TSTP Solution File: SWW471+7 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW471+7 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 126.03s 126.26s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWW471+7 : TPTP v8.1.0. Released v5.3.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 5 07:35:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.87/2.28 ============================== Prover9 ===============================
% 1.87/2.28 Prover9 (32) version 2009-11A, November 2009.
% 1.87/2.28 Process 7095 was started by sandbox2 on n019.cluster.edu,
% 1.87/2.28 Sun Jun 5 07:35:12 2022
% 1.87/2.28 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_6942_n019.cluster.edu".
% 1.87/2.28 ============================== end of head ===========================
% 1.87/2.28
% 1.87/2.28 ============================== INPUT =================================
% 1.87/2.28
% 1.87/2.28 % Reading from file /tmp/Prover9_6942_n019.cluster.edu
% 1.87/2.28
% 1.87/2.28 set(prolog_style_variables).
% 1.87/2.28 set(auto2).
% 1.87/2.28 % set(auto2) -> set(auto).
% 1.87/2.28 % set(auto) -> set(auto_inference).
% 1.87/2.28 % set(auto) -> set(auto_setup).
% 1.87/2.28 % set(auto_setup) -> set(predicate_elim).
% 1.87/2.28 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.87/2.28 % set(auto) -> set(auto_limits).
% 1.87/2.28 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.87/2.28 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.87/2.28 % set(auto) -> set(auto_denials).
% 1.87/2.28 % set(auto) -> set(auto_process).
% 1.87/2.28 % set(auto2) -> assign(new_constants, 1).
% 1.87/2.28 % set(auto2) -> assign(fold_denial_max, 3).
% 1.87/2.28 % set(auto2) -> assign(max_weight, "200.000").
% 1.87/2.28 % set(auto2) -> assign(max_hours, 1).
% 1.87/2.28 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.87/2.28 % set(auto2) -> assign(max_seconds, 0).
% 1.87/2.28 % set(auto2) -> assign(max_minutes, 5).
% 1.87/2.28 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.87/2.28 % set(auto2) -> set(sort_initial_sos).
% 1.87/2.28 % set(auto2) -> assign(sos_limit, -1).
% 1.87/2.28 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.87/2.28 % set(auto2) -> assign(max_megs, 400).
% 1.87/2.28 % set(auto2) -> assign(stats, some).
% 1.87/2.28 % set(auto2) -> clear(echo_input).
% 1.87/2.28 % set(auto2) -> set(quiet).
% 1.87/2.28 % set(auto2) -> clear(print_initial_clauses).
% 1.87/2.28 % set(auto2) -> clear(print_given).
% 1.87/2.28 assign(lrs_ticks,-1).
% 1.87/2.28 assign(sos_limit,10000).
% 1.87/2.28 assign(order,kbo).
% 1.87/2.28 set(lex_order_vars).
% 1.87/2.28 clear(print_given).
% 1.87/2.28
% 1.87/2.28 % formulas(sos). % not echoed (1168 formulas)
% 1.87/2.28
% 1.87/2.28 ============================== end of input ==========================
% 1.87/2.28
% 1.87/2.28 % From the command line: assign(max_seconds, 300).
% 1.87/2.28
% 1.87/2.28 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.87/2.28
% 1.87/2.28 % Formulas that are not ordinary clauses:
% 1.87/2.28 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].
% 1.87/2.28 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].
% 1.87/2.28 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].
% 1.87/2.28 4 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),big_semilattice_big(X_b)) = big_semilattice_big(X_b)) # label(tsy_c_Big__Operators_Osemilattice__big_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 5 (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].
% 1.87/2.28 6 (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].
% 1.87/2.28 7 (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].
% 1.87/2.28 8 (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].
% 1.87/2.28 9 (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].
% 1.87/2.28 10 (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].
% 1.87/2.28 11 (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].
% 1.87/2.28 12 (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].
% 1.87/2.28 13 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b)),finite_fold1(X_b)) = finite_fold1(X_b)) # label(tsy_c_Finite__Set_Ofold1_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 14 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool))),finite_fold1Set(X_b)) = finite_fold1Set(X_b)) # label(tsy_c_Finite__Set_Ofold1Set_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 15 (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].
% 1.87/2.28 16 (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].
% 1.87/2.28 17 (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].
% 1.87/2.28 18 (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].
% 1.87/2.28 19 (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].
% 1.87/2.28 20 (all X_c (minus(X_c) -> ti(fun(X_c,fun(X_c,X_c)),minus_minus(X_c)) = minus_minus(X_c))) # label(tsy_c_Groups_Ominus__class_Ominus_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 21 (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].
% 1.87/2.28 22 (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_0_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 23 (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_1_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 24 (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_2_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 25 (all X_a (monoid_mult(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_0_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 26 (all X_a (no_zero_divisors(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_1_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 27 (all X_a (mult_zero(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_2_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 28 (all X_a (ab_semigroup_mult(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_3_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 29 (all X_a (semiring(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_4_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 30 (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].
% 1.87/2.28 31 (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].
% 1.87/2.28 32 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 33 (all X_b ti(fun(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool)),hoare_1301688828derivs(X_b)) = hoare_1301688828derivs(X_b)) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Ohoare__derivs_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 34 (all X_b ti(fun(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool)),hoare_902341502valids(X_b)) = hoare_902341502valids(X_b)) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Ohoare__valids_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 35 (all X_b ti(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hoare_759811442triple(X_b)) = hoare_759811442triple(X_b)) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Otriple_Otriple_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 36 (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_2118899576triple(X_c),X_b)),hoare_225284258e_case(X_c,X_b)) = hoare_225284258e_case(X_c,X_b)) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Otriple_Otriple__case_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 37 (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_2118899576triple(X_c),X_b)),hoare_1759541758le_rec(X_c,X_b)) = hoare_1759541758le_rec(X_c,X_b)) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Otriple_Otriple__rec_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 38 (all X_b ti(fun(fun(X_b,nat),fun(hoare_2118899576triple(X_b),nat)),hoare_2043812435e_size(X_b)) = hoare_2043812435e_size(X_b)) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Otriple_Otriple__size_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 39 (all X_b ti(fun(nat,fun(hoare_2118899576triple(X_b),bool)),hoare_1942962616_valid(X_b)) = hoare_1942962616_valid(X_b)) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Otriple__valid_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 40 (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].
% 1.87/2.28 41 (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].
% 1.87/2.28 42 (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].
% 1.87/2.28 43 (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].
% 1.87/2.28 44 (all X_b ti(fun(hoare_2118899576triple(X_b),nat),size_size(hoare_2118899576triple(X_b))) = size_size(hoare_2118899576triple(X_b))) # label(tsy_c_Nat_Osize__class_Osize_1_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 45 (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].
% 1.87/2.28 46 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,bool)),ord_less(X_a)) = ord_less(X_a))) # label(tsy_c_Orderings_Oord__class_Oless_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 47 (all X_c (ord(X_c) -> ti(fun(X_c,fun(X_c,bool)),ord_less_eq(X_c)) = ord_less_eq(X_c))) # label(tsy_c_Orderings_Oord__class_Oless__eq_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 48 (all X_b ti(fun(X_b,fun(fun(X_b,bool),X_b)),partial_flat_lub(X_b)) = partial_flat_lub(X_b)) # label(tsy_c_Partial__Function_Oflat__lub_res) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 49 (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].
% 1.87/2.28 50 (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].
% 1.87/2.28 51 (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].
% 1.87/2.28 52 (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].
% 1.87/2.28 53 (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].
% 1.87/2.28 54 (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].
% 1.87/2.28 55 (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].
% 1.87/2.28 56 (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].
% 1.87/2.28 57 (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].
% 1.87/2.28 58 (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].
% 1.87/2.28 59 (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].
% 1.87/2.28 60 (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].
% 1.87/2.28 61 (all X_b all Fun1 all Com_1 all Fun2 all Fun1_2 all Com all Fun2_2 (hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1),Com_1),Fun2) = hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1_2),Com),Fun2_2) <-> Fun1 = Fun1_2 & Com_1 = Com & Fun2 = Fun2_2)) # label(fact_0_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 62 (all X_b all Ga all Ts (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_902341502valids(X_b),Ga),Ts)) <-> (all N ((all X (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),bool),member(hoare_2118899576triple(X_b)),X),Ga)) -> hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N),X)))) -> (all X (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),bool),member(hoare_2118899576triple(X_b)),X),Ts)) -> hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N),X)))))))) # label(fact_1_hoare__valids__def) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 63 (all X_b all Ga all Pa all Qa all Procsa (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),semilattice_sup_sup(fun(hoare_2118899576triple(X_b),bool)),Ga),hAPP(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(pname,hoare_2118899576triple(X_b)),fun(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool)),image(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),pname),hoare_759811442triple(X_b)),Pa)),body)),Qa)),Procsa))),hAPP(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(pname,hoare_2118899576triple(X_b)),fun(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool)),image(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),pname),hoare_759811442triple(X_b)),Pa)),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body_1))),Qa)),Procsa))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(pname,hoare_2118899576triple(X_b)),fun(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool)),image(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),pname),hoare_759811442triple(X_b)),Pa)),body)),Qa)),Procsa))))) # label(fact_2_hoare__derivs_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 64 (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].
% 1.87/2.28 65 (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].
% 1.87/2.28 66 (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].
% 1.87/2.28 67 (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].
% 1.87/2.28 68 (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].
% 1.87/2.28 69 (all X_c all X_b all F1 all Fun1 all Com_1 all Fun2 hAPP(hoare_2118899576triple(X_c),X_b,hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b),hoare_1759541758le_rec(X_c,X_b),F1),hAPP(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hoare_759811442triple(X_c),Fun1),Com_1),Fun2)) = hAPP(fun(X_c,fun(state,bool)),X_b,hAPP(com,fun(fun(X_c,fun(state,bool)),X_b),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b)),F1,Fun1),Com_1),Fun2)) # label(fact_8_triple_Orecs) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 70 (all X_c all X_b all F1 all Fun1 all Com_1 all Fun2 hAPP(hoare_2118899576triple(X_c),X_b,hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b),hoare_225284258e_case(X_c,X_b),F1),hAPP(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hoare_759811442triple(X_c),Fun1),Com_1),Fun2)) = hAPP(fun(X_c,fun(state,bool)),X_b,hAPP(com,fun(fun(X_c,fun(state,bool)),X_b),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b)),F1,Fun1),Com_1),Fun2)) # label(fact_9_triple_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 71 (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].
% 1.87/2.28 72 (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].
% 1.87/2.28 73 (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].
% 1.87/2.28 74 (all X_b all Ga all G_1 all Ts (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),G_1),Ts)) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),G_1)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts))))) # label(fact_13_cut) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 75 (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].
% 1.87/2.28 76 (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].
% 1.87/2.28 77 (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].
% 1.87/2.28 78 (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].
% 1.87/2.28 79 (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].
% 1.87/2.28 80 (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].
% 1.87/2.28 81 (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].
% 1.87/2.28 82 (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].
% 1.87/2.28 83 (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].
% 1.87/2.28 84 (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].
% 1.87/2.28 85 (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].
% 1.87/2.28 86 (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].
% 1.87/2.28 87 (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].
% 1.87/2.28 88 (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].
% 1.87/2.28 89 (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].
% 1.87/2.28 90 (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].
% 1.87/2.28 91 (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].
% 1.87/2.28 92 (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].
% 1.87/2.28 93 (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].
% 1.87/2.28 94 (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].
% 1.87/2.28 95 (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].
% 1.87/2.28 96 (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].
% 1.87/2.28 97 (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].
% 1.87/2.28 98 (all X_b all A_3 all B_2 all C_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),C_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3))) # label(fact_37_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 99 (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].
% 1.87/2.28 100 (all X_b all A_3 all B_2 all C_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),C_3))) # label(fact_39_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 101 (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].
% 1.87/2.28 102 (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].
% 1.87/2.28 103 (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].
% 1.87/2.28 104 (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].
% 1.87/2.28 105 (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].
% 1.87/2.28 106 (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].
% 1.87/2.28 107 (all X_b all R_1 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_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S_1)),X)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),R_1),S_1))))) # label(fact_46_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 108 (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].
% 1.87/2.28 109 (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].
% 1.87/2.28 110 (all X_b all N_1 all Pa all Pn_1 all Qa (hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N_1),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn_1))),Qa))) <-> hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),hAPP(nat,nat,suc,N_1)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(pname,com,body,Pn_1)),Qa))))) # label(fact_49_Body__triple__valid__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 111 (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_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1_1),Com_2),Fun2_1))) # label(fact_50_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 112 (all X_b all Pn_1 all Ga all Pa all Qa all Procsa (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),semilattice_sup_sup(fun(hoare_2118899576triple(X_b),bool)),Ga),hAPP(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(pname,hoare_2118899576triple(X_b)),fun(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool)),image(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),pname),hoare_759811442triple(X_b)),Pa)),body)),Qa)),Procsa))),hAPP(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool),hAPP(fun(pname,hoare_2118899576triple(X_b)),fun(fun(pname,bool),fun(hoare_2118899576triple(X_b),bool)),image(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_2118899576triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),pname),hoare_759811442triple(X_b)),Pa)),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body_1))),Qa)),Procsa))) -> (hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),Pn_1),Procsa)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(pname,fun(X_b,fun(state,bool)),Pa,Pn_1)),hAPP(pname,com,body,Pn_1)),hAPP(pname,fun(X_b,fun(state,bool)),Qa,Pn_1))),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))))) # label(fact_51_Body1) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 113 (all X_c all X_b all F all G all M_5 all N_3 (ti(fun(X_b,bool),M_5) = ti(fun(X_b,bool),N_3) -> ((all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),N_3)) -> hAPP(X_b,X_c,F,X) = hAPP(X_b,X_c,G,X))) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),M_5) = hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),G),N_3)))) # label(fact_52_image__cong) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 114 (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].
% 1.87/2.28 115 (all X_b all Pa all Pn_1 all Qa hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),zero_zero(nat)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(pname,com,body,Pn_1)),Qa)))) # label(fact_54_Body__triple__valid__0) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 116 (all Pname_3 all Pname (hAPP(pname,com,body,Pname_3) = hAPP(pname,com,body,Pname) <-> ti(pname,Pname_3) = ti(pname,Pname))) # label(fact_55_com_Osimps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 117 (all Pn all S0 all S1_2 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn))),S0),S1_2)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(pname,com,body,Pn)),S0),S1_2)))) # label(fact_56_evalc_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 118 (all P all S all S1_2 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(pname,com,body,P)),S),S1_2)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,P))),S),S1_2)))) # label(fact_57_evalc__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 119 (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].
% 1.87/2.28 120 (all X_b all N_1 all Ts ((all X (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),bool),member(hoare_2118899576triple(X_b)),X),Ts)) -> hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),hAPP(nat,nat,suc,N_1)),X)))) -> (all X (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),bool),member(hoare_2118899576triple(X_b)),X),Ts)) -> hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N_1),X)))))) # label(fact_59_triples__valid__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 121 (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_60_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 122 (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_61_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 123 (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_62_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 124 (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_63_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 125 (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_64_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 126 (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_65_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 127 (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_66_empty__def) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 128 (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_67_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 129 (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_68_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 130 (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_69_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 131 (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_70_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 132 (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_71_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 133 (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_72_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 134 (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_73_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.28 135 (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].
% 1.87/2.28 136 (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].
% 1.87/2.28 137 (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].
% 1.87/2.29 138 (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_77_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 139 (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_78_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 140 (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_79_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 141 (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_80_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 142 (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_81_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 143 (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_82_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 144 (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_83_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 145 (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_84_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 146 (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_85_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 147 (all X_b all A_2 all B_1 all C_1 all D (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_1),bot_bot(fun(X_b,bool)))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),D),bot_bot(fun(X_b,bool)))) <-> ti(X_b,A_2) = ti(X_b,C_1) & ti(X_b,B_1) = ti(X_b,D) | ti(X_b,A_2) = ti(X_b,D) & ti(X_b,B_1) = ti(X_b,C_1))) # label(fact_86_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 148 (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_87_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 149 (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_88_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 150 (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_89_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 151 (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_90_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 152 (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_91_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 153 (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_92_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 154 (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_93_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 155 (all U_1 all C all S all T_3 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C),S),T_3)) -> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C),S),U_1)) -> U_1 = T_3))) # label(fact_94_com__det) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 156 (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_95_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 157 (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_96_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 158 (all X_b all Ga all T_4 all Ts (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),T_4),Ts))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),T_4),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) & hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts)))) # label(fact_97_derivs__insertD) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 159 (all X_b all Ts all Ga all T_4 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),T_4),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),T_4),Ts)))))) # label(fact_98_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 160 (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_99_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 161 (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_100_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 162 (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_101_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 163 (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_102_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 164 (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_103_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 165 (all X_b all A_2 all B_2 all C_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)),C_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3))) # label(fact_104_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 166 (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_105_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 167 (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_106_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 168 (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_107_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 169 (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_108_ball__empty) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 170 (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_109_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 171 (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_110_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 172 (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_111_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 173 (all X_b all Ga all Pa all C_1 all Qa all C_3 ((hBOOL(C_3) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(bool,fun(X_b,fun(state,bool)),hAPP(fun(X_b,fun(bool,fun(state,bool))),fun(bool,fun(X_b,fun(state,bool))),combc(X_b,bool,fun(state,bool)),hAPP(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(bool,fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(bool,fun(state,bool))),fun(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(bool,fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X_b),combc(state,bool,bool)),hAPP(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),Pa))),C_3)),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))) # label(fact_112_constant) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 174 (all X_b all Ga hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) # label(fact_113_empty) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 175 (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_114_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 176 (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_115_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 177 (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_116_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 178 (all X_a all N_2 all T_3 (hBOOL(hAPP(hoare_2118899576triple(X_a),bool,hAPP(nat,fun(hoare_2118899576triple(X_a),bool),hoare_1942962616_valid(X_a),hAPP(nat,nat,suc,N_2)),T_3)) -> hBOOL(hAPP(hoare_2118899576triple(X_a),bool,hAPP(nat,fun(hoare_2118899576triple(X_a),bool),hoare_1942962616_valid(X_a),N_2),T_3)))) # label(fact_117_triple__valid__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 179 (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_118_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 180 (all X_b all Ga all Pa all Pn_1 all Qa (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn_1))),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(pname,com,body,Pn_1)),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))) # label(fact_119_weak__Body) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 181 (all X_b all Pa all Pn_1 all Qa all Ga (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(pname,com,body,Pn_1)),Qa)),Ga)),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn_1))),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(pname,com,body,Pn_1)),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))) # label(fact_120_BodyN) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 182 (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_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(fun(state,bool),fun(X_b,fun(state,bool)),combk(fun(state,bool),X_b),hAPP(state,fun(state,bool),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),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_2118899576triple(X_b),bool))))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))) # label(fact_121_escape) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 183 (all X_b all Pa all Ga all P_1 all C_1 all Qa (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),P_1),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> ((all Z_3 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_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))))) # label(fact_122_conseq1) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 184 (all X_b all Qa all Ga all Pa all C_1 all Q_1 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Q_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> ((all Z_3 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_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))))) # label(fact_123_conseq2) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 185 (all X_b all Fa all Fun1 all Com_1 all Fun2 hAPP(hoare_2118899576triple(X_b),nat,hAPP(fun(X_b,nat),fun(hoare_2118899576triple(X_b),nat),hoare_2043812435e_size(X_b),Fa),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1),Com_1),Fun2)) = zero_zero(nat)) # label(fact_124_triple_Osize_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 186 (all C_1 hAPP(com,hoare_2118899576triple(state),hoare_Mirabelle_MGT,C_1) = hAPP(fun(state,fun(state,bool)),hoare_2118899576triple(state),hAPP(com,fun(fun(state,fun(state,bool)),hoare_2118899576triple(state)),hAPP(fun(state,fun(state,bool)),fun(com,fun(fun(state,fun(state,bool)),hoare_2118899576triple(state))),hoare_759811442triple(state),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].
% 1.87/2.29 187 (all X_b all Fun1 all Com_1 all Fun2 hAPP(hoare_2118899576triple(X_b),nat,size_size(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1),Com_1),Fun2)) = zero_zero(nat)) # label(fact_126_triple_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 188 (all X_b all Qa all Pa all Ga all P_1 all C_1 all Q_1 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),P_1),C_1),Q_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> ((all Z_3 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_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))))) # label(fact_127_conseq12) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 189 (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].
% 1.87/2.29 190 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_129_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 191 (all N_2 N_2 != hAPP(nat,nat,suc,N_2)) # label(fact_131_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 192 (all N_2 hAPP(nat,nat,suc,N_2) != N_2) # label(fact_132_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 193 (all Nat all Nat_4 (hAPP(nat,nat,suc,Nat) = hAPP(nat,nat,suc,Nat_4) <-> Nat = Nat_4)) # label(fact_133_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 194 (all X_1 all Y (hAPP(nat,nat,suc,X_1) = hAPP(nat,nat,suc,Y) -> X_1 = Y)) # label(fact_134_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 195 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_135_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 196 (all Nat_3 zero_zero(nat) != hAPP(nat,nat,suc,Nat_3)) # label(fact_136_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 197 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_137_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 198 (all Nat_2 hAPP(nat,nat,suc,Nat_2) != zero_zero(nat)) # label(fact_138_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 199 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_139_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 200 (all N_2 (N_2 != zero_zero(nat) -> (exists M_2 N_2 = hAPP(nat,nat,suc,M_2)))) # label(fact_140_not0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 201 (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_141_nat__induct) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 202 (all Pa all K_1 (hBOOL(hAPP(nat,bool,Pa,K_1)) -> ((all N (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N))) -> hBOOL(hAPP(nat,bool,Pa,N)))) -> hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))))) # label(fact_142_zero__induct) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 203 (all Y (Y != zero_zero(nat) -> -(all Nat_1 Y != hAPP(nat,nat,suc,Nat_1)))) # label(fact_143_nat_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 204 (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_144_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 205 (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_145_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 206 (all Pn all S0 all N_2 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,hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn))),S0),N_2),S1_2)) -> hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(pname,com,body,Pn)),S0),hAPP(nat,nat,suc,N_2)),S1_2)))) # label(fact_146_evaln_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 207 (all X_b all Ga all Pa hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),skip),Pa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))) # label(fact_147_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 208 (all X_b all Ga all Pa all B_1 all C_1 hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(fun(state,bool),fun(X_b,fun(state,bool)),hAPP(fun(X_b,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(X_b,fun(state,bool))),combc(X_b,fun(state,bool),fun(state,bool)),hAPP(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),X_b),combs(state,bool,bool)),hAPP(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),Pa))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),B_1))),hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),Pa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))) # label(fact_148_LoopF) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 209 (all C_1 all N_1 all B_1 all S_2 (-hBOOL(hAPP(state,bool,B_1,S_2)) -> hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S_2),N_1),S_2)))) # label(fact_149_evaln_OWhileFalse) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 210 (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_150_evaln_OWhileTrue) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 211 (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_151_evalc_OWhileTrue) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 212 (all C_1 all B_1 all S_2 (-hBOOL(hAPP(state,bool,B_1,S_2)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S_2),S_2)))) # label(fact_152_evalc_OWhileFalse) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 213 (all S 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),N_2),S))) # label(fact_153_evaln_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 214 (all S all N_2 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,skip),S),N_2),T_3)) -> T_3 = S)) # label(fact_154_evaln__elim__cases_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 215 (all S all T_3 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,skip),S),T_3)) -> T_3 = S)) # label(fact_155_evalc__elim__cases_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 216 (all S hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,skip),S),S))) # label(fact_156_evalc_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 217 (all Fun all Com skip != hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com)) # label(fact_157_com_Osimps_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 218 (all Fun all Com hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com) != skip) # label(fact_158_com_Osimps_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 219 (all Fun_1 all Com_1 all Fun all Com (hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1) = hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com) <-> Fun_1 = Fun & Com_1 = Com)) # label(fact_159_com_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 220 (all C all S 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),N_2),S_5)) -> hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C),S),hAPP(nat,nat,suc,N_2)),S_5)))) # label(fact_160_evaln__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 221 (all C all S all N_2 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,C),S),N_2),T_3)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C),S),T_3)))) # label(fact_161_evaln__evalc) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 222 (all C_1 all S_2 all T_4 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S_2),T_4)) <-> (exists N hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C_1),S_2),N),T_4))))) # label(fact_162_eval__eq) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 223 (all Pname all Fun_1 all Com_1 hAPP(pname,com,body,Pname) != hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1)) # label(fact_163_com_Osimps_I59_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 224 (all Fun_1 all Com_1 all Pname hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1) != hAPP(pname,com,body,Pname)) # label(fact_164_com_Osimps_I58_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 225 (all Pname_2 skip != hAPP(pname,com,body,Pname_2)) # label(fact_165_com_Osimps_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 226 (all Pname_2 hAPP(pname,com,body,Pname_2) != skip) # label(fact_166_com_Osimps_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 227 (all X_b all N_1 all Pa all C_1 all Qa (hBOOL(hAPP(hoare_2118899576triple(X_b),bool,hAPP(nat,fun(hoare_2118899576triple(X_b),bool),hoare_1942962616_valid(X_b),N_1),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa))) <-> (all Z_3 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_167_triple__valid__def2) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 228 (all P all S all N_2 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,hAPP(pname,com,body,P)),S),N_2),S1_2)) -> -(all N (N_2 = hAPP(nat,nat,suc,N) -> -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,P))),S),N),S1_2)))))) # label(fact_168_evaln__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 229 (all B_1 all C_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(fun(state,bool),fun(com,com),while,B_1),C_1)),S_2),T_4)) -> ((T_4 = S_2 -> hBOOL(hAPP(state,bool,B_1,S_2))) -> -(hBOOL(hAPP(state,bool,B_1,S_2)) -> (all S1_1 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S_2),S1_1)) -> -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S1_1),T_4)))))))) # label(fact_169_evalc__WHILE__case) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 230 (all B_1 all C_1 all S_2 all N_1 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(fun(state,bool),fun(com,com),while,B_1),C_1)),S_2),N_1),T_4)) -> ((T_4 = S_2 -> hBOOL(hAPP(state,bool,B_1,S_2))) -> -(hBOOL(hAPP(state,bool,B_1,S_2)) -> (all S1_1 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C_1),S_2),N_1),S1_1)) -> -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S1_1),N_1),T_4)))))))) # label(fact_170_evaln__WHILE__case) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 231 (all C all S all T_3 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C),S),T_3)) -> (exists N hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C),S),N),T_3))))) # label(fact_171_evalc__evaln) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 232 (all X_b all D all R_1 all Ga all Pa all C_1 all Qa (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),C_1),Qa)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Qa),D),R_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(com,com,hAPP(com,fun(com,com),semi,C_1),D)),R_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))))) # label(fact_172_Comp) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 233 (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_173_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 234 (all X_c all X_b all Pa all Qa all Ga all P_1 all C0 all Q_1 all U_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),U_2)) -> ((all P_2 (hBOOL(hAPP(fun(hoare_2118899576triple(X_c),bool),bool,hAPP(fun(hoare_2118899576triple(X_c),bool),fun(fun(hoare_2118899576triple(X_c),bool),bool),hoare_1301688828derivs(X_c),Ga),hAPP(fun(hoare_2118899576triple(X_c),bool),fun(hoare_2118899576triple(X_c),bool),hAPP(hoare_2118899576triple(X_c),fun(fun(hoare_2118899576triple(X_c),bool),fun(hoare_2118899576triple(X_c),bool)),insert(hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hoare_759811442triple(X_c),hAPP(X_b,fun(X_c,fun(state,bool)),P_1,P_2)),hAPP(X_b,com,C0,P_2)),hAPP(X_b,fun(X_c,fun(state,bool)),Q_1,P_2))),bot_bot(fun(hoare_2118899576triple(X_c),bool))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_c),bool),bool,hAPP(fun(hoare_2118899576triple(X_c),bool),fun(fun(hoare_2118899576triple(X_c),bool),bool),hoare_1301688828derivs(X_c),Ga),hAPP(fun(hoare_2118899576triple(X_c),bool),fun(hoare_2118899576triple(X_c),bool),hAPP(hoare_2118899576triple(X_c),fun(fun(hoare_2118899576triple(X_c),bool),fun(hoare_2118899576triple(X_c),bool)),insert(hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hoare_759811442triple(X_c),hAPP(X_b,fun(X_c,fun(state,bool)),Pa,P_2)),hAPP(X_b,com,C0,P_2)),hAPP(X_b,fun(X_c,fun(state,bool)),Qa,P_2))),bot_bot(fun(hoare_2118899576triple(X_c),bool))))))) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_c),bool),bool,hAPP(fun(hoare_2118899576triple(X_c),bool),fun(fun(hoare_2118899576triple(X_c),bool),bool),hoare_1301688828derivs(X_c),Ga),hAPP(fun(X_b,bool),fun(hoare_2118899576triple(X_c),bool),hAPP(fun(X_b,hoare_2118899576triple(X_c)),fun(fun(X_b,bool),fun(hoare_2118899576triple(X_c),bool)),image(X_b,hoare_2118899576triple(X_c)),hAPP(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,hoare_2118899576triple(X_c)),hAPP(fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),fun(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,hoare_2118899576triple(X_c))),combs(X_b,fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_b,com),fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hAPP(fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),fun(fun(X_b,com),fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),combs(X_b,com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hAPP(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),fun(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))))),combb(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),X_b),hoare_759811442triple(X_c)),P_1)),C0)),Q_1)),U_2))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_c),bool),bool,hAPP(fun(hoare_2118899576triple(X_c),bool),fun(fun(hoare_2118899576triple(X_c),bool),bool),hoare_1301688828derivs(X_c),Ga),hAPP(fun(X_b,bool),fun(hoare_2118899576triple(X_c),bool),hAPP(fun(X_b,hoare_2118899576triple(X_c)),fun(fun(X_b,bool),fun(hoare_2118899576triple(X_c),bool)),image(X_b,hoare_2118899576triple(X_c)),hAPP(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,hoare_2118899576triple(X_c)),hAPP(fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),fun(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,hoare_2118899576triple(X_c))),combs(X_b,fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_b,com),fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hAPP(fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),fun(fun(X_b,com),fun(X_b,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),combs(X_b,com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hAPP(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)))),fun(fun(X_b,fun(X_c,fun(state,bool))),fun(X_b,fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))))),combb(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),X_b),hoare_759811442triple(X_c)),Pa)),C0)),Qa)),U_2))))))) # label(fact_174_finite__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 235 (all C2_1 all S2 all N2 all T2 all C1_1 all S1_2 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_2),N1),T1)) -> (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2_1),S2),N2),T2)) -> (exists N (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1_1),S1_2),N),T1)) & hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2_1),S2),N),T2))))))) # label(fact_175_evaln__max2) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 236 (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_176_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 237 (all C1_1 all S2 all C0_1 all S0 all N_2 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,C0_1),S0),N_2),S1_2)) -> (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1_1),S1_2),N_2),S2)) -> hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),semi,C0_1),C1_1)),S0),N_2),S2))))) # label(fact_177_evaln_OSemi) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 238 (all C1_1 all S2 all C0_1 all S0 all S1_2 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C0_1),S0),S1_2)) -> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1_1),S1_2),S2)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),semi,C0_1),C1_1)),S0),S2))))) # label(fact_178_evalc_OSemi) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 239 (all Com1_1 all Com2_1 all Com1 all Com2 (hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1) = hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2) <-> Com1_1 = Com1 & Com2_1 = Com2)) # label(fact_179_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.29 240 (all Com1_2 all Com2_2 all Pname_2 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2) != hAPP(pname,com,body,Pname_2)) # label(fact_180_com_Osimps_I48_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 241 (all Pname_2 all Com1_2 all Com2_2 hAPP(pname,com,body,Pname_2) != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2)) # label(fact_181_com_Osimps_I49_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 242 (all Fun all Com all Com1_1 all Com2_1 hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com) != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1)) # label(fact_182_com_Osimps_I47_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 243 (all Com1_1 all Com2_1 all Fun all Com hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1) != hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com)) # label(fact_183_com_Osimps_I46_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 244 (all Com1_3 all Com2_3 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_3),Com2_3) != skip) # label(fact_184_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 245 (all Com1_3 all Com2_3 skip != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_3),Com2_3)) # label(fact_185_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 246 (all C1_1 all C2_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(com,fun(com,com),semi,C1_1),C2_1)),S),T_3)) -> -(all S1_1 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1_1),S),S1_1)) -> -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C2_1),S1_1),T_3)))))) # label(fact_186_evalc__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 247 (all C1_1 all C2_1 all S all N_2 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),semi,C1_1),C2_1)),S),N_2),T_3)) -> -(all S1_1 (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1_1),S),N_2),S1_1)) -> -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2_1),S1_1),N_2),T_3)))))) # label(fact_187_evaln__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 248 (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_188_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 249 (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_189_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 250 (all X_b hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),bot_bot(fun(X_b,bool))))) # label(fact_190_finite_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 251 (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_191_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 252 (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].
% 1.87/2.30 253 (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].
% 1.87/2.30 254 (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_194_finite__code) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 255 (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_195_finite) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 256 (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_196_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 257 (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_197_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 258 (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_198_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 259 (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_5 exists A_4 (ti(fun(X_b,bool),A_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),A_5) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_5)))))) # label(fact_199_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 260 (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_200_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 261 (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_201_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 262 (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_202_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 263 (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_203_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 264 (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_204_image__eq__fold__image) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 265 (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_205_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 266 (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_206_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 267 (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_207_fold__image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 268 (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_208_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 269 (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_209_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 270 (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_210_comm__monoid__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 271 (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_211_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 272 (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_212_the__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 273 (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_213_the__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 274 (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].
% 1.87/2.30 275 (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_215_folding__image__simple__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 276 (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_216_folding__image__simple__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 277 (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_217_folding__image__simple__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 278 (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_218_comm__monoid__big_Oinfinite) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 279 (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_219_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 280 (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_220_folding__image__simple__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 281 (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_221_the__equality) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 282 (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_222_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 283 (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_223_comm__monoid__big_OF__cong) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 284 (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_224_theI) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 285 (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_225_the1__equality) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 286 (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_226_theI_H) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 287 (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].
% 1.87/2.30 288 (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].
% 1.87/2.30 289 (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].
% 1.87/2.30 290 (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_230_Sup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 291 (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_231_Sup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 292 (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_232_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 293 (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_233_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 294 (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_234_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 295 (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_235_inf1I) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 296 (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_236_IntI) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 297 (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_237_IntE) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 298 (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_238_inf1E) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 299 (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_239_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 300 (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_240_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 301 (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_241_finite__Int) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 302 (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_242_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 303 (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_243_inf__Sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 304 (all X_b all A_3 all B_2 all C_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),C_3))) # label(fact_244_Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 305 (all X_b all A_3 all B_2 all C_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),C_3))) # label(fact_245_Diff__Un) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 306 (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_246_Un__Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 307 (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_247_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 308 (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_248_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 309 (all X_b all R_1 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_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S_1)),X)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),R_1),S_1))))) # label(fact_249_inf__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 310 (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_250_Int__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 311 (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_251_inf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 312 (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_252_inf__idem) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 313 (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_253_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 314 (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_254_inf__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 315 (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_255_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 316 (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_256_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 317 (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_257_Int__commute) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 318 (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_258_inf_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 319 (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_259_inf__sup__aci_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 320 (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_260_inf__commute) # label(axiom) # label(non_clause). [assumption].
% 1.87/2.30 321 (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_261_Int__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 322 (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_262_inf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 323 (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_263_inf__sup__aci_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 324 (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_264_inf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 325 (all X_b all A_3 all B_2 all C_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),C_3))) # label(fact_265_Int__left__commute) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 326 (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_266_inf_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 327 (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_267_inf__sup__aci_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 328 (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_268_inf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 329 (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_269_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 330 (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_270_Int__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 331 (all X_b all C_3 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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),C_3),A_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),C_3),B_2))) # label(fact_271_Diff__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 332 (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_272_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 333 (all X_b all A_3 all B_2 all C_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),C_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_2),C_3))) # label(fact_273_Int__Diff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 334 (all X_b all A_3 all B_2 all C_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),C_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3))) # label(fact_274_Int__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 335 (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_275_inf_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 336 (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_276_inf__sup__aci_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 337 (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_277_inf__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 338 (all X_b all A_3 all B_2 all C_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),C_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),C_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3))) # label(fact_278_Diff__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 339 (all X_b all A_3 all C_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)),semilattice_inf_inf(fun(X_b,bool)),A_3),C_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),C_3)),B_2)) # label(fact_279_Diff__Int2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 340 (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_280_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 341 (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_281_inf__apply) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 342 (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_282_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 343 (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_283_IntD1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 344 (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_284_IntD2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 345 (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_285_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 346 (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_286_inf1D1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 347 (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_287_inf1D2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 348 (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_288_Inf__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 349 (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_289_Diff__triv) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 350 (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_290_Diff__disjoint) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 351 (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_291_inf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 352 (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_292_inf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 353 (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_293_inf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 354 (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_294_sup__inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 355 (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_295_inf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 356 (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_296_sup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 357 (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_297_inf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 358 (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_298_sup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 359 (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_299_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 360 (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_300_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 361 (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_301_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 362 (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_302_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 363 (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_303_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 364 (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_304_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 365 (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_305_Int__empty__left) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 366 (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_306_Int__empty__right) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 367 (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_307_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.30 368 (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_308_Un__Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 369 (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_309_Un__Diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 370 (all X_b all A_3 all B_2 all C_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),C_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),C_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_2),C_3))) # label(fact_310_Un__Diff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 371 (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_311_Int__insert__right) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 372 (all X_b all B_2 all A_2 all C_3 ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),C_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)),C_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),C_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)),C_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3)))) # label(fact_312_Int__insert__left) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 373 (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_313_insert__inter__insert) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 374 (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_314_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 375 (all X_b all B_2 all A_2 all C_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),C_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)),C_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3))) # label(fact_315_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 376 (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_316_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 377 (all X_b all B_2 all A_2 all C_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),C_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)),C_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3)))) # label(fact_317_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 378 (all X_b all A_3 all B_2 all C_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),C_3))) # label(fact_318_Int__Un__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 379 (all X_b all A_3 all B_2 all C_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),C_3))) # label(fact_319_Un__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 380 (all X_b all B_2 all C_3 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_3)),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),A_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),C_3),A_3))) # label(fact_320_Int__Un__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 381 (all X_b all B_2 all C_3 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_3)),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),A_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),C_3),A_3))) # label(fact_321_Un__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 382 (all X_b all A_3 all B_2 all C_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),C_3))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),C_3),A_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),C_3),A_3))) # label(fact_322_Un__Int__crazy) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 383 (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_323_Sup__fin_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 384 (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_324_Sup__fin_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 385 (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_325_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 386 (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_326_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 387 (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_327_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 388 (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_328_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 389 (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_329_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 390 (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_330_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 391 (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_331_Sup__fin_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 392 (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_332_Sup__fin_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 393 (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_333_Sup__fin_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 394 (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_334_Sup__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 395 (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_335_if__image__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 396 (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_336_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 397 (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_337_Sup__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 398 (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_338_Sup__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 399 (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_4 all A_5 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_5)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),A_5)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_5)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_5),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),bot_bot(fun(X_b,bool)))))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))))))) # label(fact_339_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 400 (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_340_distrib__imp1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 401 (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_341_distrib__imp2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 402 (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_342_folding__image__simple_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 403 (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_343_folding__image__simple_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 404 (all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N_2) = zero_zero(nat)) # label(fact_344_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 405 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat)) = M) # label(fact_345_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 406 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M) = zero_zero(nat)) # label(fact_346_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 407 (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_347_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 408 (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_348_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 409 (all M all N_2 all K_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N_2)),hAPP(nat,nat,suc,K_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)),K_2)) # label(fact_349_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 410 (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_350_folding__image__simple_Oempty) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 411 (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_351_folding__image__simple_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 412 (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_352_folding__image__simple_Oeq__fold__g) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 413 (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_353_folding__image__simple_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 414 (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_354_folding__image__simple_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 415 (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_355_folding__image__simple_Ounion__inter__neutral) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 416 (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_356_folding__image__simple_Oneutral) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 417 (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_357_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 418 (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_358_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 419 (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_359_diff__self) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 420 (all I all J_1 all K_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J_1)),K_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),K_2)),J_1)) # label(fact_360_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 421 (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_361_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 422 (all X_b (ab_group_add(X_b) -> (all A_2 all B_1 all C_1 all D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D) -> (ti(X_b,A_2) = ti(X_b,B_1) <-> ti(X_b,C_1) = ti(X_b,D)))))) # label(fact_362_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 423 (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_363_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 424 (all I_1 all Pa all K_1 (hBOOL(hAPP(nat,bool,Pa,K_1)) -> ((all N (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N))) -> hBOOL(hAPP(nat,bool,Pa,N)))) -> hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K_1),I_1)))))) # label(fact_364_zero__induct__lemma) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 425 (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_365_Inf__fin_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 426 (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_366_Inf__fin_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 427 (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_367_Inf__fin_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 428 (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_368_Inf__fin_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 429 (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_369_Inf__fin_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 430 (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_370_sup__Inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 431 (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_371_Inf__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 432 (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_372_Inf__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 433 (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_373_Inf__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 434 (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_374_Inf__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 435 (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_375_Inf__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 436 (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_376_Inf__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 437 (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_377_diff__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 438 (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_378_comp__fun__idem__remove) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 439 (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_379_card__insert) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 440 (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_380_comp__fun__idem_Ofun__left__idem) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 441 (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_381_comp__fun__idem__insert) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 442 (all X_b hAPP(fun(X_b,bool),nat,finite_card(X_b),bot_bot(fun(X_b,bool))) = zero_zero(nat)) # label(fact_382_card_Oempty) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 443 (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_383_card__infinite) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 444 (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_384_comp__fun__idem__sup) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 445 (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_385_comp__fun__idem__inf) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 446 (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].
% 2.10/2.31 447 (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].
% 2.10/2.31 448 (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].
% 2.10/2.31 449 (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_389_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 450 (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_390_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 451 (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].
% 2.10/2.31 452 (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].
% 2.10/2.31 453 (all X_b all A_3 all K_1 (hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(nat,nat,suc,K_1) <-> (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_1 & (K_1 = 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].
% 2.10/2.31 454 (all X_b all A_3 all K_1 (hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(nat,nat,suc,K_1) -> (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_1 & (K_1 = 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].
% 2.10/2.31 455 (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),hAPP(fun(X_b,bool),fun(X_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_395_card__Diff__singleton__if) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 456 (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_396_card__Diff__singleton) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 457 (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_397_card__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 458 (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_398_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 459 (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_400_diff__Suc__1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 460 (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_401_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 461 (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].
% 2.10/2.31 462 (all X_a (zero_neq_one(X_a) -> one_one(X_a) != zero_zero(X_a))) # label(fact_403_one__neq__zero) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 463 (all X_a (zero_neq_one(X_a) -> zero_zero(X_a) != one_one(X_a))) # label(fact_404_zero__neq__one) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 464 (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_405_card_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 465 (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_406_card_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 466 (all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N_2) = N_2) # label(fact_407_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 467 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),zero_zero(nat)) = M) # label(fact_408_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 468 (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_409_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.31 469 (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_410_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 470 (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_411_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 471 (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,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2))) # label(fact_412_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 472 (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,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N_2))) # label(fact_413_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 473 (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_414_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 474 (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_415_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 475 (all M all N_2 all K_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)),K_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K_2))) # label(fact_416_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 476 (all K_1 all M_1 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_1) <-> M_1 = N_1)) # label(fact_417_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 477 (all M_1 all K_1 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K_1) <-> M_1 = N_1)) # label(fact_418_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 478 (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_419_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 479 (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_420_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 480 (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_421_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 481 (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_422_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 482 (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_423_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 483 (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_424_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 484 (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_425_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 485 (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_426_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 486 (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_427_double__zero__sym) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 487 (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_428_add__0) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 488 (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_429_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 489 (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_430_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 490 (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_431_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 491 (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_432_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 492 (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_433_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 493 (all I all J_1 all K_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J_1)),K_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),K_2))) # label(fact_434_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 494 (all K_2 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_2),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),N_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)) # label(fact_435_diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 495 (all M all K_2 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_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)) # label(fact_436_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 496 (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_437_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 497 (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_438_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 498 (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_439_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 499 (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_440_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 500 (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_441_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 501 (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_442_card__Un__Int) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 502 (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_443_card_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 503 (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].
% 2.10/2.32 504 (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].
% 2.10/2.32 505 (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_446_card_Oeq__fold__g) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 506 (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_447_card__def) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 507 (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].
% 2.10/2.32 508 (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].
% 2.10/2.32 509 (all Com1_2 all Com2_2 hAPP(com,nat,com_size,hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,com_size,Com1_2)),hAPP(com,nat,com_size,Com2_2))),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_450_com_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 510 (all Fun_1 all Com_1 hAPP(com,nat,com_size,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,com_size,Com_1)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_451_com_Osize_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 511 (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_452_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 512 (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_453_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 513 (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_454_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 514 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),D_1))))) # label(fact_455_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 515 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),D_1)))) # label(fact_456_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 516 (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_457_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 517 (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_458_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 518 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))))) # label(fact_459_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 519 (all Pname_1 hAPP(com,nat,com_size,hAPP(pname,com,body,Pname_1)) = zero_zero(nat)) # label(fact_460_com_Osize_I7_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 520 (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_462_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 521 (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_463_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 522 (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].
% 2.10/2.32 523 (all Com1_2 all Com2_2 hAPP(com,nat,size_size(com),hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,size_size(com),Com1_2)),hAPP(com,nat,size_size(com),Com2_2))),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_465_com_Osize_I12_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 524 (all Fun_1 all Com_1 hAPP(com,nat,size_size(com),hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,size_size(com),Com_1)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_466_com_Osize_I14_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 525 (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_467_fold__Un__disjoint) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 526 (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_468_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 527 (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_469_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 528 (all K_2 all M all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),N_2))) # label(fact_470_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 529 (all M all N_2 all K_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)),K_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_2))) # label(fact_471_add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 530 (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_472_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 531 (all X_a (semiring(X_a) -> (all A_1 all E_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),times_times(X_a),A_1),E_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),E_1)),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),E_1)),C)))) # label(fact_473_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 532 (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_474_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 533 (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_475_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 534 (all X_a (comm_semiring(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_476_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 535 (all X_b (semiri456707255roduct(X_b) -> (all C_1 all D 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) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_1),D)) != hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),D)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_1),C_1)))))) # label(fact_477_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 536 (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_478_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 537 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_1) = zero_zero(X_a)))) # label(fact_479_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 538 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_480_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 539 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)))) # label(fact_481_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 540 (all X_a (comm_semiring_1(X_a) -> (all Lx all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ry))))) # label(fact_482_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 541 (all X_a (comm_semiring_1(X_a) -> (all Lx all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ry)))) # label(fact_483_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 542 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Rx))))) # label(fact_484_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 543 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ly)))) # label(fact_485_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 544 (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),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)))))) # label(fact_486_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 545 (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),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Ry))))) # label(fact_487_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 546 (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_488_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 547 (all M_1 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1) = one_one(nat) <-> M_1 = one_one(nat) & N_1 = one_one(nat))) # label(fact_489_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 548 (all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),one_one(nat)) = N_2) # label(fact_490_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 549 (all M_1 all N_1 (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1) <-> M_1 = one_one(nat) & N_1 = one_one(nat))) # label(fact_491_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 550 (all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N_2) = N_2) # label(fact_492_nat__mult__1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 551 (all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),N_2) = zero_zero(nat)) # label(fact_493_mult__0) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 552 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),zero_zero(nat)) = zero_zero(nat)) # label(fact_494_mult__0__right) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 553 (all M_1 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1) = zero_zero(nat) <-> M_1 = zero_zero(nat) | N_1 = zero_zero(nat))) # label(fact_495_mult__is__0) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 554 (all K_1 all M_1 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1) <-> M_1 = N_1 | K_1 = zero_zero(nat))) # label(fact_496_mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 555 (all M_1 all K_1 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K_1) <-> M_1 = N_1 | K_1 = zero_zero(nat))) # label(fact_497_mult__cancel2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 556 (all K_1 all M_1 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_1) <-> M_1 = N_1)) # label(fact_498_Suc__mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 557 (all X_a (ab_sem1668676832m_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1) = ti(X_a,A_1)))) # label(fact_499_times_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 558 (all X_a (ab_sem1668676832m_mult(X_a) -> (all X_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1) = ti(X_a,X_1)))) # label(fact_500_mult__idem) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 559 (all X_a (ab_sem1668676832m_mult(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))) # label(fact_501_mult__left__idem) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 560 (all X_a (ab_semigroup_mult(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),times_times(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))) # label(fact_502_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 561 (all M all N_2 all K_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)),K_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_2))) # label(fact_503_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 562 (all K_2 all M all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),N_2))) # label(fact_504_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 563 (all X_a (mult_zero(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_1) = zero_zero(X_a)))) # label(fact_505_mult__zero__left) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 564 (all X_a (mult_zero(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_506_mult__zero__right) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 565 (all X_b (ring_n68954251visors(X_b) -> (all A_2 all B_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_1) = zero_zero(X_b) <-> ti(X_b,A_2) = zero_zero(X_b) | ti(X_b,B_1) = zero_zero(X_b))))) # label(fact_507_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 566 (all X_a (no_zero_divisors(X_a) -> (all B all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) != zero_zero(X_a)))))) # label(fact_508_no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 567 (all X_a (no_zero_divisors(X_a) -> (all A_1 all B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) = zero_zero(X_a) -> ti(X_a,A_1) = zero_zero(X_a) | ti(X_a,B) = zero_zero(X_a))))) # label(fact_509_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 568 (all X_a (monoid_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_510_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 569 (all X_a (comm_monoid_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_511_mult__1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 570 (all X_a (monoid_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)))) # label(fact_512_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 571 (all X_a (comm_monoid_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)))) # label(fact_513_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 572 (all X_b (ab_sem1668676832m_mult(X_b) -> hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),times_times(X_b))))) # label(fact_514_comp__fun__idem) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 573 (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_515_finite__PlusD_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 574 (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_516_finite__PlusD_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 575 (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_517_finite__Plus) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 576 (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_518_finite__Plus__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 577 (all X_b (linord581940658strict(X_b) -> (all X_2 all Y_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),X_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_1),Y_1)) = zero_zero(X_b) <-> ti(X_b,X_2) = zero_zero(X_b) & ti(X_b,Y_1) = zero_zero(X_b))))) # label(fact_519_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 578 (all X_a (semiri456707255roduct(X_a) -> (all C all D_1 all A_1 all B all R_2 (ti(X_a,R_2) != zero_zero(X_a) -> (ti(X_a,A_1) = ti(X_a,B) & ti(X_a,C) != ti(X_a,D_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_2),C)) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_2),D_1))))))) # label(fact_520_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 579 (all X_b (ring(X_b) -> (all A_2 all E all C_1 all B_1 all D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_1),E)),D) <-> ti(X_b,C_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_1),A_2)),E)),D))))) # label(fact_521_eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 580 (all X_b (ring(X_b) -> (all A_2 all E all C_1 all B_1 all D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_1),E)),D) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1)),E)),C_1) = ti(X_b,D))))) # label(fact_522_eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 581 (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_523_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 582 (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_524_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 583 (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_525_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 584 (all M_1 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1) = hAPP(nat,nat,suc,zero_zero(nat)) <-> M_1 = hAPP(nat,nat,suc,zero_zero(nat)) & N_1 = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_526_mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 585 (all M all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,M)),N_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2))) # label(fact_527_mult__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 586 (all M all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,suc,N_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2))) # label(fact_528_mult__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 587 (all M all N_2 (M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2) -> N_2 = one_one(nat) | M = zero_zero(nat))) # label(fact_529_mult__eq__self__implies__10) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 588 (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_530_fold__image__insert) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 589 (all Pname_1 hAPP(com,nat,size_size(com),hAPP(pname,com,body,Pname_1)) = zero_zero(nat)) # label(fact_531_com_Osize_I15_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 590 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,X_c)),combs(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combb(X_c,fun(X_c,X_c),X_b),times_times(X_c)),G)),H)),one_one(X_c)),A_3) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),one_one(X_c)),A_3)),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),H),one_one(X_c)),A_3)))))) # label(fact_532_fold__image__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 591 (all N_2 all M ((M = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2) = zero_zero(nat)) & (M != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N_2))))) # label(fact_534_mult__eq__if) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 592 (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_535_card__Plus) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 593 (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(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),one_one(X_c)),A_3)),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),one_one(X_c)),B_2)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),one_one(X_c)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2))),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),one_one(X_c)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)))))))) # label(fact_536_fold__image__Un__Int) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 594 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all T_5 all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),T_5)) -> ((all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),S_1),T_5))) -> hAPP(X_b,X_c,F,X) = one_one(X_c))) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),F),one_one(X_c)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),S_1),T_5)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),F),one_one(X_c)),S_1)),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),F),one_one(X_c)),T_5)))))))) # label(fact_537_fold__image__Un__one) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 595 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> ((all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),S_1)) -> hAPP(X_b,X_c,F,X) = one_one(X_c))) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),F),one_one(X_c)),S_1) = one_one(X_c)))))) # label(fact_538_fold__image__1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 596 (all X_b all X_c (ab_semigroup_mult(X_c) -> (all Z_1 all G all H all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3)) -> hAPP(X_b,X_c,G,X) = hAPP(X_b,X_c,H,X))) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_1),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),H),Z_1),A_3)))))) # label(fact_539_fold__image__cong) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 597 (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_540_Plus__eq__empty__conv) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 598 (all M all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),M)) # label(fact_541_nat__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 599 (all M all N_2 all K_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_2)),K_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_2))) # label(fact_542_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 600 (all I all U_1 all J_1 all K_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U_1)),K_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_1)),U_1)),K_2)) # label(fact_543_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 601 (all K_1 all M_1 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1) <-> K_1 = zero_zero(nat) | M_1 = N_1)) # label(fact_544_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 602 (all X_c all X_b all X_d (comm_monoid_mult(X_d) -> (all E all G all F all H all K_1 all T_5 all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> ((all Y_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Y_2),T_5)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_c,X_b,K_1,Y_2)),S_1)) & hAPP(X_b,X_c,H,hAPP(X_c,X_b,K_1,Y_2)) = ti(X_c,Y_2))) -> ((all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),S_1)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,H,X)),T_5)) & hAPP(X_c,X_b,K_1,hAPP(X_b,X_c,H,X)) = ti(X_b,X) & hAPP(X_c,X_d,G,hAPP(X_b,X_c,H,X)) = hAPP(X_b,X_d,F,X))) -> hAPP(fun(X_b,bool),X_d,hAPP(X_d,fun(fun(X_b,bool),X_d),hAPP(fun(X_b,X_d),fun(X_d,fun(fun(X_b,bool),X_d)),hAPP(fun(X_d,fun(X_d,X_d)),fun(fun(X_b,X_d),fun(X_d,fun(fun(X_b,bool),X_d))),finite_fold_image(X_d,X_b),times_times(X_d)),F),E),S_1) = hAPP(fun(X_c,bool),X_d,hAPP(X_d,fun(fun(X_c,bool),X_d),hAPP(fun(X_c,X_d),fun(X_d,fun(fun(X_c,bool),X_d)),hAPP(fun(X_d,fun(X_d,X_d)),fun(fun(X_c,X_d),fun(X_d,fun(fun(X_c,bool),X_d))),finite_fold_image(X_d,X_c),times_times(X_d)),G),E),T_5))))))) # label(fact_545_fold__image__eq__general__inverses) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 603 (all X_c all X_b (comm_monoid_mult(X_b) -> (all H all G all S_1 all R_1 all E (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,E),E)) -> ((all X1 all Y1 all X2 all Y2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,X1),X2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,Y1),Y2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X1),Y1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X2),Y2))))) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),S_1)) -> ((all X (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X),S_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_c,X_b,H,X)),hAPP(X_c,X_b,G,X))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),H),E),S_1)),hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),G),E),S_1)))))))))) # label(fact_546_fold__image__related) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 604 (all X_b (ab_semigroup_mult(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,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),B_2)))))))))) # label(fact_547_fold1__Un) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 605 (all Fun_1 all Com1_1 all Com2_1 hAPP(com,nat,size_size(com),hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,size_size(com),Com1_1)),hAPP(com,nat,size_size(com),Com2_1))),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_548_com_Osize_I13_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 606 (all Fun_1 all Com1_1 all Com2_1 hAPP(com,nat,com_size,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(com,nat,com_size,Com1_1)),hAPP(com,nat,com_size,Com2_1))),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_549_com_Osize_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 607 (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(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))) # label(fact_550_card__Diff1__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 608 (all X_a (preorder(X_a) -> (all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),X_1))))) # label(fact_551_order__refl) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 609 (all K_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),K_1))))) # label(fact_552_finite__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 610 (all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N_2))) # label(fact_553_le0) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 611 (all B_1 all C1 all C2 all S_2 all N_1 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),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C1),C2)),S_2),N_1),T_4)) -> ((hBOOL(hAPP(state,bool,B_1,S_2)) -> -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1),S_2),N_1),T_4))) -> -(-hBOOL(hAPP(state,bool,B_1,S_2)) -> -hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C2),S_2),N_1),T_4)))))) # label(fact_554_evaln__elim__cases_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 612 (all C1 all C0 all N_1 all S1 all B_1 all S_2 (hBOOL(hAPP(state,bool,B_1,S_2)) -> (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C0),S_2),N_1),S1)) -> hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C0),C1)),S_2),N_1),S1))))) # label(fact_555_evaln_OIfTrue) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 613 (all C0 all C1 all N_1 all S1 all B_1 all S_2 (-hBOOL(hAPP(state,bool,B_1,S_2)) -> (hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C1),S_2),N_1),S1)) -> hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C0),C1)),S_2),N_1),S1))))) # label(fact_556_evaln_OIfFalse) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.32 614 (all C0 all C1 all S1 all B_1 all S_2 (-hBOOL(hAPP(state,bool,B_1,S_2)) -> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1),S_2),S1)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C0),C1)),S_2),S1))))) # label(fact_557_evalc_OIfFalse) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 615 (all C1 all C0 all S1 all B_1 all S_2 (hBOOL(hAPP(state,bool,B_1,S_2)) -> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C0),S_2),S1)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C0),C1)),S_2),S1))))) # label(fact_558_evalc_OIfTrue) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 616 (all B_1 all C1 all C2 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),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,B_1),C1),C2)),S_2),T_4)) -> ((hBOOL(hAPP(state,bool,B_1,S_2)) -> -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1),S_2),T_4))) -> -(-hBOOL(hAPP(state,bool,B_1,S_2)) -> -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C2),S_2),T_4)))))) # label(fact_559_evalc__elim__cases_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 617 (all Pname all Fun_1 all Com1_1 all Com2_1 hAPP(pname,com,body,Pname) != hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1)) # label(fact_560_com_Osimps_I55_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 618 (all Fun_1 all Com1_1 all Com2_1 all Pname hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1) != hAPP(pname,com,body,Pname)) # label(fact_561_com_Osimps_I54_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 619 (all X_a (linorder(X_a) -> (all X_1 all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X_1)))))) # label(fact_562_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 620 (all X_b all X_c (ord(X_c) -> (all X_2 all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2))))))) # label(fact_563_le__funE) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 621 (all X_a (order(X_a) -> (all Z all Y all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X_1))))))) # label(fact_564_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 622 (all X_a (order(X_a) -> (all Y all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y)) -> ti(X_a,X_1) = ti(X_a,Y)))))) # label(fact_565_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 623 (all X_a (preorder(X_a) -> (all Z all X_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z))))))) # label(fact_566_order__trans) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 624 (all X_a (order(X_a) -> (all X_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X_1)) -> ti(X_a,X_1) = ti(X_a,Y)))))) # label(fact_567_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 625 (all X_a (order(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1))))))) # label(fact_568_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 626 (all X_a (ord(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (B = C -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_569_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 627 (all X_a (order(X_a) -> (all C all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1))))))) # label(fact_570_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 628 (all X_a (ord(X_a) -> (all C all A_1 all B (A_1 = B -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_571_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 629 (all X_b (order(X_b) -> (all Y_1 all X_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_1)) <-> ti(X_b,X_2) = ti(X_b,Y_1)))))) # label(fact_572_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 630 (all X_b all X_c (ord(X_c) -> (all X_2 all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2))))))) # label(fact_573_le__funD) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 631 (all X_a (preorder(X_a) -> (all X_1 all Y (X_1 = Y -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y)))))) # label(fact_574_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 632 (all X_b (order(X_b) -> (all X_2 all Y_1 (ti(X_b,X_2) = ti(X_b,Y_1) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_1)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_2)))))) # label(fact_575_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 633 (all X_a (linorder(X_a) -> (all X_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X_1)))))) # label(fact_576_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 634 (all X_b all X_c (ord(X_c) -> (all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) <-> (all X hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X)),hAPP(X_b,X_c,G,X)))))))) # label(fact_577_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 635 (all Fun_1 all Com1_1 all Com2_1 all Fun all Com1 all Com2 (hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1) = hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun),Com1),Com2) <-> Fun_1 = Fun & Com1_1 = Com1 & Com2_1 = Com2)) # label(fact_578_com_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 636 (all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),M)) -> M = N_2))) # label(fact_579_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 637 (all K_2 all I all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),K_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),K_2))))) # label(fact_580_le__trans) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 638 (all M all N_2 (M = N_2 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_2)))) # label(fact_581_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 639 (all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_2)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),M)))) # label(fact_582_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 640 (all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),N_2))) # label(fact_583_le__refl) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 641 (all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_2)))) # label(fact_584_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 642 (all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N_2))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_2)) -> M = hAPP(nat,nat,suc,N_2)))) # label(fact_585_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 643 (all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N_2))))) # label(fact_586_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 644 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),hAPP(nat,nat,suc,M_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)))) # label(fact_587_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 645 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,suc,N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) | M_1 = hAPP(nat,nat,suc,N_1))) # label(fact_588_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 646 (all M_1 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),M_1)))) # label(fact_589_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 647 (all N_2 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_2)),N_2))) # label(fact_590_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 648 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),zero_zero(nat))) <-> N_1 = zero_zero(nat))) # label(fact_591_le__0__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 649 (all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N_2))) # label(fact_592_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 650 (all X_a (lattice(X_a) -> (all X_1 all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)),X_1))))) # label(fact_593_inf__sup__ord_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 651 (all X_a (semilattice_inf(X_a) -> (all X_1 all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)),X_1))))) # label(fact_594_inf__le1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 652 (all X_a (lattice(X_a) -> (all X_1 all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)),Y))))) # label(fact_595_inf__sup__ord_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 653 (all X_a (semilattice_inf(X_a) -> (all X_1 all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)),Y))))) # label(fact_596_inf__le2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 654 (all X_b (semilattice_inf(X_b) -> (all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_1)) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),X_2),Y_1) = ti(X_b,X_2))))) # label(fact_597_le__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 655 (all X_b (semilattice_inf(X_b) -> (all X_2 all Y_1 all Z_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),Y_1),Z_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_1)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Z_1)))))) # label(fact_598_le__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 656 (all X_a (semilattice_inf(X_a) -> (all B all A_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)),X_1)))))) # label(fact_599_le__infI1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 657 (all X_a (semilattice_inf(X_a) -> (all A_1 all B all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)),X_1)))))) # label(fact_600_le__infI2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 658 (all X_a (semilattice_inf(X_a) -> (all X_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y) = ti(X_a,X_1))))) # label(fact_601_inf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 659 (all X_a (semilattice_inf(X_a) -> (all Y all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y) = ti(X_a,Y))))) # label(fact_602_inf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 660 (all X_a (semilattice_inf(X_a) -> (all B all X_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)))))))) # label(fact_603_le__infI) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 661 (all X_a (semilattice_inf(X_a) -> (all Z all X_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(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_604_inf__greatest) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 662 (all X_a (semilattice_inf(X_a) -> (all B all D_1 all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),C),D_1)))))))) # label(fact_605_inf__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 663 (all X_a (semilattice_inf(X_a) -> (all X_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B))) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),A_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),B))))))) # label(fact_606_le__infE) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 664 (all X_a (lattice(X_a) -> (all X_1 all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(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)))))) # label(fact_607_inf__sup__ord_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 665 (all X_a (semilattice_sup(X_a) -> (all X_1 all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(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)))))) # label(fact_608_sup__ge1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 666 (all X_a (lattice(X_a) -> (all Y all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)))))) # label(fact_609_inf__sup__ord_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 667 (all X_a (semilattice_sup(X_a) -> (all Y all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)))))) # label(fact_610_sup__ge2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 668 (all X_b (semilattice_sup(X_b) -> (all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_1)) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),Y_1) = ti(X_b,Y_1))))) # label(fact_611_le__iff__sup) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 669 (all X_b (semilattice_sup(X_b) -> (all X_2 all Y_1 all Z_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),X_2),Y_1)),Z_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Z_1)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),Z_1)))))) # label(fact_612_le__sup__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 670 (all X_a (semilattice_sup(X_a) -> (all B all X_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B))))))) # label(fact_613_le__supI1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 671 (all X_a (semilattice_sup(X_a) -> (all A_1 all X_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B))))))) # label(fact_614_le__supI2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 672 (all X_a (semilattice_sup(X_a) -> (all X_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y) = ti(X_a,Y))))) # label(fact_615_sup__absorb2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 673 (all X_a (semilattice_sup(X_a) -> (all Y all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y) = ti(X_a,X_1))))) # label(fact_616_sup__absorb1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 674 (all X_a (semilattice_sup(X_a) -> (all B all A_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B)),X_1))))))) # label(fact_617_le__supI) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 675 (all X_a (semilattice_sup(X_a) -> (all Z all Y all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)),X_1))))))) # label(fact_618_sup__least) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 676 (all X_a (semilattice_sup(X_a) -> (all B all D_1 all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),C),D_1)))))))) # label(fact_619_sup__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 677 (all X_a (semilattice_sup(X_a) -> (all A_1 all B all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B)),X_1)) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X_1))))))) # label(fact_620_le__supE) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 678 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all B_1 all C_1 all D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),D))))))) # label(fact_621_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 679 (all M all C all S all N_2 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,C),S),N_2),T_3)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),M)) -> hBOOL(hAPP(state,bool,hAPP(nat,fun(state,bool),hAPP(state,fun(nat,fun(state,bool)),hAPP(com,fun(state,fun(nat,fun(state,bool))),evaln,C),S),M),T_3))))) # label(fact_622_evaln__nonstrict) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 680 (all M all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)),M))) # label(fact_623_diff__le__self) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 681 (all L all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M))))) # label(fact_624_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 682 (all L all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),L)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),L))))) # label(fact_625_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 683 (all I all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),N_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),I)) = I)) # label(fact_626_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 684 (all N_1 all K_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K_1) <-> M_1 = N_1)))) # label(fact_627_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 685 (all N_2 all K_2 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),N_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),K_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)))) # label(fact_628_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 686 (all N_1 all K_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))))) # label(fact_629_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 687 (all X_a (ordere236663937imp_le(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_630_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 688 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_631_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 689 (all X_a (ordere779506340up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_632_add__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 690 (all X_a (ordere779506340up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))))))) # label(fact_633_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 691 (all X_a (ordere779506340up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))))) # label(fact_634_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 692 (all X_b (ordere236663937imp_le(X_b) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_1)))))) # label(fact_635_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 693 (all X_b (ordere236663937imp_le(X_b) -> (all A_2 all C_1 all B_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_1),C_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_1)))))) # label(fact_636_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 694 (all M all K_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)),N_2)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_2)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),N_2))))) # label(fact_637_add__leE) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 695 (all M all K_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_2)))) # label(fact_638_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 696 (all M all K_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),N_2)))) # label(fact_639_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 697 (all K_2 all L all I all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),L)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),L)))))) # label(fact_640_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 698 (all K_2 all I all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),K_2))))) # label(fact_641_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 699 (all M all I all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J_1))))) # label(fact_642_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 700 (all M all I all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),M))))) # label(fact_643_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 701 (all K_1 all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))) # label(fact_644_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 702 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) <-> (exists K N_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K)))) # label(fact_645_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 703 (all N_2 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),M)))) # label(fact_646_le__add1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 704 (all N_2 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_2)))) # label(fact_647_le__add2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 705 (all N_1 hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),N_1))) = hAPP(nat,nat,suc,N_1)) # label(fact_648_card__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 706 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1)),N_1)))) # label(fact_649_less__eq__nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 707 (all X_b (semilattice_inf(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)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),semilattice_inf_inf(X_b)),A_3))) <-> (all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),X)))))))))) # label(fact_650_below__fold1__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 708 (all X_a (bot(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),bot_bot(X_a))) -> ti(X_a,A_1) = bot_bot(X_a))))) # label(fact_651_le__bot) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 709 (all X_b (bot(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),bot_bot(X_b))) <-> ti(X_b,A_2) = bot_bot(X_b))))) # label(fact_652_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 710 (all X_a (bot(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),bot_bot(X_a)),A_1))))) # label(fact_653_bot__least) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 711 (all X_b (semilattice_inf(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)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),semilattice_inf_inf(X_b)),A_3)),A_2))))))) # label(fact_654_fold1__belowI) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 712 (all K_2 all L all I all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),L)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),L)))))) # label(fact_655_mult__le__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 713 (all K_2 all I all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),I)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),J_1))))) # label(fact_656_mult__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 714 (all K_2 all I all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),K_2))))) # label(fact_657_mult__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 715 (all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M))))) # label(fact_658_le__cube) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 716 (all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M)))) # label(fact_659_le__square) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 717 (all Fun_1 all Com1_1 all Com2_1 all Fun all Com hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1) != hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com)) # label(fact_660_com_Osimps_I52_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 718 (all Fun all Com all Fun_1 all Com1_1 all Com2_1 hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com) != hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun_1),Com1_1),Com2_1)) # label(fact_661_com_Osimps_I53_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 719 (all Fun all Com1 all Com2 all Com1_1 all Com2_1 hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun),Com1),Com2) != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1)) # label(fact_662_com_Osimps_I45_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 720 (all Com1_1 all Com2_1 all Fun all Com1 all Com2 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1) != hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun),Com1),Com2)) # label(fact_663_com_Osimps_I44_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 721 (all Fun all Com1 all Com2 hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun),Com1),Com2) != skip) # label(fact_664_com_Osimps_I15_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 722 (all Fun all Com1 all Com2 skip != hAPP(com,com,hAPP(com,fun(com,com),hAPP(fun(state,bool),fun(com,fun(com,com)),cond,Fun),Com1),Com2)) # label(fact_665_com_Osimps_I14_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 723 (all X_b (linord219039673up_add(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),A_2)))))) # label(fact_666_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 724 (all X_b (linord219039673up_add(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),zero_zero(X_b))))))) # label(fact_667_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 725 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_668_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 726 (all X_b (ordere216010020id_add(X_b) -> (all Y_1 all X_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),X_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),Y_1)) -> (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),X_2),Y_1) = zero_zero(X_b) <-> ti(X_b,X_2) = zero_zero(X_b) & ti(X_b,Y_1) = zero_zero(X_b))))))) # label(fact_669_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 727 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_670_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 728 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_671_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 729 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_672_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 730 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a))))))) # label(fact_673_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 731 (all X_a (ordered_ring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))))) # label(fact_674_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 732 (all X_a (ordered_semiring(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1)))))))))) # label(fact_675_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 733 (all X_a (ordered_semiring(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1)))))))))) # label(fact_676_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 734 (all X_a (ordered_ring(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_677_mult__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 735 (all X_a (ordered_ring(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),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_678_mult__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 736 (all X_a (ordere1490568538miring(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_679_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 737 (all X_a (ordered_semiring(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_680_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 738 (all X_a (ordered_semiring(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),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_681_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 739 (all X_a (ordered_ring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_682_mult__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 740 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_683_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 741 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),zero_zero(X_a)))))))) # label(fact_684_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 742 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_685_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 743 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_686_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 744 (all X_b (linord581940658strict(X_b) -> (all A_2 all B_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_1)),zero_zero(X_b))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),A_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B_1),zero_zero(X_b))) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),zero_zero(X_b))) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),B_1)))))) # label(fact_687_mult__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 745 (all X_b (linord581940658strict(X_b) -> (all A_2 all B_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),A_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),B_1)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),zero_zero(X_b))) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B_1),zero_zero(X_b))))))) # label(fact_688_zero__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 746 (all X_a (linordered_ring(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)))))) # label(fact_689_zero__le__square) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 747 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all B_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1)),zero_zero(X_b))))))) # label(fact_690_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 748 (all X_a (linordered_semidom(X_a) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),zero_zero(X_a))))) # label(fact_691_not__one__le__zero) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 749 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),one_one(X_a))))) # label(fact_692_zero__le__one) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 750 (all X_a (lattice(X_a) -> (all X_1 all Y all Z hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Z))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z))))))) # label(fact_693_distrib__inf__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 751 (all X_a (lattice(X_a) -> (all X_1 all Y all Z hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_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_694_distrib__sup__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 752 (all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2) = zero_zero(nat))) # label(fact_695_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 753 (all M_1 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1) = zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))) # label(fact_696_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 754 (all N_2 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N_2) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)))) # label(fact_697_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 755 (all K_1 all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))) # label(fact_698_Suc__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 756 (all I all K_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),J_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_2)),J_1))) # label(fact_699_diff__diff__right) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 757 (all J_2 all K_1 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)),I_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1))))) # label(fact_700_le__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 758 (all M all K_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),M)),K_2))))) # label(fact_701_le__add__diff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 759 (all N_2 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)) = M)) # label(fact_702_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 760 (all I all K_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),J_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_1)),K_2))) # label(fact_703_add__diff__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 761 (all I_1 all K_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_2))))) # label(fact_704_le__diff__conv2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 762 (all N_2 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)),N_2) = M)) # label(fact_705_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 763 (all K_1 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1) = K_1 <-> J_2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),I_1)))) # label(fact_706_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 764 (all I all K_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),J_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_1)),K_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2)))) # label(fact_707_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 765 (all I all K_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),J_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2)),I) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),I)),K_2))) # label(fact_708_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 766 (all I all K_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),J_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),I)),K_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2)),I))) # label(fact_709_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 767 (all X_b all F all A_2 hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) = ti(X_b,A_2)) # label(fact_710_fold1__singleton) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 768 (all X_b all A_2 all G all F (G = hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F) -> hAPP(fun(X_b,bool),X_b,G,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) = ti(X_b,A_2))) # label(fact_711_fold1__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 769 (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)) -> hAPP(fun(X_b,bool),X_b,F_1,A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_3)))) # label(fact_712_folding__one_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 770 (all X_b (linord581940658strict(X_b) -> (all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),X_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_1),Y_1))),zero_zero(X_b))) <-> ti(X_b,X_2) = zero_zero(X_b) & ti(X_b,Y_1) = zero_zero(X_b))))) # label(fact_713_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.33 771 (all X_a (linordered_ring(X_a) -> (all X_1 all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y))))))) # label(fact_714_sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 772 (all X_a (linordered_idom(X_a) -> (all Y all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Y)),X_1)))))))) # label(fact_715_mult__right__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 773 (all X_a (linordered_idom(X_a) -> (all Y all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),X_1)),X_1)))))))) # label(fact_716_mult__left__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 774 (all X_b (ordered_ring(X_b) -> (all A_2 all E all C_1 all B_1 all D (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_1),E)),D))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1)),E)),C_1)),D)))))) # label(fact_717_le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 775 (all X_b (ordered_ring(X_b) -> (all A_2 all E all C_1 all B_1 all D (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_1),E)),D))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_1),A_2)),E)),D))))))) # label(fact_718_le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 776 (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(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)))))) # label(fact_719_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 777 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1)))) # label(fact_720_one__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 778 (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(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_c,bool),nat,finite_card(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))) # label(fact_721_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 779 (all M all K_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),J_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2))),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,J_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),M)))) # label(fact_722_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 780 (all M all K_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),J_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)),hAPP(nat,nat,suc,J_1)))) # label(fact_723_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 781 (all U all M_1 all N_1 all J_2 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),I_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U)),M_1)),N_1))))) # label(fact_724_nat__le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 782 (all U_1 all M all N_2 all J_1 all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),I)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U_1)),N_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J_1)),U_1)),M)),N_2))) # label(fact_725_nat__diff__add__eq1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 783 (all U all M_1 all N_1 all J_2 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),I_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_1) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U)),M_1) = N_1))) # label(fact_726_nat__eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 784 (all U all M_1 all N_1 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N_1)))))) # label(fact_727_nat__le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 785 (all U_1 all M all N_2 all I all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U_1)),N_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I)),U_1)),N_2)))) # label(fact_728_nat__diff__add__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 786 (all U all M_1 all N_1 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_1) <-> M_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N_1)))) # label(fact_729_nat__eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 787 (all X_b (lattice(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),semilattice_sup_sup(X_b)),A_3))))) # label(fact_730_Sup__fin_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 788 (all X_b (lattice(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),semilattice_inf_inf(X_b)),A_3))))) # label(fact_731_Inf__fin_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 789 (all X_a (linord1278240602ring_1(X_a) -> (all V all U_1 all Y all X_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U_1),V) = one_one(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)))))))))) # label(fact_732_convex__bound__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 790 (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(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2))),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)))))) # label(fact_733_diff__card__le__card__Diff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 791 (all X_b (lattice(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)))))))) # label(fact_734_Inf__le__Sup) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 792 (all X_b (ab_semigroup_mult(X_b) -> (all X_2 all A_3 (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3)))))))) # label(fact_735_fold1__insert) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 793 (all X_b (ab_sem1668676832m_mult(X_b) -> (all X_2 all A_3 (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3))))))) # label(fact_736_fold1__insert__idem) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 794 (all X_b (ab_sem1668676832m_mult(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,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),B_2))))))))) # label(fact_737_fold1__Un2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 795 (all X_b (ab_sem1668676832m_mult(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),times_times(X_b),X),Y_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,H,X)),hAPP(X_b,X_b,H,Y_2))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (ti(fun(X_b,bool),N_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),N_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_3)))))))) # label(fact_738_hom__fold1__commute) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 796 (all X_b (ab_semigroup_mult(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> ((all X all Y_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X),Y_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3)),A_3)))))))) # label(fact_739_fold1__in) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 797 (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),big_semilattice_big(X_b),F),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,F_1,A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_3)))) # label(fact_740_semilattice__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 798 (all X_b all A_3 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),bot_bot(fun(X_b,bool))),A_3))) # label(fact_741_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 799 (all X_b all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(fun(fun(X_b,bool),bool),bool,finite_finite_1(fun(X_b,bool)),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,bool),bool),collect(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),combc(fun(X_b,bool),fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool))),A_3)))))) # label(fact_742_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 800 (all X_b all X_c all B_2 all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) <-> (exists AA (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),AA),A_3)) & ti(fun(X_b,bool),B_2) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),AA))))) # label(fact_743_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 801 (all X_c all X_b all F all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),B_2))))) # label(fact_744_image__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 802 (all X_b all A_3 all B_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),A_3))) # label(fact_745_Int__lower1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 803 (all X_b all A_3 all B_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),B_2))) # label(fact_746_Int__lower2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 804 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_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_747_Int__absorb2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 805 (all X_b all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2) = ti(fun(X_b,bool),B_2))) # label(fact_748_Int__absorb1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 806 (all X_b all B_2 all C_3 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),C_3),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),C_3),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),C_3),hAPP(fun(X_b,bool),fun(X_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_749_Int__greatest) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 807 (all X_b all B_2 all D_2 all A_3 all C_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),C_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),D_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),C_3),D_2)))))) # label(fact_750_Int__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 808 (all X_b all A_3 all B_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_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_751_Un__upper1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 809 (all X_b all B_2 all A_3 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_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_752_Un__upper2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 810 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) <-> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2) = ti(fun(X_b,bool),B_2))) # label(fact_753_subset__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 811 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2) = ti(fun(X_b,bool),B_2))) # label(fact_754_Un__absorb1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 812 (all X_b all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2) = ti(fun(X_b,bool),A_3))) # label(fact_755_Un__absorb2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 813 (all X_b all B_2 all A_3 all C_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),C_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),C_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),C_3))))) # label(fact_756_Un__least) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 814 (all X_b all B_2 all D_2 all A_3 all C_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),C_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),D_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),C_3),D_2)))))) # label(fact_757_Un__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 815 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(fun(X_b,bool),bool),bool,hAPP(fun(fun(X_b,bool),bool),fun(fun(fun(X_b,bool),bool),bool),ord_less_eq(fun(fun(X_b,bool),bool)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),powp(X_b),A_3)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),powp(X_b),B_2))))) # label(fact_758_Powp__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 816 (all X_b all B_2 all A_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_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_759_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 817 (all X_b all X_2 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_3)),B_2)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)) & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)))) # label(fact_760_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 818 (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(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),B_2))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))))) # label(fact_761_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 819 (all X_b all B_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),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_762_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 820 (all X_b all A_2 all C_3 all D_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),C_3),D_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),C_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),D_2))))) # label(fact_763_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 821 (all X_b all Ga all G_1 all Ts (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),G_1),Ts)) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),ord_less_eq(fun(hoare_2118899576triple(X_b),bool)),G_1),Ga)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts))))) # label(fact_764_thin) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 822 (all X_b all Ts all Ga all Ts_1 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts_1)) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),ord_less_eq(fun(hoare_2118899576triple(X_b),bool)),Ts),Ts_1)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts))))) # label(fact_765_weaken) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 823 (all X_b all Ts all Ga (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),ord_less_eq(fun(hoare_2118899576triple(X_b),bool)),Ts),Ga)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts)))) # label(fact_766_asm) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 824 (all X_b all A_3 all B_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),A_3))) # label(fact_767_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 825 (all X_b all D_2 all B_2 all A_3 all C_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),C_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),D_2),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),C_3),D_2)))))) # label(fact_768_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 826 (all X_b all C_3 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),C_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),C_3),A_3)) = ti(fun(X_b,bool),A_3)))) # label(fact_769_double__diff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 827 (all X_b all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool)))) <-> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)))) # label(fact_770_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 828 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))))) # label(fact_771_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 829 (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,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))))) # label(fact_772_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 830 (all X_b all A_3 all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool))))) -> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) | ti(fun(X_b,bool),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool))))) # label(fact_773_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 831 (all X_c all X_b all B_2 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,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),B_2),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))))) # label(fact_774_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 832 (all X_b all X_c all F all A_3 all B_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_inf_inf(fun(X_c,bool)),A_3),B_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B_2))))) # label(fact_775_image__Int__subset) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 833 (all X_b all A_3 all B_2 all C_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),B_2)),C_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),C_3),A_3)))) # label(fact_776_Un__Int__assoc__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 834 (all X_b all X_c all F all A_3 all B_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B_2))),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),B_2))))) # label(fact_777_image__diff__subset) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 835 (all X_b all A_3 all B_2 all C_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),C_3)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_2),C_3))))) # label(fact_778_Diff__subset__conv) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 836 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_2),A_3)) = ti(fun(X_b,bool),B_2))) # label(fact_779_Diff__partition) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 837 (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,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),B_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,B_2)),hAPP(fun(X_c,bool),X_b,F_1,A_3)) = hAPP(fun(X_c,bool),X_b,F_1,A_3))))) # label(fact_780_folding__image__simple__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 838 (all X_b all A_3 all X_2 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),B_2))) <-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool))))),B_2))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))))) # label(fact_781_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 839 (all X_b all A_3 all X_2 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool))))),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(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)))))) # label(fact_782_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 840 (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,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(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_783_card__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 841 (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,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))) -> ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2))))) # label(fact_784_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 842 (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),B_2) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_1,B_2)),hAPP(fun(X_b,bool),X_b,F_1,A_3)) = hAPP(fun(X_b,bool),X_b,F_1,A_3)))))) # label(fact_785_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 843 (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,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2))))) # label(fact_786_card__Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 844 (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),B_2) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),B_2)),hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3)) = hAPP(fun(X_b,bool),X_b,big_lattice_Sup_fin(X_b),A_3))))))) # label(fact_787_Sup__fin_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 845 (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),B_2) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),B_2)),hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3)) = hAPP(fun(X_b,bool),X_b,big_lattice_Inf_fin(X_b),A_3))))))) # label(fact_788_Inf__fin_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 846 (all X_b (order(X_b) -> (all N_1 all N_4 all F ((all N hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,F,N)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_4)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,F,N_1)),hAPP(nat,X_b,F,N_4)))))))) # label(fact_789_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 847 (all X_b all Pa all A_3 all F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),F_1),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))) -> ((all A_4 all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),F_2)))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1))))))) # label(fact_790_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 848 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)) -> ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2)))) # label(fact_791_equalityI) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 849 (all X_b all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_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_792_subsetD) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 850 (all X_b all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) -> -(hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3))))) # label(fact_793_equalityE) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 851 (all X_b all C_3 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),C_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),C_3))))) # label(fact_794_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 852 (all X_b all X_2 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2))))) # label(fact_795_set__mp) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 853 (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(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(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))))) # label(fact_796_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 854 (all X_b all X_2 all Pa all Qa (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),Pa),Qa)) -> (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> hBOOL(hAPP(X_b,bool,Qa,X_2))))) # label(fact_797_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 855 (all X_b all X_2 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2))))) # label(fact_798_in__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 856 (all X_b all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)))) # label(fact_799_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 857 (all X_b all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)))) # label(fact_800_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 858 (all X_b all Qa all Pa all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),Pa),Qa)) -> hBOOL(hAPP(X_b,bool,Qa,X_2))))) # label(fact_801_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 859 (all X_b all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)))) # label(fact_802_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 860 (all X_b all A_3 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),A_3))) # label(fact_803_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 861 (all X_b all R_1 all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),R_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S_1))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),R_1),S_1)))) # label(fact_804_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 862 (all X_b all B_2 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)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),B_2)))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)))) # label(fact_805_subsetI) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 863 (all X_c all X_b all F 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,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) -> (exists C_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),C_2),A_3)) & hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),C_2)) & ti(fun(X_b,bool),B_2) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),C_2)))))) # label(fact_806_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 864 (all X_b all Qa all Pa all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> ((all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_3)) -> (hBOOL(hAPP(X_b,bool,Pa,X)) -> hBOOL(hAPP(X_b,bool,Qa,X))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Qa))))))) # label(fact_807_Int__Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 865 (all N_2 all M_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_2)),M_4)) -> (exists M_2 M_4 = hAPP(nat,nat,suc,M_2)))) # label(fact_808_Suc__le__D) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 866 (all Pa all N_1 all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),M_3)) -> ((all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2)) -> hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,M_2))))) -> hBOOL(hAPP(nat,bool,Pa,M_3))))) # label(fact_809_Suc__le__D__lemma) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 867 (all X_c all X_b all F all B_2 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)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,X)),B_2)))) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)),B_2)))) # label(fact_810_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 868 (all X_b all X_c (ord(X_c) -> (all F all G ((all X hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X)),hAPP(X_b,X_c,G,X)))) -> hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)))))) # label(fact_811_le__funI) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 869 (all N_3 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3)) <-> (exists M_2 all X (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X),N_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),M_2)))))) # label(fact_812_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 870 (all U all F ((all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,F,N)))) -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),F)),U)))))) # label(fact_813_finite__less__ub) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 871 (all Z all X_1 all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))))) # label(fact_814_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 872 (all Y all X_1 all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Z)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))))) # label(fact_815_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 873 (all X_b all A_3 all B_1 ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_1),bot_bot(fun(X_b,bool))))) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),B_1),A_3) = ti(X_b,B_1)) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_1),bot_bot(fun(X_b,bool))))) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),B_1),A_3) = hAPP(fun(X_b,bool),X_b,the_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_1),bot_bot(fun(X_b,bool))))))))) # label(fact_816_flat__lub__def) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 874 (all X_b all F all A_3 hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_3) = hAPP(fun(X_b,bool),X_b,the_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_3))) # label(fact_817_fold1__def) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 875 (all X_b all F all A_3 all X_2 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_3),X_2)) -> ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)))) # label(fact_818_fold1Set__nonempty) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 876 (all X_b all F all X_2 -hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),bot_bot(fun(X_b,bool))),X_2))) # label(fact_819_empty__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 877 (all X_b all F all A_2 all B_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))),B_1)) <-> ti(X_b,A_2) = ti(X_b,B_1))) # label(fact_820_fold1Set__sing) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 878 (all X_b all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (exists X1 hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_3),X1)))))) # label(fact_821_finite__nonempty__imp__fold1Set) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 879 (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)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))))) # label(fact_822_card__Diff1__less) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 880 (all N_2 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),zero_zero(nat)))) # label(fact_823_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 881 (all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,N_2)))) # label(fact_824_lessI) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 882 (all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N_2))))) # label(fact_825_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 883 (all K_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),K_1))))) # label(fact_826_finite__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 884 (all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_2)))) # label(fact_827_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 885 (all Pa all I_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),Pa)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1)))))) # label(fact_828_finite__M__bounded__by__nat) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 886 (all N_3 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3)) <-> (exists M_2 all X (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X),N_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),M_2)))))) # label(fact_829_finite__nat__set__iff__bounded) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 887 (all X_a (order(X_a) -> (all Z all Y all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X_1))))))) # label(fact_830_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 888 (all X_a (preorder(X_a) -> (all Z all X_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z))))))) # label(fact_831_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 889 (all X_a (order(X_a) -> (all Z all Y all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X_1))))))) # label(fact_832_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 890 (all X_a (preorder(X_a) -> (all Z all X_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z))))))) # label(fact_833_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 891 (all X_a (order(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (ti(X_a,A_1) != ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_834_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 892 (all X_a (order(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (ti(X_a,A_1) != ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_835_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 893 (all X_a (order(X_a) -> (all X_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)) | ti(X_a,X_1) = ti(X_a,Y))))) # label(fact_836_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 894 (all X_b (linorder(X_b) -> (all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_1)) -> (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1)) <-> ti(X_b,X_2) = ti(X_b,Y_1)))))) # label(fact_837_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 895 (all X_a (preorder(X_a) -> (all X_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y)))))) # label(fact_838_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 896 (all X_a (linorder(X_a) -> (all Y all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)))))) # label(fact_839_leD) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 897 (all X_a (order(X_a) -> (all A_1 all B (ti(X_a,A_1) != ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_840_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 898 (all X_a (order(X_a) -> (all A_1 all B (ti(X_a,A_1) != ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_841_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 899 (all X_b (linorder(X_b) -> (all X_2 all Y_1 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_1)) <-> ti(X_b,X_2) = ti(X_b,Y_1)))))) # label(fact_842_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 900 (all X_a (linorder(X_a) -> (all Y all X_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)))))) # label(fact_843_not__leE) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 901 (all X_a (linorder(X_a) -> (all X_1 all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X_1)))))) # label(fact_844_leI) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 902 (all X_b (order(X_b) -> (all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1)) | ti(X_b,X_2) = ti(X_b,Y_1))))) # label(fact_845_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 903 (all X_b (preorder(X_b) -> (all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_1)) & -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_2)))))) # label(fact_846_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 904 (all X_b (order(X_b) -> (all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_1)) & ti(X_b,X_2) != ti(X_b,Y_1))))) # label(fact_847_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 905 (all X_a (linorder(X_a) -> (all X_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1)))))) # label(fact_848_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 906 (all X_b (linorder(X_b) -> (all X_2 all Y_1 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2)))))) # label(fact_849_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 907 (all X_b (linorder(X_b) -> (all X_2 all Y_1 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_2)))))) # label(fact_850_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.34 908 (all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2)) | M = N_2 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_2)))) # label(fact_851_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 909 (all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_2)) -> (M != N_2 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))))) # label(fact_852_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 910 (all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_2)))) # label(fact_853_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 911 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) | M_1 = N_1)) # label(fact_854_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 912 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) & M_1 != N_1)) # label(fact_855_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 913 (all X_b all A_3 all F all N_1 (ti(fun(X_b,bool),A_3) = hAPP(fun(nat,bool),fun(X_b,bool),hAPP(fun(nat,X_b),fun(fun(nat,bool),fun(X_b,bool)),image(nat,X_b),F),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)))) # label(fact_856_nat__seg__image__imp__finite) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 914 (all X_a (ordere223160158up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_857_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 915 (all X_a (ordere223160158up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_858_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 916 (all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2)))) # label(fact_859_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 917 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M_1))) <-> N_1 = M_1))) # label(fact_860_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 918 (all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N_2)))) # label(fact_861_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 919 (all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N_2))))) # label(fact_862_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 920 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)))) # label(fact_863_Suc__le__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 921 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))) # label(fact_864_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 922 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),M_1)))) # label(fact_865_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 923 (all N_1 all K_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)))))) # label(fact_866_less__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 924 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_1),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),C)))))) # label(fact_867_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 925 (all X_a (bot(X_a) -> (all A_1 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),bot_bot(X_a)))))) # label(fact_868_not__less__bot) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 926 (all X_b (bot(X_b) -> (all A_2 (ti(X_b,A_2) != bot_bot(X_b) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),bot_bot(X_b)),A_2)))))) # label(fact_869_bot__less) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 927 (all I all J_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_1)),I))) # label(fact_870_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 928 (all J_1 all I -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),I)),I))) # label(fact_871_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 929 (all K_1 all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)))) # label(fact_872_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 930 (all M all I all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),M))))) # label(fact_873_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 931 (all M all I all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J_1))))) # label(fact_874_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 932 (all K_2 all I all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),K_2))))) # label(fact_875_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 933 (all K_2 all L all I all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),L)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),L)))))) # label(fact_876_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 934 (all M all N_2 all K_2 all L (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),L)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),L) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),N_2) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2))))) # label(fact_877_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 935 (all I all J_1 all K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_1)),K_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K_2)))) # label(fact_878_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 936 (all X_b (ordere236663937imp_le(X_b) -> (all A_2 all C_1 all B_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_1),C_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1)))))) # label(fact_879_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 937 (all X_b (ordere236663937imp_le(X_b) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1)))))) # label(fact_880_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 938 (all X_a (ordere223160158up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))))) # label(fact_881_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 939 (all X_a (ordere223160158up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))))))) # label(fact_882_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 940 (all X_a (ordere223160158up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_883_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 941 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_884_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 942 (all X_a (ordere236663937imp_le(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_885_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 943 (all L all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M)))))) # label(fact_886_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 944 (all N_2 all J_1 all K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),K_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),N_2)),K_2)))) # label(fact_887_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 945 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all B_1 all C_1 all D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),D))))))) # label(fact_888_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 946 (all X_a (semilattice_sup(X_a) -> (all A_1 all X_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B))))))) # label(fact_889_less__supI2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 947 (all X_a (semilattice_sup(X_a) -> (all B all X_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_1),B))))))) # label(fact_890_less__supI1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 948 (all X_a (semilattice_inf(X_a) -> (all A_1 all B all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)),X_1)))))) # label(fact_891_less__infI2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 949 (all X_a (semilattice_inf(X_a) -> (all B all A_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_1),B)),X_1)))))) # label(fact_892_less__infI1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 950 (all N_2 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),zero_zero(nat)))) # label(fact_893_not__less0) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 951 (all N_1 (N_1 != zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)))) # label(fact_894_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 952 (all N_2 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),zero_zero(nat)))) # label(fact_895_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 953 (all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2)) -> N_2 != zero_zero(nat))) # label(fact_896_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 954 (all N_2 (N_2 != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)))) # label(fact_897_gr0I) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 955 (all M_1 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M_1))))) # label(fact_898_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 956 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) | M_1 = N_1)) # label(fact_899_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 957 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)))) # label(fact_900_Suc__less__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 958 (all N_1 all M_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M_1))) <-> N_1 = M_1))) # label(fact_901_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 959 (all N_2 all M (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M))) -> M = N_2))) # label(fact_902_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 960 (all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N_2))))) # label(fact_903_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 961 (all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2)) -> (hAPP(nat,nat,suc,M) != N_2 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N_2))))) # label(fact_904_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 962 (all K_2 all I all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),K_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I)),K_2))))) # label(fact_905_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 963 (all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N_2))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2)) -> M = N_2))) # label(fact_906_less__SucE) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 964 (all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2)))) # label(fact_907_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 965 (all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N_2))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2)))) # label(fact_908_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 966 (all N_2 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),N_2))) # label(fact_909_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 967 (all M_1 all N_1 (M_1 != N_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1)))) # label(fact_910_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 968 (all X_1 all Y (X_1 != Y -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X_1))))) # label(fact_911_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 969 (all N_2 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),N_2))) # label(fact_912_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 970 (all N_2 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M)) -> M != N_2)) # label(fact_913_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 971 (all S all T_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3)) -> S != T_3)) # label(fact_914_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 972 (all Pa all M_1 all N_1 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N_1),M_1))) -> ((M_1 = N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N_1),M_1))) -> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N_1),M_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N_1),M_1)))))) # label(fact_915_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 973 (all X_a (preorder(X_a) -> (all X_1 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),X_1))))) # label(fact_916_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 974 (all X_b (linorder(X_b) -> (all X_2 all Y_1 (ti(X_b,X_2) != ti(X_b,Y_1) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2)))))) # label(fact_917_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 975 (all X_b (linorder(X_b) -> (all X_2 all Y_1 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2)) | ti(X_b,X_2) = ti(X_b,Y_1))))) # label(fact_918_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 976 (all X_a (linorder(X_a) -> (all X_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)) | ti(X_a,X_1) = ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1)))))) # label(fact_919_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 977 (all X_b (linorder(X_b) -> (all Y_1 all X_2 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2)) -> (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1)) <-> ti(X_b,X_2) = ti(X_b,Y_1)))))) # label(fact_920_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 978 (all X_a (linorder(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),ord_less(X_a),X_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1))))))) # label(fact_921_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 979 (all X_a (order(X_a) -> (all X_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)) -> ti(X_a,X_1) != ti(X_a,Y))))) # label(fact_922_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 980 (all X_a (preorder(X_a) -> (all X_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1)))))) # label(fact_923_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 981 (all X_a (preorder(X_a) -> (all X_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1)))))) # label(fact_924_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 982 (all X_a (order(X_a) -> (all X_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)) -> ti(X_a,X_1) != ti(X_a,Y))))) # label(fact_925_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 983 (all X_a (order(X_a) -> (all X_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)) -> ti(X_a,Y) != ti(X_a,X_1))))) # label(fact_926_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 984 (all X_b (preorder(X_b) -> (all Pa all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2)) -> hBOOL(Pa)))))) # label(fact_927_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 985 (all X_a (preorder(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)))))) # label(fact_928_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 986 (all X_a (order(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_929_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 987 (all X_a (ord(X_a) -> (all C all A_1 all B (A_1 = B -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))))))) # label(fact_930_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 988 (all X_a (order(X_a) -> (all C all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1))))))) # label(fact_931_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 989 (all X_a (ord(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (B = C -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))))))) # label(fact_932_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 990 (all X_a (order(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1))))))) # label(fact_933_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 991 (all X_a (preorder(X_a) -> (all Z all X_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z))))))) # label(fact_934_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 992 (all X_a (order(X_a) -> (all Z all Y all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X_1))))))) # label(fact_935_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 993 (all X_a (preorder(X_a) -> (all X_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1)))))) # label(fact_936_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 994 (all X_a (linorder(X_a) -> (all X_1 all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)) -> (ti(X_a,X_1) != ti(X_a,Y) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1))))))) # label(fact_937_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 995 (all X_a (linordered_idom(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),ord_less(X_a),X_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X_1))))))) # label(fact_938_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 996 (all I_1 all J_2 all K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_2)))) # label(fact_939_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 997 (all M all N_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)) = M)) # label(fact_940_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 998 (all K_1 all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)))) # label(fact_941_Suc__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 999 (all M all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)),hAPP(nat,nat,suc,M)))) # label(fact_942_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1000 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)))) # label(fact_943_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1001 (all K_1 all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)))) # label(fact_944_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1002 (all M_1 all K_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)))) # label(fact_945_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1003 (all K_2 all I all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),K_2)))))) # label(fact_946_mult__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1004 (all K_2 all I all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),I)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),J_1)))))) # label(fact_947_mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1005 (all M_1 all N_1 all K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1) <-> M_1 = N_1))) # label(fact_948_nat__mult__eq__cancel1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1006 (all M_1 all N_1 all K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))))) # label(fact_949_nat__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1007 (all M all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_2)),M))))) # label(fact_950_diff__less) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1008 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)))) # label(fact_951_zero__less__diff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1009 (all I all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),M))))) # label(fact_952_less__add__Suc1) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1010 (all I all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),I))))) # label(fact_953_less__add__Suc2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1011 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) <-> (exists K N_1 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K))))) # label(fact_954_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1012 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)))) # label(fact_955_add__gr__0) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1013 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) <-> (exists M_2 N_1 = hAPP(nat,nat,suc,M_2)))) # label(fact_956_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1014 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))) <-> N_1 = zero_zero(nat))) # label(fact_957_less__Suc0) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1015 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1))) <-> M_1 = zero_zero(nat) | (exists J (M_1 = hAPP(nat,nat,suc,J) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),N_1)))))) # label(fact_958_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1016 (all X_a (linordered_semidom(X_a) -> (all N_2 all M (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),N_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M),N_2)))))))) # label(fact_959_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1017 (all X_a (linordered_semidom(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))))))) # label(fact_960_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1018 (all X_a (linordered_semidom(X_a) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a))))) # label(fact_961_not__one__less__zero) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1019 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),one_one(X_a))))) # label(fact_962_zero__less__one) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1020 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all B_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1)),zero_zero(X_b))))))) # label(fact_963_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1021 (all X_a (linord581940658strict(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_964_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1022 (all X_a (linord581940658strict(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_965_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1023 (all X_a (linord893533164strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_966_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1024 (all X_a (linord20386208strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_967_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1025 (all X_a (linord20386208strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_968_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1026 (all X_a (linord581940658strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_969_mult__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1027 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_970_mult__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1028 (all X_b (linord581940658strict(X_b) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_1),A_2))))))) # label(fact_971_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1029 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))))))) # label(fact_972_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1030 (all X_a (linord20386208strict(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))))))) # label(fact_973_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1031 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),zero_zero(X_a)))))))) # label(fact_974_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1032 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_975_mult__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1033 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_976_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1034 (all X_b (linord581940658strict(X_b) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1))))))) # label(fact_977_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1035 (all X_b (linord581940658strict(X_b) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_1),A_2)))))) # label(fact_978_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1036 (all X_b (linord581940658strict(X_b) -> (all A_2 all C_1 all B_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_1),C_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_1)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_1),A_2)))))) # label(fact_979_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1037 (all X_a (linordered_ring(X_a) -> (all A_1 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)),zero_zero(X_a)))))) # label(fact_980_not__square__less__zero) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1038 (all X_b (linordered_idom(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))))))) # label(fact_981_even__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1039 (all X_b (linord219039673up_add(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),A_2)))))) # label(fact_982_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1040 (all X_b (linord219039673up_add(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))))))) # label(fact_983_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1041 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_984_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1042 (all X_a (linordered_semidom(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_985_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1043 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_986_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1044 (all N_1 hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_1))) = N_1) # label(fact_987_card__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1045 (all X hAPP(nat,fun(nat,bool),ord_less(nat),X) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X))) # label(fact_988_less__eq__Suc__le__raw) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1046 (all Z all X_1 all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))))) # label(fact_989_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1047 (all Y all X_1 all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Z)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))))) # label(fact_990_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1048 (all X_1 all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y)))) # label(fact_991_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1049 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_992_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1050 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_993_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1051 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_994_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1052 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_995_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1053 (all T_2 all T_1 (bounded_lattice(T_1) -> bounded_lattice(fun(T_2,T_1)))) # label(arity_fun___Lattices_Obounded__lattice) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1054 (all T_2 all T_1 (bounded_lattice(T_1) -> bounded_lattice_bot(fun(T_2,T_1)))) # label(arity_fun___Lattices_Obounded__lattice__bot) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1055 (all T_2 all T_1 (lattice(T_1) -> semilattice_sup(fun(T_2,T_1)))) # label(arity_fun___Lattices_Osemilattice__sup) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1056 (all T_2 all T_1 (lattice(T_1) -> semilattice_inf(fun(T_2,T_1)))) # label(arity_fun___Lattices_Osemilattice__inf) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1057 (all T_2 all T_1 (distrib_lattice(T_1) -> distrib_lattice(fun(T_2,T_1)))) # label(arity_fun___Lattices_Odistrib__lattice) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1058 (all T_2 all T_1 (preorder(T_1) -> preorder(fun(T_2,T_1)))) # label(arity_fun___Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1059 (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].
% 2.10/2.35 1060 (all T_2 all T_1 (lattice(T_1) -> lattice(fun(T_2,T_1)))) # label(arity_fun___Lattices_Olattice) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1061 (all T_2 all T_1 (order(T_1) -> order(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oorder) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1062 (all T_2 all T_1 (ord(T_1) -> ord(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oord) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1063 (all T_2 all T_1 (bot(T_1) -> bot(fun(T_2,T_1)))) # label(arity_fun___Orderings_Obot) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1064 (all T_2 all T_1 (minus(T_1) -> minus(fun(T_2,T_1)))) # label(arity_fun___Groups_Ominus) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1065 (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].
% 2.10/2.35 1066 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1067 (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].
% 2.10/2.35 1068 (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].
% 2.10/2.35 1069 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_If_3_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1070 (all P (-hBOOL(hAPP(bool,bool,fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1071 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1072 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R) = hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R))) # label(help_COMBB_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1073 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q)) # label(help_COMBC_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1074 (all X_a all P hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P)) # label(help_COMBI_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1075 (all X_b all X_a all P all Q hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P)) # label(help_COMBK_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1076 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c)),combs(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R))) # label(help_COMBS_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1077 (all Q all P (-hBOOL(P) | -hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1078 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1079 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1080 (all Q all P (-hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1081 (all P all Q (-hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1082 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | hBOOL(P) | hBOOL(Q))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1083 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1084 (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].
% 2.10/2.35 1085 (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].
% 2.10/2.35 1086 (all Q all P (hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1087 (all P all Q (-hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1088 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)) | -hBOOL(P) | hBOOL(Q))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.10/2.35 1089 (all N ((all X (hBOOL(hAPP(fun(hoare_2118899576triple(x_a),bool),bool,hAPP(hoare_2118899576triple(x_a),fun(fun(hoare_2118899576triple(x_a),bool),bool),member(hoare_2118899576triple(x_a)),X),hAPP(fun(hoare_2118899576triple(x_a),bool),fun(hoare_2118899576triple(x_a),bool),hAPP(fun(hoare_2118899576triple(x_a),bool),fun(fun(hoare_2118899576triple(x_a),bool),fun(hoare_2118899576triple(x_a),bool)),semilattice_sup_sup(fun(hoare_2118899576triple(x_a),bool)),g),hAPP(fun(pname,bool),fun(hoare_2118899576triple(x_a),bool),hAPP(fun(pname,hoare_2118899576triple(x_a)),fun(fun(pname,bool),fun(hoare_2118899576triple(x_a),bool)),image(pname,hoare_2118899576triple(x_a)),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_2118899576triple(x_a)),hAPP(fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_2118899576triple(x_a))),combs(pname,fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)),hAPP(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hAPP(fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),fun(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),combs(pname,com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),hAPP(fun(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))))),combb(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),pname),hoare_759811442triple(x_a)),p)),body)),q)),procs)))) -> hBOOL(hAPP(hoare_2118899576triple(x_a),bool,hAPP(nat,fun(hoare_2118899576triple(x_a),bool),hoare_1942962616_valid(x_a),N),X)))) -> (all X (hBOOL(hAPP(fun(hoare_2118899576triple(x_a),bool),bool,hAPP(hoare_2118899576triple(x_a),fun(fun(hoare_2118899576triple(x_a),bool),bool),member(hoare_2118899576triple(x_a)),X),hAPP(fun(pname,bool),fun(hoare_2118899576triple(x_a),bool),hAPP(fun(pname,hoare_2118899576triple(x_a)),fun(fun(pname,bool),fun(hoare_2118899576triple(x_a),bool)),image(pname,hoare_2118899576triple(x_a)),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_2118899576triple(x_a)),hAPP(fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_2118899576triple(x_a))),combs(pname,fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)),hAPP(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hAPP(fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),fun(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),combs(pname,com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),hAPP(fun(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))))),combb(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),pname),hoare_759811442triple(x_a)),p)),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body_1))),q)),procs))) -> hBOOL(hAPP(hoare_2118899576triple(x_a),bool,hAPP(nat,fun(hoare_2118899576triple(x_a),bool),hoare_1942962616_valid(x_a),N),X)))))) # label(conj_0) # label(hypothesis) # label(non_clause). [assumption].
% 2.10/2.36 1090 -((all X (hBOOL(hAPP(fun(hoare_2118899576triple(x_a),bool),bool,hAPP(hoare_2118899576triple(x_a),fun(fun(hoare_2118899576triple(x_a),bool),bool),member(hoare_2118899576triple(x_a)),X),g)) -> hBOOL(hAPP(hoare_2118899576triple(x_a),bool,hAPP(nat,fun(hoare_2118899576triple(x_a),bool),hoare_1942962616_valid(x_a),n),X)))) -> (all X (hBOOL(hAPP(fun(hoare_2118899576triple(x_a),bool),bool,hAPP(hoare_2118899576triple(x_a),fun(fun(hoare_2118899576triple(x_a),bool),bool),member(hoare_2118899576triple(x_a)),X),hAPP(fun(pname,bool),fun(hoare_2118899576triple(x_a),bool),hAPP(fun(pname,hoare_2118899576triple(x_a)),fun(fun(pname,bool),fun(hoare_2118899576triple(x_a),bool)),image(pname,hoare_2118899576triple(x_a)),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_2118899576triple(x_a)),hAPP(fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_2118899576triple(x_a))),combs(pname,fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)),hAPP(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hAPP(fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),fun(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),combs(pname,com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),hAPP(fun(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))))),combb(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),pname),hoare_759811442triple(x_a)),p)),body)),q)),procs))) -> hBOOL(hAPP(hoare_2118899576triple(x_a),bool,hAPP(nat,fun(hoare_2118899576triple(x_a),bool),hoare_1942962616_valid(x_a),n),X))))) # label(conj_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.49/2.75
% 2.49/2.75 ============================== end of process non-clausal formulas ===
% 2.49/2.75
% 2.49/2.75 ============================== PROCESS INITIAL CLAUSES ===============
% 2.49/2.75
% 2.49/2.75 ============================== PREDICATE ELIMINATION =================
% 2.49/2.75 1091 one(nat) # label(arity_Nat_Onat___Groups_Oone) # label(axiom). [assumption].
% 2.49/2.75 1092 -one(A) | one_one(A) = ti(A,one_one(A)) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom). [clausify(21)].
% 2.49/2.75 Derived: one_one(nat) = ti(nat,one_one(nat)). [resolve(1091,a,1092,a)].
% 2.49/2.75 1093 monoid_add(nat) # label(arity_Nat_Onat___Groups_Omonoid__add) # label(axiom). [assumption].
% 2.49/2.75 1094 -monoid_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(22)].
% 2.49/2.75 1095 -monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_426_add__0__right) # label(axiom). [clausify(485)].
% 2.49/2.75 1096 -monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_429_add__0__left) # label(axiom). [clausify(488)].
% 2.49/2.75 Derived: plus_plus(nat) = ti(fun(nat,fun(nat,nat)),plus_plus(nat)). [resolve(1093,a,1094,a)].
% 2.49/2.75 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),zero_zero(nat)) = ti(nat,A). [resolve(1093,a,1095,a)].
% 2.49/2.75 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),A) = ti(nat,A). [resolve(1093,a,1096,a)].
% 2.49/2.75 1097 cancel_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.49/2.75 1098 -cancel_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(23)].
% 2.49/2.75 1099 -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_420_add__left__cancel) # label(axiom). [clausify(479)].
% 2.49/2.75 1100 -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_420_add__left__cancel) # label(axiom). [clausify(479)].
% 2.49/2.75 1101 -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_421_add__right__cancel) # label(axiom). [clausify(480)].
% 2.49/2.75 1102 -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_421_add__right__cancel) # label(axiom). [clausify(480)].
% 2.49/2.75 1103 -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_422_add__left__imp__eq) # label(axiom). [clausify(481)].
% 2.49/2.75 1104 -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_424_add__right__imp__eq) # label(axiom). [clausify(483)].
% 2.49/2.75 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(1097,a,1099,a)].
% 2.49/2.75 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(1097,a,1100,a)].
% 2.49/2.75 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(1097,a,1101,a)].
% 2.49/2.75 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(1097,a,1102,a)].
% 2.49/2.75 1105 ab_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 2.49/2.75 1106 -ab_semigroup_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(24)].
% 2.49/2.75 1107 -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_419_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom). [clausify(478)].
% 2.91/3.11 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(1105,a,1107,a)].
% 2.91/3.11 1108 monoid_mult(nat) # label(arity_Nat_Onat___Groups_Omonoid__mult) # label(axiom). [assumption].
% 2.91/3.11 1109 -monoid_mult(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_0_res) # label(axiom). [clausify(25)].
% 2.91/3.11 1110 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) = ti(A,B) # label(fact_510_mult__1__left) # label(axiom). [clausify(568)].
% 2.91/3.11 1111 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) = ti(A,B) # label(fact_512_mult__1__right) # label(axiom). [clausify(570)].
% 2.91/3.11 Derived: times_times(nat) = ti(fun(nat,fun(nat,nat)),times_times(nat)). [resolve(1108,a,1109,a)].
% 2.91/3.11 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),A) = ti(nat,A). [resolve(1108,a,1110,a)].
% 2.91/3.11 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),one_one(nat)) = ti(nat,A). [resolve(1108,a,1111,a)].
% 2.91/3.11 1112 no_zero_divisors(nat) # label(arity_Nat_Onat___Rings_Ono__zero__divisors) # label(axiom). [assumption].
% 2.91/3.11 1113 -no_zero_divisors(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_1_res) # label(axiom). [clausify(26)].
% 2.91/3.11 1114 -no_zero_divisors(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) != zero_zero(A) # label(fact_508_no__zero__divisors) # label(axiom). [clausify(566)].
% 2.91/3.11 1115 -no_zero_divisors(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) != zero_zero(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) # label(fact_509_divisors__zero) # label(axiom). [clausify(567)].
% 2.91/3.11 Derived: zero_zero(nat) = ti(nat,A) | zero_zero(nat) = ti(nat,B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B) != zero_zero(nat). [resolve(1112,a,1114,a)].
% 2.91/3.11 1116 mult_zero(nat) # label(arity_Nat_Onat___Rings_Omult__zero) # label(axiom). [assumption].
% 2.91/3.11 1117 -mult_zero(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_2_res) # label(axiom). [clausify(27)].
% 2.91/3.11 1118 -mult_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) = zero_zero(A) # label(fact_505_mult__zero__left) # label(axiom). [clausify(563)].
% 2.91/3.11 1119 -mult_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) = zero_zero(A) # label(fact_506_mult__zero__right) # label(axiom). [clausify(564)].
% 2.91/3.11 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),A) = zero_zero(nat). [resolve(1116,a,1118,a)].
% 2.91/3.11 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),zero_zero(nat)) = zero_zero(nat). [resolve(1116,a,1119,a)].
% 2.91/3.11 1120 ab_semigroup_mult(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.91/3.11 1121 -ab_semigroup_mult(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_3_res) # label(axiom). [clausify(28)].
% 2.91/3.11 1122 -ab_semigroup_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_502_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom). [clausify(560)].
% 2.91/3.11 1123 -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_530_fold__image__insert) # label(axiom). [clausify(588)].
% 2.91/3.11 1124 -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),f99(B,A,D,E,F,C)),C)) | hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),F),D),C) = hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),E),D),C) # label(fact_539_fold__image__cong) # label(axiom). [clausify(596)].
% 2.91/3.11 1125 -ab_semigroup_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(B,A,D,f99(B,A,E,F,D,C)) != hAPP(B,A,F,f99(B,A,E,F,D,C)) | hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),D),E),C) = hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),F),E),C) # label(fact_539_fold__image__cong) # label(axiom). [clausify(596)].
% 2.91/3.11 1126 -ab_semigroup_mult(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),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),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),semilattice_sup_sup(fun(A,bool)),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),B)),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),C)) # label(fact_547_fold1__Un) # label(axiom). [clausify(604)].
% 2.91/3.11 1127 -ab_semigroup_mult(A) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),B)) # label(fact_735_fold1__insert) # label(axiom). [clausify(792)].
% 2.91/3.11 1128 -ab_semigroup_mult(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f112(A,B)),f113(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f112(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f113(A,B)),bot_bot(fun(A,bool)))))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),B)),B)) # label(fact_739_fold1__in) # label(axiom). [clausify(796)].
% 2.91/3.11 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(1120,a,1122,a)].
% 2.91/3.11 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(1120,a,1123,a)].
% 3.00/3.20 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),f99(A,nat,C,D,E,B)),B)) | hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),E),C),B) = hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),D),C),B). [resolve(1120,a,1124,a)].
% 3.00/3.20 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,nat,C,f99(A,nat,D,E,C,B)) != hAPP(A,nat,E,f99(A,nat,D,E,C,B)) | hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),C),D),B) = hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),E),D),B). [resolve(1120,a,1125,a)].
% 3.00/3.20 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),B) | hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),semilattice_inf_inf(fun(nat,bool)),A),B) != bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),semilattice_sup_sup(fun(nat,bool)),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),A)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),B)). [resolve(1120,a,1126,a)].
% 3.00/3.20 Derived: bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),A)). [resolve(1120,a,1127,a)].
% 3.00/3.20 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f112(nat,A)),f113(nat,A))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f112(nat,A)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f113(nat,A)),bot_bot(fun(nat,bool)))))) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),A)),A)). [resolve(1120,a,1128,a)].
% 3.00/3.20 1129 semiring(nat) # label(arity_Nat_Onat___Rings_Osemiring) # label(axiom). [assumption].
% 3.10/3.38 1130 -semiring(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_4_res) # label(axiom). [clausify(29)].
% 3.10/3.38 1131 -semiring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(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)),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),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),E)) # label(fact_473_combine__common__factor) # label(axiom). [clausify(531)].
% 3.10/3.38 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),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),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)),D)). [resolve(1129,a,1131,a)].
% 3.10/3.38 1132 zero(nat) # label(arity_Nat_Onat___Groups_Ozero) # label(axiom). [assumption].
% 3.10/3.38 1133 -zero(A) | zero_zero(A) = ti(A,zero_zero(A)) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom). [clausify(30)].
% 3.10/3.38 Derived: zero_zero(nat) = ti(nat,zero_zero(nat)). [resolve(1132,a,1133,a)].
% 3.10/3.38 1134 -lattice(A) | semilattice_inf(fun(B,A)) # label(arity_fun___Lattices_Osemilattice__inf) # label(axiom). [clausify(1056)].
% 3.10/3.38 1135 -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(41)].
% 3.10/3.38 1136 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),B) = ti(A,B) # label(fact_251_inf_Oidem) # label(axiom). [clausify(311)].
% 3.10/3.38 1137 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),B) = ti(A,B) # label(fact_252_inf__idem) # label(axiom). [clausify(312)].
% 3.10/3.38 1138 -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_258_inf_Ocommute) # label(axiom). [clausify(318)].
% 3.10/3.38 1139 -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__commute) # label(axiom). [clausify(320)].
% 3.10/3.38 1140 -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_262_inf_Oleft__idem) # label(axiom). [clausify(322)].
% 3.10/3.38 1141 -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__left__idem) # label(axiom). [clausify(324)].
% 3.10/3.38 1142 -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_266_inf_Oleft__commute) # label(axiom). [clausify(326)].
% 3.10/3.38 1143 -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__left__commute) # label(axiom). [clausify(328)].
% 3.10/3.38 1144 -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_Oassoc) # label(axiom). [clausify(335)].
% 3.10/3.38 1145 -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_277_inf__assoc) # label(axiom). [clausify(337)].
% 3.10/3.38 1146 -semilattice_inf(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite_comp_fun_idem(A,A),semilattice_inf_inf(A))) # label(fact_385_comp__fun__idem__inf) # label(axiom). [clausify(445)].
% 3.10/3.38 1147 -semilattice_inf(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C)),B)) # label(fact_594_inf__le1) # label(axiom). [clausify(651)].
% 3.10/3.38 1148 -semilattice_inf(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C)),C)) # label(fact_596_inf__le2) # label(axiom). [clausify(653)].
% 3.10/3.38 1149 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) = ti(A,B) # label(fact_597_le__iff__inf) # label(axiom). [clausify(654)].
% 3.10/3.38 1150 -semilattice_inf(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) != ti(A,B) # label(fact_597_le__iff__inf) # label(axiom). [clausify(654)].
% 3.10/3.38 1151 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_598_le__inf__iff) # label(axiom). [clausify(655)].
% 3.10/3.38 1152 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_598_le__inf__iff) # label(axiom). [clausify(655)].
% 3.10/3.38 1153 -semilattice_inf(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_598_le__inf__iff) # label(axiom). [clausify(655)].
% 3.10/3.38 1154 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),D)),C)) # label(fact_599_le__infI1) # label(axiom). [clausify(656)].
% 3.10/3.38 1155 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),D),B)),C)) # label(fact_600_le__infI2) # label(axiom). [clausify(657)].
% 3.10/3.38 1156 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) = ti(A,B) # label(fact_601_inf__absorb1) # label(axiom). [clausify(658)].
% 3.10/3.38 1157 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),B) = ti(A,B) # label(fact_602_inf__absorb2) # label(axiom). [clausify(659)].
% 3.10/3.38 1158 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) # label(fact_603_le__infI) # label(axiom). [clausify(660)].
% 3.10/3.38 1159 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) # label(fact_604_inf__greatest) # label(axiom). [clausify(661)].
% 3.10/3.38 1160 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),E))) # label(fact_605_inf__mono) # label(axiom). [clausify(662)].
% 3.10/3.38 1161 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_606_le__infE) # label(axiom). [clausify(663)].
% 3.10/3.38 1162 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_606_le__infE) # label(axiom). [clausify(663)].
% 3.10/3.38 1163 -semilattice_inf(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),semilattice_inf_inf(A)),B))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_650_below__fold1__iff) # label(axiom). [clausify(707)].
% 3.10/3.38 1164 -semilattice_inf(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),semilattice_inf_inf(A)),B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f109(A,C,B)),B)) # label(fact_650_below__fold1__iff) # label(axiom). [clausify(707)].
% 3.10/3.38 1165 -semilattice_inf(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),semilattice_inf_inf(A)),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),f109(A,C,B))) # label(fact_650_below__fold1__iff) # label(axiom). [clausify(707)].
% 3.10/3.38 1166 -semilattice_inf(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),semilattice_inf_inf(A)),B)),C)) # label(fact_654_fold1__belowI) # label(axiom). [clausify(711)].
% 3.10/3.38 1167 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),D),B)),C)) # label(fact_891_less__infI2) # label(axiom). [clausify(948)].
% 3.10/3.38 1168 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),D)),C)) # label(fact_892_less__infI1) # label(axiom). [clausify(949)].
% 3.10/3.38 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(1134,b,1135,a)].
% 3.10/3.38 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(1134,b,1136,a)].
% 3.10/3.38 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(1134,b,1138,a)].
% 3.10/3.38 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(1134,b,1140,a)].
% 3.10/3.38 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(1134,b,1142,a)].
% 3.10/3.38 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(1134,b,1144,a)].
% 3.10/3.38 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(1134,b,1146,a)].
% 3.10/3.38 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D)),C)). [resolve(1134,b,1147,a)].
% 3.10/3.38 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D)),D)). [resolve(1134,b,1148,a)].
% 3.10/3.38 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D) = ti(fun(B,A),C). [resolve(1134,b,1149,a)].
% 3.10/3.38 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D) != ti(fun(B,A),C). [resolve(1134,b,1150,a)].
% 3.10/3.38 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),E))) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)). [resolve(1134,b,1151,a)].
% 3.10/3.38 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),E))) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),E)). [resolve(1134,b,1152,a)].
% 3.10/3.38 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),E))) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),E)). [resolve(1134,b,1153,a)].
% 3.10/3.38 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),E)),D)). [resolve(1134,b,1154,a)].
% 3.10/3.38 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),E),C)),D)). [resolve(1134,b,1155,a)].
% 3.10/3.38 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),C) = ti(fun(B,A),C). [resolve(1134,b,1157,a)].
% 3.10/3.38 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),E),F)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),E)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),F))). [resolve(1134,b,1160,a)].
% 3.10/3.38 Derived: -lattice(A) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,finite_finite_1(fun(B,A)),C)) | bot_bot(fun(fun(B,A),bool)) = ti(fun(fun(B,A),bool),C) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),D),hAPP(fun(fun(B,A),bool),fun(B,A),hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),fun(fun(fun(B,A),bool),fun(B,A)),finite_fold1(fun(B,A)),semilattice_inf_inf(fun(B,A))),C))) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,hAPP(fun(B,A),fun(fun(fun(B,A),bool),bool),member(fun(B,A)),E),C)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),D),E)). [resolve(1134,b,1163,a)].
% 3.10/3.38 Derived: -lattice(A) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,finite_finite_1(fun(B,A)),C)) | bot_bot(fun(fun(B,A),bool)) = ti(fun(fun(B,A),bool),C) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),D),hAPP(fun(fun(B,A),bool),fun(B,A),hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),fun(fun(fun(B,A),bool),fun(B,A)),finite_fold1(fun(B,A)),semilattice_inf_inf(fun(B,A))),C))) | hBOOL(hAPP(fun(fun(B,A),bool),bool,hAPP(fun(B,A),fun(fun(fun(B,A),bool),bool),member(fun(B,A)),f109(fun(B,A),D,C)),C)). [resolve(1134,b,1164,a)].
% 3.10/3.38 Derived: -lattice(A) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,finite_finite_1(fun(B,A)),C)) | bot_bot(fun(fun(B,A),bool)) = ti(fun(fun(B,A),bool),C) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),D),hAPP(fun(fun(B,A),bool),fun(B,A),hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),fun(fun(fun(B,A),bool),fun(B,A)),finite_fold1(fun(B,A)),semilattice_inf_inf(fun(B,A))),C))) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),D),f109(fun(B,A),D,C))). [resolve(1134,b,1165,a)].
% 3.10/3.38 Derived: -lattice(A) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,finite_finite_1(fun(B,A)),C)) | -hBOOL(hAPP(fun(fun(B,A),bool),bool,hAPP(fun(B,A),fun(fun(fun(B,A),bool),bool),member(fun(B,A)),D),C)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(fun(B,A),bool),fun(B,A),hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),fun(fun(fun(B,A),bool),fun(B,A)),finite_fold1(fun(B,A)),semilattice_inf_inf(fun(B,A))),C)),D)). [resolve(1134,b,1166,a)].
% 3.10/3.38 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less(fun(B,A)),C),D)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),E),C)),D)). [resolve(1134,b,1167,a)].
% 3.10/3.38 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less(fun(B,A)),C),D)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),E)),D)). [resolve(1134,b,1168,a)].
% 3.10/3.38 1169 semilattice_inf(nat) # label(arity_Nat_Onat___Lattices_Osemilattice__inf) # label(axiom). [assumption].
% 3.10/3.38 Derived: semilattice_inf_inf(nat) = ti(fun(nat,fun(nat,nat)),semilattice_inf_inf(nat)). [resolve(1169,a,1135,a)].
% 3.10/3.38 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),A) = ti(nat,A). [resolve(1169,a,1136,a)].
% 3.10/3.38 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(1169,a,1138,a)].
% 3.10/3.38 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(1169,a,1140,a)].
% 3.10/3.38 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(1169,a,1142,a)].
% 3.10/3.38 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(1169,a,1144,a)].
% 3.10/3.38 Derived: hBOOL(hAPP(fun(nat,fun(nat,nat)),bool,finite_comp_fun_idem(nat,nat),semilattice_inf_inf(nat))). [resolve(1169,a,1146,a)].
% 3.10/3.38 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),B)),A)). [resolve(1169,a,1147,a)].
% 3.10/3.38 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),B)),B)). [resolve(1169,a,1148,a)].
% 3.10/3.38 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),B) = ti(nat,A). [resolve(1169,a,1149,a)].
% 3.10/3.38 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),B) != ti(nat,A). [resolve(1169,a,1150,a)].
% 3.10/3.38 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1169,a,1151,a)].
% 3.10/3.38 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1169,a,1152,a)].
% 3.10/3.38 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),B),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1169,a,1153,a)].
% 3.10/3.38 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),C)),B)). [resolve(1169,a,1154,a)].
% 3.10/3.38 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),C),A)),B)). [resolve(1169,a,1155,a)].
% 3.10/3.38 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),B),A) = ti(nat,A). [resolve(1169,a,1157,a)].
% 3.10/3.38 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),B),D))). [resolve(1169,a,1160,a)].
% 3.10/3.38 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),semilattice_inf_inf(nat)),A))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),C),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1169,a,1163,a)].
% 3.10/3.38 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),semilattice_inf_inf(nat)),A))) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f109(nat,B,A)),A)). [resolve(1169,a,1164,a)].
% 3.10/3.38 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),semilattice_inf_inf(nat)),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f109(nat,B,A))). [resolve(1169,a,1165,a)].
% 3.10/3.38 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),semilattice_inf_inf(nat)),A)),B)). [resolve(1169,a,1166,a)].
% 3.10/3.39 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),C),A)),B)). [resolve(1169,a,1167,a)].
% 3.10/3.39 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_inf_inf(nat),A),C)),B)). [resolve(1169,a,1168,a)].
% 3.10/3.39 1170 semilattice_inf(bool) # label(arity_HOL_Obool___Lattices_Osemilattice__inf) # label(axiom). [assumption].
% 3.10/3.39 Derived: semilattice_inf_inf(bool) = ti(fun(bool,fun(bool,bool)),semilattice_inf_inf(bool)). [resolve(1170,a,1135,a)].
% 3.10/3.39 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),A) = ti(bool,A). [resolve(1170,a,1136,a)].
% 3.10/3.39 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(1170,a,1138,a)].
% 3.10/3.39 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(1170,a,1140,a)].
% 3.10/3.39 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(1170,a,1142,a)].
% 3.10/3.39 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(1170,a,1144,a)].
% 3.10/3.39 Derived: hBOOL(hAPP(fun(bool,fun(bool,bool)),bool,finite_comp_fun_idem(bool,bool),semilattice_inf_inf(bool))). [resolve(1170,a,1146,a)].
% 3.10/3.39 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B)),A)). [resolve(1170,a,1147,a)].
% 3.10/3.39 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B)),B)). [resolve(1170,a,1148,a)].
% 3.10/3.39 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B) = ti(bool,A). [resolve(1170,a,1149,a)].
% 3.10/3.39 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B) != ti(bool,A). [resolve(1170,a,1150,a)].
% 3.10/3.39 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),C))) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)). [resolve(1170,a,1151,a)].
% 3.10/3.39 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),C))) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),C)). [resolve(1170,a,1152,a)].
% 3.10/3.39 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),C))) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),C)). [resolve(1170,a,1153,a)].
% 3.10/3.39 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),C)),B)). [resolve(1170,a,1154,a)].
% 3.10/3.39 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),C),A)),B)). [resolve(1170,a,1155,a)].
% 3.21/3.47 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),A) = ti(bool,A). [resolve(1170,a,1157,a)].
% 3.21/3.47 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),C),D)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),C)),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),D))). [resolve(1170,a,1160,a)].
% 3.21/3.47 Derived: -hBOOL(hAPP(fun(bool,bool),bool,finite_finite_1(bool),A)) | bot_bot(fun(bool,bool)) = ti(fun(bool,bool),A) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),B),hAPP(fun(bool,bool),bool,hAPP(fun(bool,fun(bool,bool)),fun(fun(bool,bool),bool),finite_fold1(bool),semilattice_inf_inf(bool)),A))) | -hBOOL(hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),member(bool),C),A)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),B),C)). [resolve(1170,a,1163,a)].
% 3.21/3.47 Derived: -hBOOL(hAPP(fun(bool,bool),bool,finite_finite_1(bool),A)) | bot_bot(fun(bool,bool)) = ti(fun(bool,bool),A) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),B),hAPP(fun(bool,bool),bool,hAPP(fun(bool,fun(bool,bool)),fun(fun(bool,bool),bool),finite_fold1(bool),semilattice_inf_inf(bool)),A))) | hBOOL(hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),member(bool),f109(bool,B,A)),A)). [resolve(1170,a,1164,a)].
% 3.21/3.47 Derived: -hBOOL(hAPP(fun(bool,bool),bool,finite_finite_1(bool),A)) | bot_bot(fun(bool,bool)) = ti(fun(bool,bool),A) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),B),hAPP(fun(bool,bool),bool,hAPP(fun(bool,fun(bool,bool)),fun(fun(bool,bool),bool),finite_fold1(bool),semilattice_inf_inf(bool)),A))) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),B),f109(bool,B,A))). [resolve(1170,a,1165,a)].
% 3.21/3.47 Derived: -hBOOL(hAPP(fun(bool,bool),bool,finite_finite_1(bool),A)) | -hBOOL(hAPP(fun(bool,bool),bool,hAPP(bool,fun(fun(bool,bool),bool),member(bool),B),A)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(fun(bool,bool),bool,hAPP(fun(bool,fun(bool,bool)),fun(fun(bool,bool),bool),finite_fold1(bool),semilattice_inf_inf(bool)),A)),B)). [resolve(1170,a,1166,a)].
% 3.21/3.47 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less(bool),A),B)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),C),A)),B)). [resolve(1170,a,1167,a)].
% 3.21/3.47 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less(bool),A),B)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),C)),B)). [resolve(1170,a,1168,a)].
% 3.21/3.47 1171 -lattice(A) | semilattice_sup(fun(B,A)) # label(arity_fun___Lattices_Osemilattice__sup) # label(axiom). [clausify(1055)].
% 3.21/3.47 1172 -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(42)].
% 3.21/3.47 1173 -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(75)].
% 3.21/3.47 1174 -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(77)].
% 3.21/3.47 1175 -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(78)].
% 3.21/3.47 1176 -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(80)].
% 3.21/3.47 1177 -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(81)].
% 3.21/3.47 1178 -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(83)].
% 3.21/3.47 1179 -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(84)].
% 3.21/3.47 1180 -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(86)].
% 3.21/3.47 1181 -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(87)].
% 3.21/3.47 1182 -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(88)].
% 3.21/3.47 1183 -semilattice_sup(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite_comp_fun_idem(A,A),semilattice_sup_sup(A))) # label(fact_384_comp__fun__idem__sup) # label(axiom). [clausify(444)].
% 3.21/3.47 1184 -semilattice_sup(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C))) # label(fact_608_sup__ge1) # label(axiom). [clausify(665)].
% 3.21/3.47 1185 -semilattice_sup(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),B))) # label(fact_610_sup__ge2) # label(axiom). [clausify(667)].
% 3.21/3.47 1186 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) = ti(A,C) # label(fact_611_le__iff__sup) # label(axiom). [clausify(668)].
% 3.21/3.47 1187 -semilattice_sup(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) != ti(A,C) # label(fact_611_le__iff__sup) # label(axiom). [clausify(668)].
% 3.21/3.47 1188 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_612_le__sup__iff) # label(axiom). [clausify(669)].
% 3.21/3.47 1189 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_612_le__sup__iff) # label(axiom). [clausify(669)].
% 3.21/3.47 1190 -semilattice_sup(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_612_le__sup__iff) # label(axiom). [clausify(669)].
% 3.21/3.47 1191 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),D))) # label(fact_613_le__supI1) # label(axiom). [clausify(670)].
% 3.21/3.47 1192 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),D),C))) # label(fact_614_le__supI2) # label(axiom). [clausify(671)].
% 3.21/3.47 1193 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) = ti(A,C) # label(fact_615_sup__absorb2) # label(axiom). [clausify(672)].
% 3.21/3.48 1194 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),B) = ti(A,C) # label(fact_616_sup__absorb1) # label(axiom). [clausify(673)].
% 3.21/3.48 1195 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),D)),C)) # label(fact_617_le__supI) # label(axiom). [clausify(674)].
% 3.21/3.48 1196 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),D)),C)) # label(fact_618_sup__least) # label(axiom). [clausify(675)].
% 3.21/3.48 1197 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),E))) # label(fact_619_sup__mono) # label(axiom). [clausify(676)].
% 3.21/3.48 1198 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_620_le__supE) # label(axiom). [clausify(677)].
% 3.21/3.48 1199 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_620_le__supE) # label(axiom). [clausify(677)].
% 3.21/3.48 1200 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),D),C))) # label(fact_889_less__supI2) # label(axiom). [clausify(946)].
% 3.21/3.48 1201 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),D))) # label(fact_890_less__supI1) # label(axiom). [clausify(947)].
% 3.21/3.48 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(1171,b,1172,a)].
% 3.21/3.48 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(1171,b,1173,a)].
% 3.21/3.48 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(1171,b,1175,a)].
% 3.21/3.48 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(1171,b,1177,a)].
% 3.21/3.48 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(1171,b,1179,a)].
% 3.21/3.48 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(1171,b,1181,a)].
% 3.21/3.48 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(1171,b,1183,a)].
% 3.21/3.48 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D))). [resolve(1171,b,1184,a)].
% 3.21/3.48 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),C))). [resolve(1171,b,1185,a)].
% 3.21/3.48 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D) = ti(fun(B,A),D). [resolve(1171,b,1186,a)].
% 3.21/3.48 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D) != ti(fun(B,A),D). [resolve(1171,b,1187,a)].
% 3.21/3.48 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D)),E)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),E)). [resolve(1171,b,1188,a)].
% 3.21/3.48 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D)),E)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),D),E)). [resolve(1171,b,1189,a)].
% 3.21/3.48 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D)),E)) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),E)) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),D),E)). [resolve(1171,b,1190,a)].
% 3.21/3.48 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),E))). [resolve(1171,b,1191,a)].
% 3.21/3.48 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),E),D))). [resolve(1171,b,1192,a)].
% 3.21/3.48 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),C) = ti(fun(B,A),D). [resolve(1171,b,1194,a)].
% 3.21/3.48 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),E),F)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),E)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),F))). [resolve(1171,b,1197,a)].
% 3.21/3.48 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less(fun(B,A)),C),D)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),E),D))). [resolve(1171,b,1200,a)].
% 3.21/3.48 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less(fun(B,A)),C),D)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less(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(1171,b,1201,a)].
% 3.21/3.48 1202 semilattice_sup(nat) # label(arity_Nat_Onat___Lattices_Osemilattice__sup) # label(axiom). [assumption].
% 3.21/3.48 Derived: semilattice_sup_sup(nat) = ti(fun(nat,fun(nat,nat)),semilattice_sup_sup(nat)). [resolve(1202,a,1172,a)].
% 3.21/3.48 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(1202,a,1173,a)].
% 3.21/3.48 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(1202,a,1175,a)].
% 3.21/3.48 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(1202,a,1177,a)].
% 3.21/3.48 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(1202,a,1179,a)].
% 3.21/3.48 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),A) = ti(nat,A). [resolve(1202,a,1181,a)].
% 3.21/3.48 Derived: hBOOL(hAPP(fun(nat,fun(nat,nat)),bool,finite_comp_fun_idem(nat,nat),semilattice_sup_sup(nat))). [resolve(1202,a,1183,a)].
% 3.21/3.48 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),B))). [resolve(1202,a,1184,a)].
% 3.21/3.48 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),B),A))). [resolve(1202,a,1185,a)].
% 3.21/3.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),B) = ti(nat,B). [resolve(1202,a,1186,a)].
% 3.21/3.48 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),B) != ti(nat,B). [resolve(1202,a,1187,a)].
% 3.21/3.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1202,a,1188,a)].
% 3.21/3.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1202,a,1189,a)].
% 3.21/3.48 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1202,a,1190,a)].
% 3.21/3.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),B),C))). [resolve(1202,a,1191,a)].
% 3.21/3.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),C),B))). [resolve(1202,a,1192,a)].
% 3.21/3.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),B),A) = ti(nat,B). [resolve(1202,a,1194,a)].
% 3.21/3.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),B),D))). [resolve(1202,a,1197,a)].
% 3.21/3.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),C),B))). [resolve(1202,a,1200,a)].
% 3.21/3.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),B),C))). [resolve(1202,a,1201,a)].
% 3.21/3.48 1203 semilattice_sup(bool) # label(arity_HOL_Obool___Lattices_Osemilattice__sup) # label(axiom). [assumption].
% 3.21/3.48 Derived: semilattice_sup_sup(bool) = ti(fun(bool,fun(bool,bool)),semilattice_sup_sup(bool)). [resolve(1203,a,1172,a)].
% 3.21/3.48 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(1203,a,1173,a)].
% 3.21/3.48 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(1203,a,1175,a)].
% 3.21/3.48 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(1203,a,1177,a)].
% 3.21/3.48 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(1203,a,1179,a)].
% 3.21/3.48 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),A) = ti(bool,A). [resolve(1203,a,1181,a)].
% 3.21/3.48 Derived: hBOOL(hAPP(fun(bool,fun(bool,bool)),bool,finite_comp_fun_idem(bool,bool),semilattice_sup_sup(bool))). [resolve(1203,a,1183,a)].
% 3.21/3.48 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B))). [resolve(1203,a,1184,a)].
% 3.21/3.48 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),A))). [resolve(1203,a,1185,a)].
% 3.21/3.48 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B) = ti(bool,B). [resolve(1203,a,1186,a)].
% 3.21/3.48 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B) != ti(bool,B). [resolve(1203,a,1187,a)].
% 3.21/3.48 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B)),C)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),C)). [resolve(1203,a,1188,a)].
% 3.21/3.48 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B)),C)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),B),C)). [resolve(1203,a,1189,a)].
% 3.21/3.48 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B)),C)) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),C)) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),B),C)). [resolve(1203,a,1190,a)].
% 3.21/3.48 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),C))). [resolve(1203,a,1191,a)].
% 3.21/3.48 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),C),B))). [resolve(1203,a,1192,a)].
% 3.31/3.58 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),A) = ti(bool,B). [resolve(1203,a,1194,a)].
% 3.31/3.58 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),C),D)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),C)),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),D))). [resolve(1203,a,1197,a)].
% 3.31/3.58 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less(bool),A),B)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),C),B))). [resolve(1203,a,1200,a)].
% 3.31/3.58 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less(bool),A),B)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),C))). [resolve(1203,a,1201,a)].
% 3.31/3.58 1204 -bounded_lattice(A) | bounded_lattice_bot(fun(B,A)) # label(arity_fun___Lattices_Obounded__lattice__bot) # label(axiom). [clausify(1054)].
% 3.31/3.58 1205 -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_114_sup__bot__left) # label(axiom). [clausify(175)].
% 3.31/3.58 1206 -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_115_sup__bot__right) # label(axiom). [clausify(176)].
% 3.31/3.58 1207 -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_116_sup__eq__bot__iff) # label(axiom). [clausify(177)].
% 3.31/3.58 1208 -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_116_sup__eq__bot__iff) # label(axiom). [clausify(177)].
% 3.31/3.58 1209 -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_116_sup__eq__bot__iff) # label(axiom). [clausify(177)].
% 3.31/3.58 1210 -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_291_inf__bot__left) # label(axiom). [clausify(351)].
% 3.31/3.58 1211 -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_292_inf__bot__right) # label(axiom). [clausify(352)].
% 3.31/3.58 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(1204,b,1205,a)].
% 3.31/3.58 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(1204,b,1206,a)].
% 3.31/3.58 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(1204,b,1207,a)].
% 3.31/3.58 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(1204,b,1208,a)].
% 3.31/3.58 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(1204,b,1209,a)].
% 3.31/3.58 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(1204,b,1210,a)].
% 3.31/3.58 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(1204,b,1211,a)].
% 3.31/3.58 1212 bounded_lattice_bot(bool) # label(arity_HOL_Obool___Lattices_Obounded__lattice__bot) # label(axiom). [assumption].
% 4.01/4.24 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),bot_bot(bool)),A) = ti(bool,A). [resolve(1212,a,1205,a)].
% 4.01/4.24 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),bot_bot(bool)) = ti(bool,A). [resolve(1212,a,1206,a)].
% 4.01/4.24 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(1212,a,1207,a)].
% 4.01/4.24 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(1212,a,1208,a)].
% 4.01/4.24 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(1212,a,1209,a)].
% 4.01/4.24 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),bot_bot(bool)),A) = bot_bot(bool). [resolve(1212,a,1210,a)].
% 4.01/4.24 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),bot_bot(bool)) = bot_bot(bool). [resolve(1212,a,1211,a)].
% 4.01/4.24 1213 zero_neq_one(nat) # label(arity_Nat_Onat___Rings_Ozero__neq__one) # label(axiom). [assumption].
% 4.01/4.24 1214 -zero_neq_one(A) | zero_zero(A) != one_one(A) # label(fact_403_one__neq__zero) # label(axiom). [clausify(462)].
% 4.01/4.24 1215 -zero_neq_one(A) | zero_zero(A) != one_one(A) # label(fact_404_zero__neq__one) # label(axiom). [clausify(463)].
% 4.01/4.24 Derived: zero_zero(nat) != one_one(nat). [resolve(1213,a,1214,a)].
% 4.01/4.24 1216 cancel146912293up_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 4.01/4.24 1217 -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_423_add__imp__eq) # label(axiom). [clausify(482)].
% 4.01/4.24 1218 comm_monoid_add(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 4.01/4.24 1219 -comm_monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_425_add_Ocomm__neutral) # label(axiom). [clausify(484)].
% 4.01/4.24 1220 -comm_monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_428_add__0) # label(axiom). [clausify(487)].
% 4.01/4.24 1221 semiri456707255roduct(nat) # label(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption].
% 4.01/4.24 1222 -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_453_add__0__iff) # label(axiom). [clausify(512)].
% 4.01/4.24 1223 -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_453_add__0__iff) # label(axiom). [clausify(512)].
% 4.01/4.24 1224 -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_472_crossproduct__eq) # label(axiom). [clausify(530)].
% 4.01/4.24 1225 -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_472_crossproduct__eq) # label(axiom). [clausify(530)].
% 4.01/4.24 1226 -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_472_crossproduct__eq) # label(axiom). [clausify(530)].
% 4.01/4.24 1227 -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_477_crossproduct__noteq) # label(axiom). [clausify(535)].
% 4.09/4.33 1228 -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_477_crossproduct__noteq) # label(axiom). [clausify(535)].
% 4.09/4.33 1229 -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_477_crossproduct__noteq) # label(axiom). [clausify(535)].
% 4.09/4.33 1230 -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_520_add__scale__eq__noteq) # label(axiom). [clausify(578)].
% 4.09/4.33 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != ti(nat,A) | zero_zero(nat) = ti(nat,B). [resolve(1221,a,1222,a)].
% 4.09/4.33 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = ti(nat,A) | zero_zero(nat) != ti(nat,B). [resolve(1221,a,1223,a)].
% 4.09/4.33 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(1221,a,1224,a)].
% 4.09/4.33 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(1221,a,1225,a)].
% 4.09/4.33 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(1221,a,1226,a)].
% 4.09/4.33 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(1221,a,1230,a)].
% 4.09/4.33 1231 comm_semiring_1(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 4.09/4.33 1232 -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_454_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom). [clausify(513)].
% 4.09/4.33 1233 -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_455_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom). [clausify(514)].
% 4.09/4.33 1234 -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_456_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom). [clausify(515)].
% 4.09/4.33 1235 -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_457_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom). [clausify(516)].
% 4.09/4.33 1236 -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_458_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom). [clausify(517)].
% 4.09/4.33 1237 -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_459_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom). [clausify(518)].
% 4.09/4.33 1238 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_462_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom). [clausify(520)].
% 4.09/4.33 1239 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_463_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom). [clausify(521)].
% 4.09/4.33 1240 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) = ti(A,B) # label(fact_468_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom). [clausify(526)].
% 4.09/4.33 1241 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) = ti(A,B) # label(fact_469_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom). [clausify(527)].
% 4.09/4.33 1242 -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_474_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom). [clausify(532)].
% 4.09/4.33 1243 -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_475_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom). [clausify(533)].
% 4.09/4.33 1244 -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_478_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom). [clausify(536)].
% 4.09/4.33 1245 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) = zero_zero(A) # label(fact_479_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom). [clausify(537)].
% 4.09/4.33 1246 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) = zero_zero(A) # label(fact_480_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom). [clausify(538)].
% 4.09/4.33 1247 -comm_semiring_1(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),C),B) # label(fact_481_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom). [clausify(539)].
% 4.09/4.33 1248 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_482_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom). [clausify(540)].
% 4.09/4.33 1249 -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)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_483_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom). [clausify(541)].
% 4.09/4.34 1250 -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)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_484_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom). [clausify(542)].
% 4.09/4.34 1251 -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)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_485_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom). [clausify(543)].
% 4.09/4.34 1252 -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),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E))) # label(fact_486_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom). [clausify(544)].
% 4.09/4.34 1253 -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),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),E)) # label(fact_487_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom). [clausify(545)].
% 4.09/4.34 1254 -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_488_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom). [clausify(546)].
% 4.09/4.34 1255 -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_523_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom). [clausify(581)].
% 4.09/4.34 1256 -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_524_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom). [clausify(582)].
% 4.09/4.34 1257 -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_525_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom). [clausify(583)].
% 4.09/4.34 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(1231,a,1232,a)].
% 4.09/4.34 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(1231,a,1233,a)].
% 4.09/4.34 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(1231,a,1236,a)].
% 4.09/4.34 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(1231,a,1237,a)].
% 4.23/4.43 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(1231,a,1242,a)].
% 4.23/4.43 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(1231,a,1244,a)].
% 4.23/4.43 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A). [resolve(1231,a,1247,a)].
% 4.23/4.43 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)). [resolve(1231,a,1248,a)].
% 4.23/4.43 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),B). [resolve(1231,a,1251,a)].
% 4.23/4.43 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(1231,a,1254,a)].
% 4.23/4.43 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(1231,a,1255,a)].
% 4.23/4.43 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(1231,a,1256,a)].
% 4.23/4.43 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(1231,a,1257,a)].
% 4.23/4.43 1258 comm_monoid_mult(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 4.23/4.43 1259 -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_467_fold__Un__disjoint) # label(axiom). [clausify(525)].
% 4.23/4.43 1260 -comm_monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) = ti(A,B) # label(fact_511_mult__1) # label(axiom). [clausify(569)].
% 4.23/4.43 1261 -comm_monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) = ti(A,B) # label(fact_513_mult_Ocomm__neutral) # label(axiom). [clausify(571)].
% 4.23/4.43 1262 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),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)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),D)),E)),one_one(A)),C) = 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)),D),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)),C)) # label(fact_532_fold__image__distrib) # label(axiom). [clausify(590)].
% 4.23/4.43 1263 -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(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)),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(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_inf_inf(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_536_fold__image__Un__Int) # label(axiom). [clausify(593)].
% 4.23/4.43 1264 -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)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f97(B,A,E,D,C)),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))) | 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_537_fold__image__Un__one) # label(axiom). [clausify(594)].
% 4.23/4.43 1265 -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(B,A,E,f97(B,A,E,D,C)) != one_one(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)),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_537_fold__image__Un__one) # label(axiom). [clausify(594)].
% 4.23/4.43 1266 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f98(B,A,D,C)),C)) | hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),D),one_one(A)),C) = one_one(A) # label(fact_538_fold__image__1) # label(axiom). [clausify(595)].
% 4.23/4.43 1267 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(B,A,D,f98(B,A,D,C)) != one_one(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)),D),one_one(A)),C) = one_one(A) # label(fact_538_fold__image__1) # label(axiom). [clausify(595)].
% 4.23/4.43 1268 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),f100(D,B,A,E,F,V6,V7,V8,V9,C)),V9)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f101(D,B,A,E,F,V6,V7,V8,V9,C)),C)) | hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),E),V9) = hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),V6),E),C) # label(fact_545_fold__image__eq__general__inverses) # label(axiom). [clausify(602)].
% 4.23/4.43 1269 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),f100(D,B,A,E,F,V6,V7,V8,V9,C)),V9)) | -hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),hAPP(B,D,V7,f101(D,B,A,E,F,V6,V7,V8,V9,C))),V9)) | hAPP(D,B,V8,hAPP(B,D,V7,f101(D,B,A,E,F,V6,V7,V8,V9,C))) != ti(B,f101(D,B,A,E,F,V6,V7,V8,V9,C)) | hAPP(D,A,F,hAPP(B,D,V7,f101(D,B,A,E,F,V6,V7,V8,V9,C))) != hAPP(B,A,V6,f101(D,B,A,E,F,V6,V7,V8,V9,C)) | hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),E),V9) = hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),V6),E),C) # label(fact_545_fold__image__eq__general__inverses) # label(axiom). [clausify(602)].
% 4.23/4.43 1270 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),hAPP(D,B,E,f100(D,B,A,F,V6,V7,V8,E,V9,C))),C)) | hAPP(B,D,V8,hAPP(D,B,E,f100(D,B,A,F,V6,V7,V8,E,V9,C))) != ti(D,f100(D,B,A,F,V6,V7,V8,E,V9,C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f101(D,B,A,F,V6,V7,V8,E,V9,C)),C)) | hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),V6),F),V9) = hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),V7),F),C) # label(fact_545_fold__image__eq__general__inverses) # label(axiom). [clausify(602)].
% 4.23/4.43 1271 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),hAPP(D,B,E,f100(D,B,A,F,V6,V7,V8,E,V9,C))),C)) | hAPP(B,D,V8,hAPP(D,B,E,f100(D,B,A,F,V6,V7,V8,E,V9,C))) != ti(D,f100(D,B,A,F,V6,V7,V8,E,V9,C)) | -hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),hAPP(B,D,V8,f101(D,B,A,F,V6,V7,V8,E,V9,C))),V9)) | hAPP(D,B,E,hAPP(B,D,V8,f101(D,B,A,F,V6,V7,V8,E,V9,C))) != ti(B,f101(D,B,A,F,V6,V7,V8,E,V9,C)) | hAPP(D,A,V6,hAPP(B,D,V8,f101(D,B,A,F,V6,V7,V8,E,V9,C))) != hAPP(B,A,V7,f101(D,B,A,F,V6,V7,V8,E,V9,C)) | hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),V6),F),V9) = hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),V7),F),C) # label(fact_545_fold__image__eq__general__inverses) # label(axiom). [clausify(602)].
% 4.23/4.43 1272 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,C),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f102(D,A,E,F,V6,B,C)),f104(D,A,E,F,V6,B,C))) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite_1(D),V6)) | hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),f106(D,A,E,F,V6,B,C)),V6)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),E),C),V6)),hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),C),V6))) # label(fact_546_fold__image__related) # label(axiom). [clausify(603)].
% 4.23/4.43 1273 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,C),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f102(D,A,E,F,V6,B,C)),f104(D,A,E,F,V6,B,C))) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite_1(D),V6)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(D,A,E,f106(D,A,E,F,V6,B,C))),hAPP(D,A,F,f106(D,A,E,F,V6,B,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),E),C),V6)),hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),C),V6))) # label(fact_546_fold__image__related) # label(axiom). [clausify(603)].
% 4.23/4.43 1274 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,C),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f103(D,A,E,F,V6,B,C)),f105(D,A,E,F,V6,B,C))) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite_1(D),V6)) | hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),f106(D,A,E,F,V6,B,C)),V6)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),E),C),V6)),hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),C),V6))) # label(fact_546_fold__image__related) # label(axiom). [clausify(603)].
% 4.23/4.43 1275 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,C),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f103(D,A,E,F,V6,B,C)),f105(D,A,E,F,V6,B,C))) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite_1(D),V6)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(D,A,E,f106(D,A,E,F,V6,B,C))),hAPP(D,A,F,f106(D,A,E,F,V6,B,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),E),C),V6)),hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),C),V6))) # label(fact_546_fold__image__related) # label(axiom). [clausify(603)].
% 4.23/4.43 1276 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,C),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f102(D,A,E,F,V6,B,C)),f103(D,A,E,F,V6,B,C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f104(D,A,E,F,V6,B,C)),f105(D,A,E,F,V6,B,C)))) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite_1(D),V6)) | hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),f106(D,A,E,F,V6,B,C)),V6)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),E),C),V6)),hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),C),V6))) # label(fact_546_fold__image__related) # label(axiom). [clausify(603)].
% 4.23/4.43 1277 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,C),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f102(D,A,E,F,V6,B,C)),f103(D,A,E,F,V6,B,C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f104(D,A,E,F,V6,B,C)),f105(D,A,E,F,V6,B,C)))) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite_1(D),V6)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(D,A,E,f106(D,A,E,F,V6,B,C))),hAPP(D,A,F,f106(D,A,E,F,V6,B,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),E),C),V6)),hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),C),V6))) # label(fact_546_fold__image__related) # label(axiom). [clausify(603)].
% 4.23/4.43 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(1258,a,1259,a)].
% 4.23/4.43 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),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)),hAPP(fun(A,nat),fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(fun(A,nat),fun(A,nat)),combs(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),times_times(nat)),C)),D)),one_one(nat)),B) = 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)),C),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)),B)). [resolve(1258,a,1262,a)].
% 4.23/4.43 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),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)),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(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_inf_inf(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(1258,a,1263,a)].
% 4.23/4.43 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f97(A,nat,D,C,B)),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))) | 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(1258,a,1264,a)].
% 4.23/4.43 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | hAPP(A,nat,D,f97(A,nat,D,C,B)) != one_one(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)),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(1258,a,1265,a)].
% 4.23/4.43 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),f98(A,nat,C,B)),B)) | hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),C),one_one(nat)),B) = one_one(nat). [resolve(1258,a,1266,a)].
% 4.23/4.43 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,nat,C,f98(A,nat,C,B)) != one_one(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)),C),one_one(nat)),B) = one_one(nat). [resolve(1258,a,1267,a)].
% 4.23/4.43 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f100(C,A,nat,D,E,F,V6,V7,V8,B)),V8)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f101(C,A,nat,D,E,F,V6,V7,V8,B)),B)) | hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),D),V8) = hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),F),D),B). [resolve(1258,a,1268,a)].
% 4.23/4.43 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f100(C,A,nat,D,E,F,V6,V7,V8,B)),V8)) | -hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),hAPP(A,C,V6,f101(C,A,nat,D,E,F,V6,V7,V8,B))),V8)) | hAPP(C,A,V7,hAPP(A,C,V6,f101(C,A,nat,D,E,F,V6,V7,V8,B))) != ti(A,f101(C,A,nat,D,E,F,V6,V7,V8,B)) | hAPP(C,nat,E,hAPP(A,C,V6,f101(C,A,nat,D,E,F,V6,V7,V8,B))) != hAPP(A,nat,F,f101(C,A,nat,D,E,F,V6,V7,V8,B)) | hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),D),V8) = hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),F),D),B). [resolve(1258,a,1269,a)].
% 4.23/4.43 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(C,A,D,f100(C,A,nat,E,F,V6,V7,D,V8,B))),B)) | hAPP(A,C,V7,hAPP(C,A,D,f100(C,A,nat,E,F,V6,V7,D,V8,B))) != ti(C,f100(C,A,nat,E,F,V6,V7,D,V8,B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f101(C,A,nat,E,F,V6,V7,D,V8,B)),B)) | hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),F),E),V8) = hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),V6),E),B). [resolve(1258,a,1270,a)].
% 4.23/4.43 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(C,A,D,f100(C,A,nat,E,F,V6,V7,D,V8,B))),B)) | hAPP(A,C,V7,hAPP(C,A,D,f100(C,A,nat,E,F,V6,V7,D,V8,B))) != ti(C,f100(C,A,nat,E,F,V6,V7,D,V8,B)) | -hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),hAPP(A,C,V7,f101(C,A,nat,E,F,V6,V7,D,V8,B))),V8)) | hAPP(C,A,D,hAPP(A,C,V7,f101(C,A,nat,E,F,V6,V7,D,V8,B))) != ti(A,f101(C,A,nat,E,F,V6,V7,D,V8,B)) | hAPP(C,nat,F,hAPP(A,C,V7,f101(C,A,nat,E,F,V6,V7,D,V8,B))) != hAPP(A,nat,V6,f101(C,A,nat,E,F,V6,V7,D,V8,B)) | hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),F),E),V8) = hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),V6),E),B). [resolve(1258,a,1271,a)].
% 4.23/4.43 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,B),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f102(C,nat,D,E,F,A,B)),f104(C,nat,D,E,F,A,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f106(C,nat,D,E,F,A,B)),F)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),D),B),F)),hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),B),F))). [resolve(1258,a,1272,a)].
% 4.23/4.43 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,B),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f102(C,nat,D,E,F,A,B)),f104(C,nat,D,E,F,A,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(C,nat,D,f106(C,nat,D,E,F,A,B))),hAPP(C,nat,E,f106(C,nat,D,E,F,A,B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),D),B),F)),hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),B),F))). [resolve(1258,a,1273,a)].
% 4.23/4.43 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,B),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f103(C,nat,D,E,F,A,B)),f105(C,nat,D,E,F,A,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f106(C,nat,D,E,F,A,B)),F)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),D),B),F)),hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),B),F))). [resolve(1258,a,1274,a)].
% 4.23/4.43 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,B),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f103(C,nat,D,E,F,A,B)),f105(C,nat,D,E,F,A,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(C,nat,D,f106(C,nat,D,E,F,A,B))),hAPP(C,nat,E,f106(C,nat,D,E,F,A,B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),D),B),F)),hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),B),F))). [resolve(1258,a,1275,a)].
% 4.23/4.43 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,B),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f102(C,nat,D,E,F,A,B)),f103(C,nat,D,E,F,A,B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f104(C,nat,D,E,F,A,B)),f105(C,nat,D,E,F,A,B)))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f106(C,nat,D,E,F,A,B)),F)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),D),B),F)),hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),B),F))). [resolve(1258,a,1276,a)].
% 4.69/4.94 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,B),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f102(C,nat,D,E,F,A,B)),f103(C,nat,D,E,F,A,B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f104(C,nat,D,E,F,A,B)),f105(C,nat,D,E,F,A,B)))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(C,nat,D,f106(C,nat,D,E,F,A,B))),hAPP(C,nat,E,f106(C,nat,D,E,F,A,B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),D),B),F)),hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),B),F))). [resolve(1258,a,1277,a)].
% 4.69/4.94 1278 comm_semiring(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring) # label(axiom). [assumption].
% 4.69/4.94 1279 -comm_semiring(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_476_comm__semiring__class_Odistrib) # label(axiom). [clausify(534)].
% 4.69/4.94 1280 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom). [assumption].
% 4.69/4.94 1281 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_562_linorder__le__cases) # label(axiom). [clausify(619)].
% 4.69/4.94 1282 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_576_linorder__linear) # label(axiom). [clausify(633)].
% 4.69/4.94 1283 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) # label(fact_837_linorder__antisym__conv2) # label(axiom). [clausify(894)].
% 4.69/4.94 1284 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_837_linorder__antisym__conv2) # label(axiom). [clausify(894)].
% 4.69/4.94 1285 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_839_leD) # label(axiom). [clausify(896)].
% 4.69/4.94 1286 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = ti(A,B) # label(fact_842_linorder__antisym__conv1) # label(axiom). [clausify(899)].
% 4.69/4.94 1287 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_842_linorder__antisym__conv1) # label(axiom). [clausify(899)].
% 4.69/4.94 1288 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_843_not__leE) # label(axiom). [clausify(900)].
% 4.69/4.94 1289 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_844_leI) # label(axiom). [clausify(901)].
% 4.69/4.94 1290 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_848_linorder__le__less__linear) # label(axiom). [clausify(905)].
% 4.69/4.94 1291 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_849_linorder__not__le) # label(axiom). [clausify(906)].
% 4.69/4.94 1292 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_849_linorder__not__le) # label(axiom). [clausify(906)].
% 4.69/4.94 1293 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_850_linorder__not__less) # label(axiom). [clausify(907)].
% 4.69/4.94 1294 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_850_linorder__not__less) # label(axiom). [clausify(907)].
% 4.69/4.94 1295 -linorder(A) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_917_linorder__neq__iff) # label(axiom). [clausify(974)].
% 4.69/4.94 1296 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_917_linorder__neq__iff) # label(axiom). [clausify(974)].
% 4.69/4.94 1297 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_917_linorder__neq__iff) # label(axiom). [clausify(974)].
% 4.69/4.94 1298 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,C) = ti(A,B) # label(fact_918_not__less__iff__gr__or__eq) # label(axiom). [clausify(975)].
% 4.69/4.94 1299 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_918_not__less__iff__gr__or__eq) # label(axiom). [clausify(975)].
% 4.69/4.94 1300 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_918_not__less__iff__gr__or__eq) # label(axiom). [clausify(975)].
% 4.69/4.94 1301 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_919_linorder__less__linear) # label(axiom). [clausify(976)].
% 4.69/4.94 1302 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,B) = ti(A,C) # label(fact_920_linorder__antisym__conv3) # label(axiom). [clausify(977)].
% 4.69/4.94 1303 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,B) != ti(A,C) # label(fact_920_linorder__antisym__conv3) # label(axiom). [clausify(977)].
% 4.69/4.94 1304 -linorder(A) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_921_linorder__neqE) # label(axiom). [clausify(978)].
% 4.69/4.94 1305 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_937_linorder__cases) # label(axiom). [clausify(994)].
% 4.69/4.94 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(1280,a,1281,a)].
% 4.69/4.94 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) = ti(nat,A). [resolve(1280,a,1283,a)].
% 4.69/4.94 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) != ti(nat,A). [resolve(1280,a,1284,a)].
% 4.69/4.94 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(1280,a,1285,a)].
% 4.69/4.94 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,B) != ti(nat,A). [resolve(1280,a,1287,a)].
% 4.69/4.94 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(1280,a,1288,a)].
% 4.91/5.11 Derived: ti(nat,A) = ti(nat,B) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1280,a,1295,a)].
% 4.91/5.11 Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(1280,a,1296,a)].
% 4.91/5.11 Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1280,a,1297,a)].
% 4.91/5.11 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(1280,a,1299,a)].
% 4.91/5.11 1306 ordere236663937imp_le(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 4.91/5.11 1307 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_630_add__le__imp__le__left) # label(axiom). [clausify(687)].
% 4.91/5.11 1308 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_631_add__le__imp__le__right) # label(axiom). [clausify(688)].
% 4.91/5.11 1309 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_635_add__le__cancel__left) # label(axiom). [clausify(692)].
% 4.91/5.11 1310 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_635_add__le__cancel__left) # label(axiom). [clausify(692)].
% 4.91/5.11 1311 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_636_add__le__cancel__right) # label(axiom). [clausify(693)].
% 4.91/5.11 1312 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_636_add__le__cancel__right) # label(axiom). [clausify(693)].
% 4.91/5.11 1313 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_879_add__less__cancel__right) # label(axiom). [clausify(936)].
% 4.91/5.11 1314 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_879_add__less__cancel__right) # label(axiom). [clausify(936)].
% 4.91/5.11 1315 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_880_add__less__cancel__left) # label(axiom). [clausify(937)].
% 4.91/5.11 1316 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_880_add__less__cancel__left) # label(axiom). [clausify(937)].
% 4.91/5.11 1317 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_884_add__less__imp__less__right) # label(axiom). [clausify(941)].
% 4.98/5.18 1318 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_885_add__less__imp__less__left) # label(axiom). [clausify(942)].
% 4.98/5.18 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(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),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1306,a,1307,a)].
% 4.98/5.18 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(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),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1306,a,1308,a)].
% 4.98/5.18 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(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),A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1306,a,1310,a)].
% 4.98/5.18 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(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),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1306,a,1312,a)].
% 4.98/5.18 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1306,a,1313,a)].
% 4.98/5.18 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1306,a,1314,a)].
% 4.98/5.18 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(1306,a,1315,a)].
% 4.98/5.18 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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),A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(1306,a,1316,a)].
% 4.98/5.18 1319 ordere779506340up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 4.98/5.18 1320 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_632_add__mono) # label(axiom). [clausify(689)].
% 4.98/5.18 1321 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_633_add__left__mono) # label(axiom). [clausify(690)].
% 4.98/5.18 1322 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_634_add__right__mono) # label(axiom). [clausify(691)].
% 4.98/5.18 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(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(1319,a,1320,a)].
% 4.98/5.26 1323 ordere216010020id_add(nat) # label(arity_Nat_Onat___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 4.98/5.26 1324 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_668_add__nonneg__nonneg) # label(axiom). [clausify(725)].
% 4.98/5.26 1325 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_669_add__nonneg__eq__0__iff) # label(axiom). [clausify(726)].
% 4.98/5.26 1326 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != zero_zero(A) | zero_zero(A) = ti(A,C) # label(fact_669_add__nonneg__eq__0__iff) # label(axiom). [clausify(726)].
% 4.98/5.26 1327 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = zero_zero(A) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_669_add__nonneg__eq__0__iff) # label(axiom). [clausify(726)].
% 4.98/5.26 1328 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_670_add__increasing) # label(axiom). [clausify(727)].
% 4.98/5.26 1329 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B))) # label(fact_671_add__increasing2) # label(axiom). [clausify(728)].
% 4.98/5.26 1330 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_672_add__nonpos__nonpos) # label(axiom). [clausify(729)].
% 4.98/5.26 1331 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_984_add__pos__pos) # label(axiom). [clausify(1041)].
% 4.98/5.26 1332 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_986_add__neg__neg) # label(axiom). [clausify(1043)].
% 4.98/5.26 1333 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_992_add__nonpos__neg) # label(axiom). [clausify(1049)].
% 4.98/5.26 1334 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_993_add__neg__nonpos) # label(axiom). [clausify(1050)].
% 4.98/5.26 1335 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_994_add__strict__increasing2) # label(axiom). [clausify(1051)].
% 4.98/5.26 1336 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_995_add__strict__increasing) # label(axiom). [clausify(1052)].
% 4.98/5.26 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))). [resolve(1323,a,1324,a)].
% 4.98/5.26 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != zero_zero(nat) | zero_zero(nat) = ti(nat,A). [resolve(1323,a,1325,a)].
% 4.98/5.26 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != zero_zero(nat) | zero_zero(nat) = ti(nat,B). [resolve(1323,a,1326,a)].
% 4.98/5.26 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = zero_zero(nat) | zero_zero(nat) != ti(nat,A) | zero_zero(nat) != ti(nat,B). [resolve(1323,a,1327,a)].
% 4.98/5.26 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(1323,a,1328,a)].
% 4.98/5.26 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),A))). [resolve(1323,a,1329,a)].
% 4.98/5.26 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))). [resolve(1323,a,1330,a)].
% 4.98/5.26 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))). [resolve(1323,a,1331,a)].
% 4.98/5.26 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))). [resolve(1323,a,1332,a)].
% 4.98/5.26 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))). [resolve(1323,a,1333,a)].
% 4.98/5.26 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))). [resolve(1323,a,1334,a)].
% 5.29/5.49 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(1323,a,1335,a)].
% 5.29/5.49 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(1323,a,1336,a)].
% 5.29/5.49 1337 ordere453448008miring(nat) # label(arity_Nat_Onat___Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 5.29/5.49 1338 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_673_split__mult__neg__le) # label(axiom). [clausify(730)].
% 5.29/5.49 1339 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_673_split__mult__neg__le) # label(axiom). [clausify(730)].
% 5.29/5.49 1340 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_683_mult__nonpos__nonneg) # label(axiom). [clausify(740)].
% 5.29/5.49 1341 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),zero_zero(A))) # label(fact_684_mult__nonneg__nonpos2) # label(axiom). [clausify(741)].
% 5.29/5.49 1342 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_685_mult__nonneg__nonpos) # label(axiom). [clausify(742)].
% 5.29/5.49 1343 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_686_mult__nonneg__nonneg) # label(axiom). [clausify(743)].
% 5.29/5.49 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),zero_zero(nat))). [resolve(1337,a,1338,a)].
% 5.29/5.49 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),zero_zero(nat))). [resolve(1337,a,1339,a)].
% 5.29/5.49 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))). [resolve(1337,a,1343,a)].
% 5.29/5.49 1344 ordered_semiring(nat) # label(arity_Nat_Onat___Rings_Oordered__semiring) # label(axiom). [assumption].
% 5.29/5.56 1345 -ordered_semiring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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_675_mult__mono) # label(axiom). [clausify(732)].
% 5.29/5.56 1346 -ordered_semiring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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_676_mult__mono_H) # label(axiom). [clausify(733)].
% 5.29/5.56 1347 -ordered_semiring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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),D),C))) # label(fact_680_mult__left__mono) # label(axiom). [clausify(737)].
% 5.29/5.56 1348 -ordered_semiring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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_681_mult__right__mono) # label(axiom). [clausify(738)].
% 5.29/5.56 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(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(1344,a,1345,a)].
% 5.29/5.56 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(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(1344,a,1346,a)].
% 5.29/5.56 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))). [resolve(1344,a,1347,a)].
% 5.29/5.56 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(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(1344,a,1348,a)].
% 5.29/5.56 1349 ordere1490568538miring(nat) # label(arity_Nat_Onat___Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 5.29/5.56 1350 -ordere1490568538miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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),D),C))) # label(fact_679_comm__mult__left__mono) # label(axiom). [clausify(736)].
% 5.72/5.93 1351 linordered_semidom(nat) # label(arity_Nat_Onat___Rings_Olinordered__semidom) # label(axiom). [assumption].
% 5.72/5.93 1352 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),zero_zero(A))) # label(fact_691_not__one__le__zero) # label(axiom). [clausify(748)].
% 5.72/5.93 1353 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),one_one(A))) # label(fact_692_zero__le__one) # label(axiom). [clausify(749)].
% 5.72/5.93 1354 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_959_less__1__mult) # label(axiom). [clausify(1016)].
% 5.72/5.93 1355 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A)))) # label(fact_960_less__add__one) # label(axiom). [clausify(1017)].
% 5.72/5.93 1356 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),zero_zero(A))) # label(fact_961_not__one__less__zero) # label(axiom). [clausify(1018)].
% 5.72/5.93 1357 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),one_one(A))) # label(fact_962_zero__less__one) # label(axiom). [clausify(1019)].
% 5.72/5.93 1358 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_985_pos__add__strict) # label(axiom). [clausify(1042)].
% 5.72/5.93 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),zero_zero(nat))). [resolve(1351,a,1352,a)].
% 5.72/5.93 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),one_one(nat))). [resolve(1351,a,1353,a)].
% 5.72/5.93 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))). [resolve(1351,a,1354,a)].
% 5.72/5.93 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat)))). [resolve(1351,a,1355,a)].
% 5.72/5.93 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),zero_zero(nat))). [resolve(1351,a,1356,a)].
% 5.72/5.93 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),one_one(nat))). [resolve(1351,a,1357,a)].
% 5.72/5.93 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(1351,a,1358,a)].
% 5.72/5.93 1359 ordere223160158up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.72/5.93 1360 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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_857_add__less__le__mono) # label(axiom). [clausify(914)].
% 5.72/5.93 1361 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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_858_add__le__less__mono) # label(axiom). [clausify(915)].
% 5.72/5.93 1362 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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),D))) # label(fact_881_add__strict__right__mono) # label(axiom). [clausify(938)].
% 5.82/6.08 1363 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_882_add__strict__left__mono) # label(axiom). [clausify(939)].
% 5.82/6.08 1364 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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_883_add__strict__mono) # label(axiom). [clausify(940)].
% 5.82/6.08 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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(1359,a,1360,a)].
% 5.82/6.08 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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(1359,a,1361,a)].
% 5.82/6.08 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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(1359,a,1364,a)].
% 5.82/6.08 1365 linord893533164strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 5.82/6.08 1366 -linord893533164strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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),D),C))) # label(fact_966_comm__mult__strict__left__mono) # label(axiom). [clausify(1023)].
% 5.82/6.08 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))). [resolve(1365,a,1366,a)].
% 5.82/6.08 1367 linord20386208strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 5.82/6.08 1368 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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),D),C))) # label(fact_967_mult__strict__left__mono) # label(axiom). [clausify(1024)].
% 5.82/6.08 1369 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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_968_mult__strict__right__mono) # label(axiom). [clausify(1025)].
% 5.82/6.08 1370 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_970_mult__neg__pos) # label(axiom). [clausify(1027)].
% 5.82/6.08 1371 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_972_zero__less__mult__pos2) # label(axiom). [clausify(1029)].
% 6.41/6.62 1372 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_973_zero__less__mult__pos) # label(axiom). [clausify(1030)].
% 6.41/6.62 1373 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),zero_zero(A))) # label(fact_974_mult__pos__neg2) # label(axiom). [clausify(1031)].
% 6.41/6.62 1374 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_975_mult__pos__neg) # label(axiom). [clausify(1032)].
% 6.41/6.62 1375 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_976_mult__pos__pos) # label(axiom). [clausify(1033)].
% 6.41/6.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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(1367,a,1369,a)].
% 6.41/6.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),zero_zero(nat))). [resolve(1367,a,1370,a)].
% 6.41/6.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(1367,a,1371,a)].
% 6.41/6.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)). [resolve(1367,a,1372,a)].
% 6.41/6.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),zero_zero(nat))). [resolve(1367,a,1374,a)].
% 6.41/6.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))). [resolve(1367,a,1375,a)].
% 6.41/6.62
% 6.41/6.62 ============================== end predicate elimination =============
% 6.41/6.62
% 6.41/6.62 Auto_denials: (non-Horn, no changes).
% 6.41/6.62
% 6.41/6.62 Term ordering decisions:
% 6.41/6.62 Function symbol KB weights: bool=1. nat=1. state=1. com=1. pname=1. suc=1. x_a=1. evaln=1. evalc=1. while=1. body=1. cond=1. fconj=1. semi=1. body_1=1. com_size=1. fdisj=1. fimplies=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. finite_fold_image=1. sum_sum=1. sum_Plus=1. finite1357897459simple=1. combk=1. finite_comp_fun_idem=1. big_comm_monoid_big=1. finite908156982e_idem=1. hoare_1759541758le_rec=1. hoare_225284258e_case=1. f12=1. f13=1. f14=1. f18=1. f19=1. f21=1. f22=1. f33=1. f34=1. f51=1. f52=1. f54=1. f55=1. f69=1. f74=1. f75=1. f89=1. f90=1. f95=1. f108=1. f112=1. f113=1. f121=1. f126=1. f127=1. f130=1. f131=1. f133=1. hoare_2118899576triple=1. ord_less_eq=1. bot_bot=1. semilattice_inf_inf=1. ord_less=1. semilattice_sup_sup=1. member=1. finite_finite_1=1. times_times=1. plus_plus=1. zero_zero=1. insert=1. minus_minus=1. finite_card=1. hoare_759811442triple=1. one_one=1. collect=1. hoare_1301688828derivs=1. big_lattice_Inf_fin=1. big_lattice_Sup_fin=1. option=1. finite_fold1=1. hoare_1942962616_valid=1. fequal=1. the_1=1. size_size=1. the=1. finite_folding_one=1. finite2073411215e_idem=1. hoare_902341502valids=1. nat_case=1. powp=1. finite_fold1Set=1. combi=1. if=1. partial_flat_lub=1. the_elem=1. big_semilattice_big=1. hoare_2043812435e_size=1. undefined=1. f32=1. f35=1. f125=1. f129=1. f132=1. f134=1. combb=1. combc=1. combs=1. f2=1. f3=1. f16=1. f17=1. f36=1. f43=1. f46=1. f49=1. f50=1. f56=1. f57=1. f58=1. f61=1. f65=1. f67=1. f68=1. f70=1. f71=1. f72=1. f73=1. f76=1. f77=1. f86=1. f87=1. f88=1. f91=1. f92=1. f93=1. f94=1. f96=1. f109=1. f118=1. f122=1. f128=1. hAPP=1. f1=1. f5=1. f6=1. f7=1. f8=1. f9=1. f10=1. f20=1. f40=1. f41=1. f47=1. f53=1. f62=1. f63=1. f66=1. f78=1. f79=1. f80=1. f81=1. f82=1. f83=1. f98=1. f107=1. f115=1. f116=1. f117=1. f124=1. f4=1. f11=1. f23=1. f24=1. f37=1. f38=1. f39=1. f42=1. f48=1. f59=1. f60=1. f97=1. f114=1. f119=1. f120=1. f123=1. f15=1. f25=1. f26=1. f27=1. f28=1. f99=1. f29=1. f30=1. f31=1. f85=1. f102=1. f103=1. f104=1. f105=1. f106=1. f45=1. f84=1. f44=1. f64=1. f100=1. f101=1.
% 10.31/10.53
% 10.31/10.53 ============================== end of process initial clauses ========
% 10.31/10.53
% 10.31/10.53 ============================== CLAUSES FOR SEARCH ====================
% 10.31/10.53
% 10.31/10.53 ============================== end of clauses for search =============
% 10.31/10.53
% 10.31/10.53 ============================== SEARCH ================================
% 10.31/10.53
% 10.31/10.53 % Starting search at 4.55 seconds.
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=149.000, iters=3404
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=147.000, iters=3396
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% 10.31/10.53 Low Water (keep): wt=146.000, iters=3407
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% 10.31/10.53 Low Water (keep): wt=142.000, iters=3352
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=139.000, iters=3344
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=133.000, iters=3434
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=130.000, iters=3338
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=129.000, iters=3355
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% 10.31/10.53 Low Water (keep): wt=125.000, iters=3349
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% 10.31/10.53 Low Water (keep): wt=123.000, iters=3431
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% 10.31/10.53 Low Water (keep): wt=120.000, iters=3364
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=116.000, iters=3334
% 10.31/10.53
% 10.31/10.53 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 43 (0.00 of 6.42 sec).
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=113.000, iters=3477
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=109.000, iters=3357
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% 10.31/10.53 Low Water (keep): wt=108.000, iters=3445
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% 10.31/10.53 Low Water (keep): wt=103.000, iters=3398
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% 10.31/10.53 Low Water (keep): wt=99.000, iters=3412
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=94.000, iters=3393
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% 10.31/10.53 Low Water (keep): wt=93.000, iters=3340
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=92.000, iters=3344
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% 10.31/10.53 Low Water (keep): wt=91.000, iters=3371
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% 10.31/10.53 Low Water (keep): wt=87.000, iters=3617
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% 10.31/10.53 Low Water (keep): wt=85.000, iters=3614
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% 10.31/10.53 Low Water (keep): wt=84.000, iters=3654
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% 10.31/10.53 Low Water (keep): wt=79.000, iters=3385
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=77.000, iters=3474
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% 10.31/10.53 Low Water (keep): wt=74.000, iters=3387
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=73.000, iters=3403
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=71.000, iters=3339
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=70.000, iters=3397
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=69.000, iters=3351
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=68.000, iters=3407
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=67.000, iters=3432
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=65.000, iters=3346
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=64.000, iters=3356
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=63.000, iters=3388
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=62.000, iters=3336
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=61.000, iters=3448
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=60.000, iters=3353
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=59.000, iters=3358
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=58.000, iters=3338
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=56.000, iters=3342
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=55.000, iters=3432
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=54.000, iters=3370
% 10.31/10.53
% 10.31/10.53 Low Water (keep): wt=53.000, iters=3354
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=52.000, iters=3511
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=51.000, iters=3364
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=50.000, iters=3403
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=49.000, iters=3385
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=48.000, iters=3343
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=46.000, iters=3570
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=42.000, iters=3391
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=41.000, iters=4239
% 126.03/126.25
% 126.03/126.25 Low Water (displace): id=5144, wt=200.000
% 126.03/126.25
% 126.03/126.25 Low Water (displace): id=4366, wt=199.000
% 126.03/126.25
% 126.03/126.25 Low Water (displace): id=4420, wt=198.000
% 126.03/126.25
% 126.03/126.25 Low Water (displace): id=15773, wt=14.000
% 126.03/126.25
% 126.03/126.25 Low Water (displace): id=15845, wt=12.000
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=34.000, iters=3352
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=33.000, iters=3357
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=32.000, iters=3420
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=31.000, iters=3350
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=30.000, iters=3348
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=29.000, iters=3397
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=25.000, iters=3342
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=24.000, iters=3386
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=23.000, iters=3377
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=22.000, iters=3335
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=21.000, iters=3376
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=20.000, iters=3333
% 126.03/126.25
% 126.03/126.25 Low Water (keep): wt=19.000, iters=3457
% 126.03/126.25
% 126.03/126.25 ============================== STATISTICS ============================
% 126.03/126.25
% 126.03/126.25 Given=10191. Generated=1646328. Kept=416496. proofs=0.
% 126.03/126.25 Usable=9863. Sos=9999. Demods=720. Limbo=817, Disabled=397658. Hints=0.
% 126.03/126.25 Kept_by_rule=0, Deleted_by_rule=156063.
% 126.03/126.25 Forward_subsumed=157606. Back_subsumed=128.
% 126.03/126.25 Sos_limit_deleted=916163. Sos_displaced=393026. Sos_removed=0.
% 126.03/126.25 New_demodulators=1352 (0 lex), Back_demodulated=2562. Back_unit_deleted=101.
% 126.03/126.25 Demod_attempts=122182528. Demod_rewrites=342069.
% 126.03/126.25 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
% 126.03/126.25 Nonunit_fsub_feature_tests=1458701. Nonunit_bsub_feature_tests=15829.
% 126.03/126.25 Megabytes=419.43.
% 126.03/126.25 User_CPU=123.08, System_CPU=1.11, Wall_clock=124.
% 126.03/126.25
% 126.03/126.25 Megs malloced by palloc(): 400.
% 126.03/126.25 type (bytes each) gets frees in use bytes
% 126.03/126.25 chunk ( 104) 93232 93232 0 0.0 K
% 126.03/126.25 string_buf ( 8) 83053 83053 0 0.0 K
% 126.03/126.25 token ( 20) 209853 209853 0 0.0 K
% 126.03/126.25 pterm ( 16) 147507 147507 0 0.0 K
% 126.03/126.25 hashtab ( 8) 1090 1090 0 0.0 K
% 126.03/126.25 hashnode ( 8) 4553 4553 0 0.0 K
% 126.03/126.25 term ( 20) 251394300 240672935 10721365 209401.7 K
% 126.03/126.25 term arg arrays: 43588.7 K
% 126.03/126.25 attribute ( 12) 7872 230 7642 89.6 K
% 126.03/126.25 ilist ( 8) 886356809 884579624 1777185 13884.3 K
% 126.03/126.25 plist ( 8) 10875281 10419440 455841 3561.3 K
% 126.03/126.25 i2list ( 12) 26236826 26236826 0 0.0 K
% 126.03/126.25 just ( 12) 2239120 1762255 476865 5588.3 K
% 126.03/126.25 parajust ( 16) 479494 418796 60698 948.4 K
% 126.03/126.25 instancejust ( 8) 0 0 0 0.0 K
% 126.03/126.25 ivyjust ( 24) 0 0 0 0.0 K
% 126.03/126.25 formula ( 28) 47762 31070 16692 456.4 K
% 126.03/126.25 formula arg arrays: 56.7 K
% 126.03/126.25 topform ( 52) 1649381 1229832 419549 21305.2 K
% 126.03/126.25 clist_pos ( 20) 1244411 825354 419057 8184.7 K
% 126.03/126.25 clist ( 16) 8 1 7 0.1 K
% 126.03/126.25 context ( 808) 11418767 11418765 2 1.6 K
% 126.03/126.25 trail ( 12) 11427351 11427348 3 0.0 K
% 126.03/126.25 ac_match_pos (70044) 0 0 0 0.0 K
% 126.03/126.25 ac_match_free_vars_pos (20020)
% 126.03/126.25 0 0 0 0.0 K
% 126.03/126.25 btm_state ( 60) 0 0 0 0.0 K
% 126.03/126.25 btu_state ( 60) 0 0 0 0.0 K
% 126.03/126.25 ac_position (285432) 0 0 0 0.0 K
% 126.03/126.25 fpa_trie ( 20) 1297373 1078916 218457 4266.7 K
% 126.03/126.25 fpa_state ( 28) 8097570 8097570 0 0.0 K
% 126.03/126.25 fpa_index ( 12) 10 0 10 0.1 K
% 126.03/126.25 fpa_chunk ( 20) 2391696 2261418 130278 2544.5 K
% 126.03/126.25 fpa_list ( 16) 1143019 0 1143019 17859.7 K
% 126.03/126.25 fpa_list chunks: 12096.5 K
% 126.03/126.26 discrim ( 12) 3656281 3539160 117121 1372.5 K
% 126.03/126.26 discrim_pos ( 16) 425333 425333 0 0.0 K
% 126.03/126.26 flat2 ( 32) 62175722 62175722 0 0.0 K
% 126.03/126.26 flat ( 48) 0 0 0 0.0 K
% 126.03/126.26 flatterm ( 32) 166615300 166615300 0 0.0 K
% 126.03/126.26 mindex ( 28) 13 0 13 0.4 K
% 126.03/126.26 mindex_pos ( 56) 6944372 6944372 0 0.0 K
% 126.03/126.26 lindex ( 12) 5 0 5 0.1 K
% 126.03/126.26 clash ( 40) 0 0 0 0.0 K
% 126.03/126.26 di_tree ( 12) 20585215 15629069 4956146 58079.8 K
% 126.03/126.26 avl_node ( 20) 829650 809652 19998 390.6 K
% 126.03/126.26
% 126.03/126.26 Memory report, 20 @ 20 = 400 megs (400.00 megs used).
% 126.03/126.26 List 1, length 8, 0.0 K
% 126.03/126.26 List 2, length 895, 7.0 K
% 126.03/126.26 List 3, length 93665, 1097.6 K
% 126.03/126.26 List 7, length 98, 2.7 K
% 126.03/126.26 List 8, length 1038, 32.4 K
% 126.03/126.26 List 10, length 22, 0.9 K
% 126.03/126.26 List 11, length 7, 0.3 K
% 126.03/126.26 List 12, length 10, 0.5 K
% 126.03/126.26 List 14, length 13, 0.7 K
% 126.03/126.26 List 15, length 14, 0.8 K
% 126.03/126.26 List 16, length 1545, 96.6 K
% 126.03/126.26 List 26, length 768, 78.0 K
% 126.03/126.26 List 32, length 434, 54.2 K
% 126.03/126.26 List 64, length 82, 20.5 K
% 126.03/126.26 List 128, length 251, 125.5 K
% 126.03/126.26 List 202, length 2, 1.6 K
% 126.03/126.26 List 256, length 76, 76.0 K
% 126.03/126.26
% 126.03/126.26 ============================== SELECTOR REPORT =======================
% 126.03/126.26 Sos_deleted=916163, Sos_displaced=393026, Sos_size=9999
% 126.03/126.26 SELECTOR PART PRIORITY ORDER SIZE SELECTED
% 126.03/126.26 I 2147483647 high age 0 1226
% 126.03/126.26 H 1 high weight 0 0
% 126.03/126.26 A 1 low age 9999 997
% 126.03/126.26 F 4 low weight 251 3984
% 126.03/126.26 T 4 low weight 9748 3984
% 126.03/126.26 ============================== end of selector report ================
% 126.03/126.26
% 126.03/126.26 ============================== end of statistics =====================
% 126.03/126.26
% 126.03/126.26 Exiting with failure.
% 126.03/126.26
% 126.03/126.26 Process 7095 exit (max_megs) Sun Jun 5 07:37:16 2022
% 126.03/126.26 Prover9 interrupted
%------------------------------------------------------------------------------