) # label(arity_Nat_Onat___Lattices_Osemilattice__sup) # label(axiom). [assumption].
% 1.91/2.14 Derived: semilattice_sup_sup(nat) = ti(fun(nat,fun(nat,nat)),semilattice_sup_sup(nat)). [resolve(628,a,616,a)].
% 1.91/2.14 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(628,a,617,a)].
% 1.91/2.14 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(628,a,619,a)].
% 1.91/2.14 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(628,a,621,a)].
% 1.91/2.14 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(628,a,623,a)].
% 1.91/2.14 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),A) = ti(nat,A). [resolve(628,a,625,a)].
% 1.91/2.14 Derived: hBOOL(hAPP(fun(nat,fun(nat,nat)),bool,finite_comp_fun_idem(nat,nat),semilattice_sup_sup(nat))). [resolve(628,a,627,a)].
% 1.91/2.14 629 semilattice_sup(bool) # label(arity_HOL_Obool___Lattices_Osemilattice__sup) # label(axiom). [assumption].
% 1.91/2.14 Derived: semilattice_sup_sup(bool) = ti(fun(bool,fun(bool,bool)),semilattice_sup_sup(bool)). [resolve(629,a,616,a)].
% 1.91/2.14 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(629,a,617,a)].
% 1.93/2.17 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(629,a,619,a)].
% 1.93/2.17 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(629,a,621,a)].
% 1.93/2.17 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(629,a,623,a)].
% 1.93/2.17 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),A) = ti(bool,A). [resolve(629,a,625,a)].
% 1.93/2.17 Derived: hBOOL(hAPP(fun(bool,fun(bool,bool)),bool,finite_comp_fun_idem(bool,bool),semilattice_sup_sup(bool))). [resolve(629,a,627,a)].
% 1.93/2.17 630 -bounded_lattice(A) | bounded_lattice_bot(fun(B,A)) # label(arity_fun___Lattices_Obounded__lattice__bot) # label(axiom). [clausify(544)].
% 1.93/2.17 631 -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_113_sup__bot__left) # label(axiom). [clausify(164)].
% 1.93/2.17 632 -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_114_sup__bot__right) # label(axiom). [clausify(165)].
% 1.93/2.17 633 -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_115_sup__eq__bot__iff) # label(axiom). [clausify(166)].
% 1.93/2.17 634 -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_115_sup__eq__bot__iff) # label(axiom). [clausify(166)].
% 1.93/2.17 635 -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_115_sup__eq__bot__iff) # label(axiom). [clausify(166)].
% 1.93/2.17 636 -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_243_inf__bot__right) # label(axiom). [clausify(293)].
% 1.93/2.17 637 -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_244_inf__bot__left) # label(axiom). [clausify(294)].
% 1.93/2.17 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(630,b,631,a)].
% 1.93/2.17 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(630,b,632,a)].
% 1.93/2.17 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(630,b,633,a)].
% 1.93/2.17 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(630,b,634,a)].
% 1.93/2.17 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(630,b,635,a)].
% 1.93/2.17 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(630,b,636,a)].
% 1.93/2.17 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(630,b,637,a)].
% 1.93/2.17 638 bounded_lattice_bot(bool) # label(arity_HOL_Obool___Lattices_Obounded__lattice__bot) # label(axiom). [assumption].
% 1.93/2.17 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),bot_bot(bool)),A) = ti(bool,A). [resolve(638,a,631,a)].
% 2.07/2.34 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),bot_bot(bool)) = ti(bool,A). [resolve(638,a,632,a)].
% 2.07/2.34 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(638,a,633,a)].
% 2.07/2.34 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(638,a,634,a)].
% 2.07/2.34 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(638,a,635,a)].
% 2.07/2.34 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),bot_bot(bool)) = bot_bot(bool). [resolve(638,a,636,a)].
% 2.07/2.34 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),bot_bot(bool)),A) = bot_bot(bool). [resolve(638,a,637,a)].
% 2.07/2.34 639 zero_neq_one(nat) # label(arity_Nat_Onat___Rings_Ozero__neq__one) # label(axiom). [assumption].
% 2.07/2.34 640 -zero_neq_one(A) | zero_zero(A) != one_one(A) # label(fact_403_zero__neq__one) # label(axiom). [clausify(452)].
% 2.07/2.34 641 -zero_neq_one(A) | zero_zero(A) != one_one(A) # label(fact_404_one__neq__zero) # label(axiom). [clausify(453)].
% 2.07/2.34 Derived: zero_zero(nat) != one_one(nat). [resolve(639,a,640,a)].
% 2.07/2.34 642 comm_monoid_add(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 2.07/2.34 643 -comm_monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_431_add_Ocomm__neutral) # label(axiom). [clausify(480)].
% 2.07/2.34 644 -comm_monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_434_add__0) # label(axiom). [clausify(483)].
% 2.07/2.34 645 cancel146912293up_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.07/2.34 646 -cancel146912293up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) = ti(A,D) # label(fact_440_add__imp__eq) # label(axiom). [clausify(489)].
% 2.07/2.34 647 comm_semiring_1(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 2.07/2.34 648 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_454_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom). [clausify(502)].
% 2.07/2.34 649 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_455_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom). [clausify(503)].
% 2.07/2.34 650 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E)) # label(fact_456_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom). [clausify(504)].
% 2.07/2.34 651 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_457_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom). [clausify(505)].
% 2.07/2.34 652 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_458_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom). [clausify(506)].
% 2.07/2.34 653 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_459_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom). [clausify(507)].
% 2.07/2.34 654 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)) # label(fact_460_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom). [clausify(508)].
% 2.07/2.34 655 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B) # label(fact_461_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom). [clausify(509)].
% 2.07/2.34 656 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),C) # label(fact_484_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom). [clausify(531)].
% 2.07/2.34 657 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_485_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom). [clausify(532)].
% 2.07/2.34 658 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A))),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) # label(fact_486_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom). [clausify(533)].
% 2.07/2.34 659 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_488_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom). [clausify(535)].
% 2.07/2.34 660 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_489_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom). [clausify(536)].
% 2.07/2.34 661 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_491_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom). [clausify(538)].
% 2.07/2.34 662 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) = ti(A,B) # label(fact_493_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom). [clausify(540)].
% 2.07/2.34 663 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) = ti(A,B) # label(fact_494_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom). [clausify(541)].
% 2.07/2.34 664 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)) # label(fact_495_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom). [clausify(542)].
% 2.07/2.34 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D)). [resolve(647,a,650,a)].
% 2.07/2.34 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),B). [resolve(647,a,651,a)].
% 2.07/2.34 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)). [resolve(647,a,654,a)].
% 2.07/2.34 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),A). [resolve(647,a,655,a)].
% 2.07/2.36 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),B). [resolve(647,a,656,a)].
% 2.07/2.36 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)). [resolve(647,a,657,a)].
% 2.07/2.36 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat))),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),A). [resolve(647,a,658,a)].
% 2.07/2.36 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(647,a,659,a)].
% 2.07/2.36 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)). [resolve(647,a,661,a)].
% 2.07/2.36 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),one_one(nat)) = ti(nat,A). [resolve(647,a,662,a)].
% 2.07/2.36 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),A) = ti(nat,A). [resolve(647,a,663,a)].
% 2.07/2.36 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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D)). [resolve(647,a,664,a)].
% 2.07/2.36 665 semiri456707255roduct(nat) # label(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption].
% 2.07/2.36 666 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != ti(A,B) | zero_zero(A) = ti(A,C) # label(fact_462_add__0__iff) # label(axiom). [clausify(510)].
% 2.07/2.36 667 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_462_add__0__iff) # label(axiom). [clausify(510)].
% 2.07/2.36 668 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,B) = ti(A,D) | ti(A,C) = ti(A,E) # label(fact_487_crossproduct__eq) # label(axiom). [clausify(534)].
% 2.07/2.36 669 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,B) != ti(A,D) # label(fact_487_crossproduct__eq) # label(axiom). [clausify(534)].
% 2.07/2.36 670 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,C) != ti(A,E) # label(fact_487_crossproduct__eq) # label(axiom). [clausify(534)].
% 2.07/2.36 671 -semiri456707255roduct(A) | ti(A,B) = ti(A,C) | ti(A,D) = ti(A,E) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_490_crossproduct__noteq) # label(axiom). [clausify(537)].
% 2.15/2.38 672 -semiri456707255roduct(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_490_crossproduct__noteq) # label(axiom). [clausify(537)].
% 2.15/2.38 673 -semiri456707255roduct(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),B)) # label(fact_490_crossproduct__noteq) # label(axiom). [clausify(537)].
% 2.15/2.38 674 -semiri456707255roduct(A) | zero_zero(A) = ti(A,B) | ti(A,C) != ti(A,D) | ti(A,E) = ti(A,F) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),F)) # label(fact_492_add__scale__eq__noteq) # label(axiom). [clausify(539)].
% 2.15/2.38 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != ti(nat,A) | zero_zero(nat) = ti(nat,B). [resolve(665,a,666,a)].
% 2.15/2.38 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = ti(nat,A) | zero_zero(nat) != ti(nat,B). [resolve(665,a,667,a)].
% 2.15/2.38 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)) | ti(nat,A) = ti(nat,C) | ti(nat,B) = ti(nat,D). [resolve(665,a,668,a)].
% 2.15/2.38 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)) | ti(nat,A) != ti(nat,C). [resolve(665,a,669,a)].
% 2.15/2.38 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)) | ti(nat,B) != ti(nat,D). [resolve(665,a,670,a)].
% 2.15/2.38 Derived: zero_zero(nat) = ti(nat,A) | ti(nat,B) != ti(nat,C) | ti(nat,D) = ti(nat,E) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),E)). [resolve(665,a,674,a)].
% 2.15/2.38 675 comm_monoid_mult(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 2.15/2.38 676 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),D)) | hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),semilattice_inf_inf(fun(B,bool)),C),D) != bot_bot(fun(B,bool)) | 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),one_one(A)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),semilattice_sup_sup(fun(B,bool)),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),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),one_one(A)),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),one_one(A)),D)) # label(fact_475_fold__Un__disjoint) # label(axiom). [clausify(522)].
% 4.64/4.86 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_inf_inf(fun(A,bool)),B),C) != bot_bot(fun(A,bool)) | 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),one_one(nat)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),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),one_one(nat)),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),one_one(nat)),C)). [resolve(675,a,676,a)].
% 4.64/4.86
% 4.64/4.86 ============================== end predicate elimination =============
% 4.64/4.86
% 4.64/4.86 Auto_denials: (non-Horn, no changes).
% 4.64/4.86
% 4.64/4.86 Term ordering decisions:
% 4.64/4.86 Function symbol KB weights: bool=1. nat=1. state=1. com=1. pname=1. x_a=1. suc=1. evaln=1. evalc=1. while=1. body=1. fconj=1. semi=1. body_1=1. cond=1. fdisj=1. fimplies=1. com_size=1. fNot=1. skip=1. fFalse=1. p=1. procs=1. q=1. fTrue=1. g=1. hoare_Mirabelle_MGT=1. n=1. c1=1. fun=1. ti=1. image=1. sum_sum=1. sum_Plus=1. finite1357897459simple=1. finite_fold_image=1. combk=1. finite_comp_fun_idem=1. big_comm_monoid_big=1. finite908156982e_idem=1. hoare_1312322281e_case=1. hoare_1632998903le_rec=1. f12=1. f13=1. f14=1. f17=1. f18=1. f19=1. f21=1. f33=1. f34=1. f45=1. f46=1. f52=1. f53=1. f69=1. f72=1. f73=1. f84=1. f85=1. f95=1. hoare_1656922687triple=1. bot_bot=1. member=1. insert=1. semilattice_sup_sup=1. semilattice_inf_inf=1. finite_finite_1=1. minus_minus=1. plus_plus=1. zero_zero=1. finite_card=1. hoare_246368825triple=1. hoare_279057269derivs=1. collect=1. times_times=1. option=1. big_lattice_Inf_fin=1. big_lattice_Sup_fin=1. one_one=1. hoare_920331057_valid=1. fequal=1. size_size=1. the_1=1. the=1. finite_folding_one=1. finite2073411215e_idem=1. hoare_2027193591valids=1. combi=1. if=1. nat_case=1. powp=1. the_elem=1. hoare_983366810e_size=1. undefined=1. f32=1. f35=1. f97=1. combb=1. combs=1. combc=1. f2=1. f3=1. f16=1. f22=1. f36=1. f41=1. f47=1. f48=1. f54=1. f55=1. f56=1. f59=1. f63=1. f65=1. f67=1. f68=1. f70=1. f71=1. f74=1. f75=1. f82=1. f83=1. f88=1. f89=1. f90=1. f91=1. f92=1. f93=1. f94=1. f96=1. hAPP=1. f1=1. f5=1. f6=1. f7=1. f8=1. f9=1. f10=1. f20=1. f40=1. f43=1. f49=1. f50=1. f60=1. f61=1. f64=1. f76=1. f77=1. f78=1. f79=1. f80=1. f81=1. f4=1. f11=1. f23=1. f24=1. f37=1. f38=1. f39=1. f44=1. f51=1. f57=1. f58=1. f15=1. f25=1. f26=1. f27=1. f28=1. f29=1. f30=1. f31=1. f87=1. f66=1. f86=1. f42=1. f62=1.
% 4.64/4.86
% 4.64/4.86 ============================== end of process initial clauses ========
% 4.64/4.86
% 4.64/4.86 ============================== CLAUSES FOR SEARCH ====================
% 4.64/4.86
% 4.64/4.86 ============================== end of clauses for search =============
% 4.64/4.86
% 4.64/4.86 ============================== SEARCH ================================
% 4.64/4.86
% 4.64/4.86 % Starting search at 0.98 seconds.
% 4.64/4.86
% 4.64/4.86 Low Water (keep): wt=197.000, iters=3938
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% 4.64/4.86 Low Water (keep): wt=189.000, iters=3876
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% 4.64/4.86 Low Water (keep): wt=159.000, iters=3354
% 4.64/4.86
% 4.64/4.86 Low Water (keep): wt=149.000, iters=3382
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% 4.64/4.86 Low Water (keep): wt=146.000, iters=3360
% 4.64/4.86
% 4.64/4.86 Low Water (keep): wt=142.000, iters=3358
% 4.64/4.86
% 4.64/4.86 Low Water (keep): wt=136.000, iters=3409
% 4.64/4.86
% 4.64/4.86 Low Water (keep): wt=131.000, iters=3404
% 4.64/4.86
% 4.64/4.86 Low Water (keep): wt=128.000, iters=3360
% 4.64/4.86
% 4.64/4.86 Low Water (keep): wt=122.000, iters=3424
% 4.64/4.86
% 4.64/4.86 Low Water (keep): wt=119.000, iters=3338
% 4.64/4.86
% 4.64/4.86 Low Water (keep): wt=118.000, iters=3343
% 4.64/4.86
% 4.64/4.86 Low Water (keep): wt=116.000, iters=3362
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=115.000, iters=3543
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=113.000, iters=3478
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=109.000, iters=3477
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=106.000, iters=3369
% 185.47/185.76
% 185.47/185.76 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 49 (0.00 of 3.39 sec).
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=105.000, iters=3390
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=104.000, iters=3350
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=103.000, iters=3368
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=102.000, iters=3360
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=98.000, iters=3357
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=95.000, iters=3348
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=94.000, iters=3357
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=93.000, iters=3364
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=91.000, iters=3341
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=90.000, iters=3364
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=89.000, iters=3386
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=88.000, iters=3364
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=87.000, iters=3439
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=86.000, iters=3364
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=84.000, iters=3373
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=82.000, iters=3358
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=81.000, iters=3395
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=80.000, iters=3343
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=79.000, iters=3443
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=77.000, iters=3435
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=76.000, iters=3442
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=75.000, iters=3388
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=63.000, iters=3360
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=62.000, iters=3352
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=60.000, iters=3546
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=59.000, iters=3909
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=55.000, iters=3714
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=53.000, iters=3692
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=50.000, iters=3492
% 185.47/185.76
% 185.47/185.76 Low Water (displace): id=5052, wt=200.000
% 185.47/185.76
% 185.47/185.76 Low Water (displace): id=4929, wt=199.000
% 185.47/185.76
% 185.47/185.76 Low Water (displace): id=13105, wt=41.000
% 185.47/185.76
% 185.47/185.76 Low Water (displace): id=13112, wt=36.000
% 185.47/185.76
% 185.47/185.76 Low Water (displace): id=13133, wt=32.000
% 185.47/185.76
% 185.47/185.76 Low Water (displace): id=13143, wt=20.000
% 185.47/185.76
% 185.47/185.76 Low Water (displace): id=13144, wt=18.000
% 185.47/185.76
% 185.47/185.76 Low Water (displace): id=13202, wt=12.000
% 185.47/185.76
% 185.47/185.76 Low Water (displace): id=13438, wt=11.000
% 185.47/185.76
% 185.47/185.76 Low Water (displace): id=14286, wt=10.000
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=42.000, iters=3578
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=41.000, iters=3433
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=40.000, iters=3333
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=39.000, iters=3339
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=38.000, iters=3373
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=35.000, iters=3404
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=34.000, iters=3343
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=33.000, iters=3335
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=32.000, iters=3476
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=31.000, iters=3339
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=30.000, iters=3333
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=29.000, iters=3333
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=28.000, iters=3335
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=27.000, iters=3333
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=26.000, iters=3336
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=25.000, iters=3343
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=24.000, iters=3333
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=23.000, iters=3336
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=22.000, iters=3339
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=21.000, iters=3380
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=20.000, iters=3375
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=19.000, iters=3333
% 185.47/185.76
% 185.47/185.76 Low Water (keep): wt=18.000, iters=3333
% 185.47/185.76
% 185.47/185.76 ============================== STATISTICS ============================
% 185.47/185.76
% 185.47/185.76 Given=12217. Generated=3036716. Kept=318426. proofs=0.
% 185.47/185.76 Usable=11409. Sos=9998. Demods=438. Limbo=21, Disabled=297925. Hints=0.
% 185.47/185.76 Kept_by_rule=0, Deleted_by_rule=152443.
% 185.47/185.76 Forward_subsumed=302502. Back_subsumed=123.
% 185.47/185.76 Sos_limit_deleted=2263344. Sos_displaced=294486. Sos_removed=0.
% 185.47/185.76 New_demodulators=1131 (0 lex), Back_demodulated=2242. Back_unit_deleted=147.
% 185.47/185.76 Demod_attempts=202735728. Demod_rewrites=518663.
% 185.47/185.76 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
% 185.47/185.76 Nonunit_fsub_feature_tests=5250314. Nonunit_bsub_feature_tests=15126.
% 185.47/185.76 Megabytes=419.43.
% 185.47/185.76 User_CPU=182.06, System_CPU=1.97, Wall_clock=184.
% 185.47/185.76
% 185.47/185.76 Megs malloced by palloc(): 400.
% 185.47/185.76 type (bytes each) gets frees in use bytes
% 185.47/185.76 chunk ( 104) 54048 54048 0 0.0 K
% 185.47/185.76 string_buf ( 8) 48531 48531 0 0.0 K
% 185.47/185.76 token ( 20) 122276 122276 0 0.0 K
% 185.47/185.76 pterm ( 16) 87076 87076 0 0.0 K
% 185.47/185.76 hashtab ( 8) 577 577 0 0.0 K
% 185.47/185.76 hashnode ( 8) 2081 2081 0 0.0 K
% 185.47/185.76 term ( 20) 313062455 302212549 10849906 211912.2 K
% 185.47/185.76 term arg arrays: 46159.9 K
% 185.47/185.76 attribute ( 12) 4255 120 4135 48.5 K
% 185.47/185.76 ilist ( 8) 849214189 847657330 1556859 12163.0 K
% 185.47/185.76 plist ( 8) 10004856 9648764 356092 2782.0 K
% 185.47/185.76 i2list ( 12) 23443173 23443173 0 0.0 K
% 185.47/185.76 just ( 12) 3902625 3528663 373962 4382.4 K
% 185.47/185.76 parajust ( 16) 1971856 1854937 116919 1826.9 K
% 185.47/185.76 instancejust ( 8) 0 0 0 0.0 K
% 185.47/185.76 ivyjust ( 24) 0 0 0 0.0 K
% 185.47/185.76 formula ( 28) 22544 14064 8480 231.9 K
% 185.47/185.76 formula arg arrays: 28.6 K
% 185.47/185.76 topform ( 52) 3038266 2718289 319977 16248.8 K
% 185.47/185.76 clist_pos ( 20) 949757 629966 319791 6245.9 K
% 185.47/185.76 clist ( 16) 8 1 7 0.1 K
% 185.47/185.76 context ( 808) 22019119 22019117 2 1.6 K
% 185.47/185.76 trail ( 12) 17580799 17580796 3 0.0 K
% 185.47/185.76 ac_match_pos (70044) 0 0 0 0.0 K
% 185.47/185.76 ac_match_free_vars_pos (20020)
% 185.47/185.76 0 0 0 0.0 K
% 185.47/185.76 btm_state ( 60) 0 0 0 0.0 K
% 185.47/185.76 btu_state ( 60) 0 0 0 0.0 K
% 185.47/185.76 ac_position (285432) 0 0 0 0.0 K
% 185.47/185.76 fpa_trie ( 20) 1568161 1288122 280039 5469.5 K
% 185.47/185.76 fpa_state ( 28) 15309666 15309666 0 0.0 K
% 185.47/185.76 fpa_index ( 12) 10 0 10 0.1 K
% 185.47/185.76 fpa_chunk ( 20) 2903215 2785649 117566 2296.2 K
% 185.47/185.76 fpa_list ( 16) 1349230 0 1349230 21081.7 K
% 185.47/185.76 fpa_list chunks: 11202.6 K
% 185.47/185.76 discrim ( 12) 3546850 3456751 90099 1055.8 K
% 185.47/185.76 discrim_pos ( 16) 643817 643817 0 0.0 K
% 185.47/185.76 flat2 ( 32) 116383758 116383758 0 0.0 K
% 185.47/185.76 flat ( 48) 0 0 0 0.0 K
% 185.47/185.76 flatterm ( 32) 251017223 251017223 0 0.0 K
% 185.47/185.76 mindex ( 28) 13 0 13 0.4 K
% 185.47/185.76 mindex_pos ( 56) 14724526 14724526 0 0.0 K
% 185.47/185.76 lindex ( 12) 5 0 5 0.1 K
% 185.47/185.76 clash ( 40) 0 0 0 0.0 K
% 185.47/185.76 di_tree ( 12) 29142331 24326467 4815864 56435.9 K
% 185.47/185.76 avl_node ( 20) 635716 615720 19996 390.5 K
% 185.47/185.76
% 185.47/185.76 Memory report, 20 @ 20 = 400 megs (400.00 megs used).
% 185.47/185.76 List 1, length 8, 0.0 K
% 185.47/185.76 List 3, length 382957, 4487.8 K
% 185.47/185.76 List 6, length 323, 7.6 K
% 185.47/185.76 List 7, length 1, 0.0 K
% 185.47/185.76 List 8, length 342, 10.7 K
% 185.47/185.76 List 10, length 12, 0.5 K
% 185.47/185.76 List 11, length 7, 0.3 K
% 185.47/185.76 List 12, length 7, 0.3 K
% 185.47/185.76 List 14, length 13, 0.7 K
% 185.47/185.76 List 16, length 6564, 410.2 K
% 185.47/185.76 List 26, length 768, 78.0 K
% 185.47/185.76 List 32, length 3296, 412.0 K
% 185.47/185.76 List 64, length 1357, 339.2 K
% 185.47/185.76 List 128, length 15, 7.5 K
% 185.47/185.76 List 202, length 2, 1.6 K
% 185.47/185.76 List 256, length 283, 283.0 K
% 185.47/185.76
% 185.47/185.76 ============================== SELECTOR REPORT =======================
% 185.47/185.76 Sos_deleted=2263344, Sos_displaced=294486, Sos_size=9998
% 185.47/185.76 SELECTOR PART PRIORITY ORDER SIZE SELECTED
% 185.47/185.76 I 2147483647 high age 0 731
% 185.47/185.76 H 1 high weight 0 0
% 185.47/185.76 A 1 low age 9998 1277
% 185.47/185.76 F 4 low weight 155 5105
% 185.47/185.76 T 4 low weight 9843 5104
% 185.47/185.76 ============================== end of selector report ================
% 185.47/185.76
% 185.47/185.76 ============================== end of statistics =====================
% 185.47/185.76
% 185.47/185.76 Exiting with failure.
% 185.47/185.76
% 185.47/185.76 Process 32742 exit (max_megs) Sun Jun 5 00:31:43 2022
% 185.47/185.76 Prover9 interrupted
%------------------------------------------------------------------------------