TSTP Solution File: SCT169+7 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT169+7 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 : Mon Jul 18 22:04:21 EDT 2022
% Result : Unknown 227.56s 227.88s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT169+7 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 2 02:34:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.96/2.20 ============================== Prover9 ===============================
% 1.96/2.20 Prover9 (32) version 2009-11A, November 2009.
% 1.96/2.20 Process 20609 was started by sandbox on n018.cluster.edu,
% 1.96/2.20 Sat Jul 2 02:34:50 2022
% 1.96/2.20 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_20456_n018.cluster.edu".
% 1.96/2.20 ============================== end of head ===========================
% 1.96/2.20
% 1.96/2.20 ============================== INPUT =================================
% 1.96/2.20
% 1.96/2.20 % Reading from file /tmp/Prover9_20456_n018.cluster.edu
% 1.96/2.20
% 1.96/2.20 set(prolog_style_variables).
% 1.96/2.20 set(auto2).
% 1.96/2.20 % set(auto2) -> set(auto).
% 1.96/2.20 % set(auto) -> set(auto_inference).
% 1.96/2.20 % set(auto) -> set(auto_setup).
% 1.96/2.20 % set(auto_setup) -> set(predicate_elim).
% 1.96/2.20 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.96/2.20 % set(auto) -> set(auto_limits).
% 1.96/2.20 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.96/2.20 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.96/2.20 % set(auto) -> set(auto_denials).
% 1.96/2.20 % set(auto) -> set(auto_process).
% 1.96/2.20 % set(auto2) -> assign(new_constants, 1).
% 1.96/2.20 % set(auto2) -> assign(fold_denial_max, 3).
% 1.96/2.20 % set(auto2) -> assign(max_weight, "200.000").
% 1.96/2.20 % set(auto2) -> assign(max_hours, 1).
% 1.96/2.20 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.96/2.20 % set(auto2) -> assign(max_seconds, 0).
% 1.96/2.20 % set(auto2) -> assign(max_minutes, 5).
% 1.96/2.20 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.96/2.20 % set(auto2) -> set(sort_initial_sos).
% 1.96/2.20 % set(auto2) -> assign(sos_limit, -1).
% 1.96/2.20 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.96/2.20 % set(auto2) -> assign(max_megs, 400).
% 1.96/2.20 % set(auto2) -> assign(stats, some).
% 1.96/2.20 % set(auto2) -> clear(echo_input).
% 1.96/2.20 % set(auto2) -> set(quiet).
% 1.96/2.20 % set(auto2) -> clear(print_initial_clauses).
% 1.96/2.20 % set(auto2) -> clear(print_given).
% 1.96/2.20 assign(lrs_ticks,-1).
% 1.96/2.20 assign(sos_limit,10000).
% 1.96/2.20 assign(order,kbo).
% 1.96/2.20 set(lex_order_vars).
% 1.96/2.20 clear(print_given).
% 1.96/2.20
% 1.96/2.20 % formulas(sos). % not echoed (1147 formulas)
% 1.96/2.20
% 1.96/2.20 ============================== end of input ==========================
% 1.96/2.20
% 1.96/2.20 % From the command line: assign(max_seconds, 300).
% 1.96/2.20
% 1.96/2.20 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.96/2.20
% 1.96/2.20 % Formulas that are not ordinary clauses:
% 1.96/2.20 1 (all X_a (linorder(X_a) -> ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a)),big_Sup_fin(X_a)) = big_Sup_fin(X_a))) # label(tsy_c_Big__Operators_Olattice_OSup__fin_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 2 (all X_a (linorder(X_a) -> ti(fun(fun(X_a,bool),X_a),big_linorder_Max(X_a)) = big_linorder_Max(X_a))) # label(tsy_c_Big__Operators_Olinorder__class_OMax_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 3 (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].
% 1.96/2.20 4 (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].
% 1.96/2.20 5 (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].
% 1.96/2.20 6 (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].
% 1.96/2.20 7 (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].
% 1.96/2.20 8 (all X_a ti(fun(nat,fun(list(X_a),list(list(X_a)))),n_lists(X_a)) = n_lists(X_a)) # label(tsy_c_Enum_On__lists_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 9 (all X_a ti(fun(list(X_a),list(list(X_a))),sublists(X_a)) = sublists(X_a)) # label(tsy_c_Enum_Osublists_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 10 (all X_b (minus(X_b) -> ti(fun(X_b,fun(X_b,X_b)),minus_minus(X_b)) = minus_minus(X_b))) # label(tsy_c_Groups_Ominus__class_Ominus_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 11 (all X_a (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_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 12 (all X_a (zero(X_a) -> ti(X_a,zero_zero(X_a)) = zero_zero(X_a))) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 13 (all X_a (cl_HOL_Oequal(X_a) -> ti(fun(X_a,fun(X_a,bool)),equal_equal(X_a)) = equal_equal(X_a))) # label(tsy_c_HOL_Oequal__class_Oequal_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 14 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 15 (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].
% 1.96/2.20 16 (all X_a ti(fun(X_a,fun(list(X_a),bool)),listMem(X_a)) = listMem(X_a)) # label(tsy_c_List_OListMem_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 17 (all X_a ti(fun(list(X_a),fun(list(X_a),list(X_a))),append(X_a)) = append(X_a)) # label(tsy_c_List_Oappend_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 18 (all X_a ti(fun(list(X_a),list(X_a)),butlast(X_a)) = butlast(X_a)) # label(tsy_c_List_Obutlast_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 19 (all X_a ti(fun(list(list(X_a)),list(X_a)),concat(X_a)) = concat(X_a)) # label(tsy_c_List_Oconcat_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 20 (all X_a ti(fun(list(X_a),bool),distinct(X_a)) = distinct(X_a)) # label(tsy_c_List_Odistinct_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 21 (all X_a ti(fun(nat,fun(list(X_a),list(X_a))),drop(X_a)) = drop(X_a)) # label(tsy_c_List_Odrop_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 22 (all X_a ti(fun(fun(X_a,bool),fun(list(X_a),list(X_a))),dropWhile(X_a)) = dropWhile(X_a)) # label(tsy_c_List_OdropWhile_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 23 (all X_a ti(fun(fun(X_a,bool),fun(list(X_a),list(X_a))),filter(X_a)) = filter(X_a)) # label(tsy_c_List_Ofilter_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 24 (all X_a all X_b ti(fun(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a))),foldl(X_a,X_b)) = foldl(X_a,X_b)) # label(tsy_c_List_Ofoldl_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 25 (all X_b all X_a ti(fun(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a))),foldr(X_b,X_a)) = foldr(X_b,X_a)) # label(tsy_c_List_Ofoldr_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 26 (all X_a ti(fun(list(X_a),X_a),hd(X_a)) = hd(X_a)) # label(tsy_c_List_Ohd_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 27 (all X_a ti(fun(X_a,fun(list(X_a),list(X_a))),insert(X_a)) = insert(X_a)) # label(tsy_c_List_Oinsert_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 28 (all X_a ti(fun(list(X_a),X_a),last(X_a)) = last(X_a)) # label(tsy_c_List_Olast_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 29 (all X_a all X_b (linorder(X_b) -> ti(fun(fun(X_a,X_b),fun(X_a,fun(list(X_a),list(X_a)))),linord2118332866rt_key(X_a,X_b)) = linord2118332866rt_key(X_a,X_b))) # label(tsy_c_List_Olinorder__class_Oinsort__insert__key_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 30 (all X_a all X_b (linorder(X_b) -> ti(fun(fun(X_a,X_b),fun(X_a,fun(list(X_a),list(X_a)))),linorder_insort_key(X_a,X_b)) = linorder_insort_key(X_a,X_b))) # label(tsy_c_List_Olinorder__class_Oinsort__key_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 31 (all X_a all X_b (linorder(X_b) -> ti(fun(fun(X_a,X_b),fun(list(X_a),list(X_a))),linorder_sort_key(X_a,X_b)) = linorder_sort_key(X_a,X_b))) # label(tsy_c_List_Olinorder__class_Osort__key_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 32 (all X_a (linorder(X_a) -> ti(fun(list(X_a),bool),linorder_sorted(X_a)) = linorder_sorted(X_a))) # label(tsy_c_List_Olinorder__class_Osorted_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 33 (all X_a ti(fun(X_a,fun(list(X_a),list(X_a))),cons(X_a)) = cons(X_a)) # label(tsy_c_List_Olist_OCons_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 34 (all X_a ti(list(X_a),nil(X_a)) = nil(X_a)) # label(tsy_c_List_Olist_ONil_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 35 (all X_a all X_b ti(fun(X_a,fun(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a))),list_case(X_a,X_b)) = list_case(X_a,X_b)) # label(tsy_c_List_Olist_Olist__case_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 36 (all X_a all X_b ti(fun(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a))),list_rec(X_a,X_b)) = list_rec(X_a,X_b)) # label(tsy_c_List_Olist_Olist__rec_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 37 (all X_a ti(fun(fun(X_a,nat),fun(list(X_a),nat)),list_size(X_a)) = list_size(X_a)) # label(tsy_c_List_Olist_Olist__size_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 38 (all X_a ti(fun(fun(X_a,bool),fun(list(X_a),bool)),list_all(X_a)) = list_all(X_a)) # label(tsy_c_List_Olist__all_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 39 (all X_a ti(fun(fun(X_a,bool),fun(list(X_a),bool)),list_ex1(X_a)) = list_ex1(X_a)) # label(tsy_c_List_Olist__ex1_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 40 (all X_a ti(fun(list(X_a),fun(nat,fun(X_a,list(X_a)))),list_update(X_a)) = list_update(X_a)) # label(tsy_c_List_Olist__update_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 41 (all X_a ti(fun(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool))),listrelp(X_a)) = listrelp(X_a)) # label(tsy_c_List_Olistrelp_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 42 (all X_a all X_b ti(fun(fun(X_a,X_b),fun(list(X_a),list(X_b))),map(X_a,X_b)) = map(X_a,X_b)) # label(tsy_c_List_Omap_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 43 (all X_b all X_a ti(fun(fun(X_b,option(X_a)),fun(list(X_b),list(X_a))),map_filter(X_b,X_a)) = map_filter(X_b,X_a)) # label(tsy_c_List_Omap__filter_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 44 (all X_b all X_a ti(fun(fun(X_b,list(X_a)),fun(list(X_b),list(X_a))),maps(X_b,X_a)) = maps(X_b,X_a)) # label(tsy_c_List_Omaps_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 45 (all X_a ti(fun(list(X_a),fun(X_a,bool)),member_1(X_a)) = member_1(X_a)) # label(tsy_c_List_Omember_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 46 (all X_a ti(fun(list(X_a),fun(nat,X_a)),nth(X_a)) = nth(X_a)) # label(tsy_c_List_Onth_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 47 (all X_a ti(fun(list(X_a),bool),null(X_a)) = null(X_a)) # label(tsy_c_List_Onull_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 48 (all X_a ti(fun(X_a,fun(list(X_a),list(X_a))),remove1(X_a)) = remove1(X_a)) # label(tsy_c_List_Oremove1_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 49 (all X_a ti(fun(nat,fun(X_a,list(X_a))),replicate(X_a)) = replicate(X_a)) # label(tsy_c_List_Oreplicate_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 50 (all X_a ti(fun(list(X_a),list(X_a)),rev(X_a)) = rev(X_a)) # label(tsy_c_List_Orev_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 51 (all X_a ti(fun(list(X_a),list(X_a)),rotate1(X_a)) = rotate1(X_a)) # label(tsy_c_List_Orotate1_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 52 (all X_a ti(fun(list(X_a),fun(X_a,bool)),set(X_a)) = set(X_a)) # label(tsy_c_List_Oset_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 53 (all X_a ti(fun(fun(X_a,bool),fun(fun(list(X_a),bool),fun(list(X_a),bool))),set_Cons(X_a)) = set_Cons(X_a)) # label(tsy_c_List_Oset__Cons_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 54 (all X_a ti(fun(list(X_a),fun(list(X_a),list(X_a))),splice(X_a)) = splice(X_a)) # label(tsy_c_List_Osplice_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 55 (all X_a ti(fun(list(X_a),fun(fun(nat,bool),list(X_a))),sublist(X_a)) = sublist(X_a)) # label(tsy_c_List_Osublist_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 56 (all X_a ti(fun(nat,fun(list(X_a),list(X_a))),take(X_a)) = take(X_a)) # label(tsy_c_List_Otake_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 57 (all X_a ti(fun(fun(X_a,bool),fun(list(X_a),list(X_a))),takeWhile(X_a)) = takeWhile(X_a)) # label(tsy_c_List_OtakeWhile_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 58 (all X_a ti(fun(list(X_a),list(X_a)),tl(X_a)) = tl(X_a)) # label(tsy_c_List_Otl_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 59 (all X_a ti(fun(list(list(X_a)),list(list(X_a))),transpose(X_a)) = transpose(X_a)) # label(tsy_c_List_Otranspose_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 60 (all X_a ti(fun(list(list(X_a)),fun(list(list(X_a)),bool)),transpose_rel(X_a)) = transpose_rel(X_a)) # label(tsy_c_List_Otranspose__rel_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 61 (all X_a ti(fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),nat_case(X_a)) = nat_case(X_a)) # label(tsy_c_Nat_Onat_Onat__case_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 62 (all X_a ti(fun(list(X_a),nat),size_size(list(X_a))) = size_size(list(X_a))) # label(tsy_c_Nat_Osize__class_Osize_0_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 63 (all X_a ti(fun(list(X_a),fun(fun(X_a,list(X_a)),fun(option(X_a),list(X_a)))),option_case(list(X_a),X_a)) = option_case(list(X_a),X_a)) # label(tsy_c_Option_Ooption_Ooption__case_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 64 (all X_a (ord(X_a) -> ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a))),max(X_a)) = max(X_a))) # label(tsy_c_Orderings_Oord_Omax_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 65 (all X_a (ord(X_a) -> ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a))),min(X_a)) = min(X_a))) # label(tsy_c_Orderings_Oord_Omin_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 66 (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].
% 1.96/2.20 67 (all X_b (ord(X_b) -> ti(fun(X_b,fun(X_b,bool)),ord_less_eq(X_b)) = ord_less_eq(X_b))) # label(tsy_c_Orderings_Oord__class_Oless__eq_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 68 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,X_a)),ord_max(X_a)) = ord_max(X_a))) # label(tsy_c_Orderings_Oord__class_Omax_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 69 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,X_a)),ord_min(X_a)) = ord_min(X_a))) # label(tsy_c_Orderings_Oord__class_Omin_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 70 (all X_a ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a)) = collect(X_a)) # label(tsy_c_Set_OCollect_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 71 (all X_a ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,bool)),accp(X_a)) = accp(X_a)) # label(tsy_c_Wellfounded_Oaccp_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 72 (all X_a ti(fun(fun(X_a,bool),bool),fEx(X_a)) = fEx(X_a)) # label(tsy_c_fEx_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 73 (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].
% 1.96/2.20 74 (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].
% 1.96/2.20 75 (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].
% 1.96/2.20 76 (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].
% 1.96/2.20 77 (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].
% 1.96/2.20 78 (all X_a ti(fun(X_a,fun(fun(X_a,bool),bool)),member(X_a)) = member(X_a)) # label(tsy_c_member_res) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 79 (exists A_3 exists B_1 exists C hBOOL(hAPP(list(arrow_2142409994le_alt),bool,distinct(arrow_2142409994le_alt),hAPP(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt)),cons(arrow_2142409994le_alt),A_3),hAPP(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt)),cons(arrow_2142409994le_alt),B_1),hAPP(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt)),cons(arrow_2142409994le_alt),C),nil(arrow_2142409994le_alt))))))) # label(fact_0_alt3) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 80 (all X_a hBOOL(hAPP(list(X_a),bool,distinct(X_a),nil(X_a)))) # label(fact_1_distinct_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 81 (all X_a all A_5 all List_4 nil(X_a) != hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_5),List_4)) # label(fact_2_list_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 82 (all X_a all A_5 all List_4 hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_5),List_4) != nil(X_a)) # label(fact_3_list_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 83 (all X_a all Xs_1 (Xs_1 != nil(X_a) <-> (exists Y_2 exists Ys_3 Xs_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_3)))) # label(fact_4_neq__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 84 (all X_a all Y (Y != nil(X_a) -> -(all A_3 all List_3 Y != hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_3),List_3)))) # label(fact_5_list_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 85 (all X_a all Xs all X Xs != hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) # label(fact_6_not__Cons__self) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 86 (all X_a all X all Xs hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs) != Xs) # label(fact_7_not__Cons__self2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 87 (all X_a all Aa all List_1 all A_4 all List_2 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Aa),List_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_4),List_2) <-> ti(X_a,Aa) = ti(X_a,A_4) & List_1 = List_2)) # label(fact_8_list_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 88 (all X_a all V_1 all Va hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),V_1),Va)),nil(X_a)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),V_1),Va)) # label(fact_9_splice_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 89 (all X_a all X hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X),nil(X_a)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a))) # label(fact_10_insert__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 90 (all X_a all P_1 all Xs_1 (Xs_1 != nil(X_a) -> ((all X_2 hBOOL(hAPP(list(X_a),bool,P_1,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),nil(X_a))))) -> ((all X_2 all Xs_2 (Xs_2 != nil(X_a) -> (hBOOL(hAPP(list(X_a),bool,P_1,Xs_2)) -> hBOOL(hAPP(list(X_a),bool,P_1,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2)))))) -> hBOOL(hAPP(list(X_a),bool,P_1,Xs_1)))))) # label(fact_11_list__nonempty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 91 (all X_a all Xs (Xs != nil(X_a) -> (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)))))) # label(fact_12_distinct__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 92 (all X_a hAPP(list(X_a),list(X_a),butlast(X_a),nil(X_a)) = nil(X_a)) # label(fact_13_butlast_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 93 (all X_a all X all Xs (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X),Xs))))) # label(fact_14_distinct__insert) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 94 (all X_a all X all Xs all Y all Ys_1 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Ys_1)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),Xs),Ys_1)))) # label(fact_15_splice_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 95 (all X_a all Xs hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),Xs),nil(X_a)) = Xs) # label(fact_16_splice__Nil2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 96 (all X_a all Ys_1 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),nil(X_a)),Ys_1) = Ys_1) # label(fact_17_splice_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 97 (all X_a all X all Xs ((Xs = nil(X_a) -> hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = nil(X_a)) & (Xs != nil(X_a) -> hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),butlast(X_a),Xs))))) # label(fact_18_butlast_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 98 (all X_b all X_a all F1 all F2 hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a)),list_case(X_a,X_b),F1),F2),nil(X_b)) = ti(X_a,F1)) # label(fact_19_list_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 99 (all X_b all X_a all F1 all F2 all Aa all List_1 hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a)),list_case(X_a,X_b),F1),F2),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Aa),List_1)) = hAPP(list(X_b),X_a,hAPP(X_b,fun(list(X_b),X_a),F2,Aa),List_1)) # label(fact_20_list_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 100 (all X_b all X_a all F1 all F2 hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a)),list_rec(X_a,X_b),F1),F2),nil(X_b)) = ti(X_a,F1)) # label(fact_21_list_Orecs_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 101 (all X_b all X_a all F1 all F2 all Aa all List_1 hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a)),list_rec(X_a,X_b),F1),F2),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Aa),List_1)) = hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(X_b,fun(list(X_b),fun(X_a,X_a)),F2,Aa),List_1),hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a)),list_rec(X_a,X_b),F1),F2),List_1))) # label(fact_22_list_Orecs_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 102 (all X_a all Xs_1 (Xs_1 = nil(X_a) <-> hBOOL(hAPP(list(X_a),bool,null(X_a),Xs_1)))) # label(fact_23_eq__Nil__null) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 103 (all X_a all Xs_1 (hBOOL(hAPP(list(X_a),bool,null(X_a),Xs_1)) <-> Xs_1 = nil(X_a))) # label(fact_24_List_Onull__def) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 104 (all X_b hBOOL(hAPP(list(X_b),bool,null(X_b),nil(X_b)))) # label(fact_25_null__rec_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 105 (all X_a all X all Xs -hBOOL(hAPP(list(X_a),bool,null(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)))) # label(fact_26_null__rec_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 106 (all X_a all Xs all X hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a)))) = Xs) # label(fact_27_butlast__snoc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 107 (all X_b all X_a all F hAPP(list(X_b),list(X_a),hAPP(fun(X_b,list(X_a)),fun(list(X_b),list(X_a)),maps(X_b,X_a),F),nil(X_b)) = nil(X_a)) # label(fact_28_maps__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 108 (all X_a (linorder(X_a) -> (all X hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a))))))) # label(fact_29_sorted__single) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 109 (all X_a all X all Xs (Xs = nil(X_a) -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = ti(X_a,X))) # label(fact_30_last__ConsL) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 110 (all X_a (linorder(X_a) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),nil(X_a))))) # label(fact_31_sorted_ONil) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 111 (all X_a all Xs all Ys_1 all Zs_2 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)),Zs_2) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs_2))) # label(fact_32_append__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 112 (all X_a all Xs_1 all Ys all Zs_1 all Ts (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs_1),Ts) <-> (exists Us (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs_1),Us) & hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us),Ys) = Ts | hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Us) = Zs_1 & Ys = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us),Ts))))) # label(fact_33_append__eq__append__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 113 (all X_a all Xs_1 all Ys all Zs_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Zs_1) <-> Ys = Zs_1)) # label(fact_34_same__append__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 114 (all X_a all Ys all Xs_1 all Zs_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs_1),Xs_1) <-> Ys = Zs_1)) # label(fact_35_append__same__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 115 (all X_a all Ys_1 all Us_1 all Xs all Xs1 all Zs_2 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Xs1) = Zs_2 -> (Ys_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs1),Us_1) -> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs_2),Us_1)))) # label(fact_36_append__eq__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 116 (all X_a all Xs all Ys_1 (Ys_1 = nil(X_a) -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),X_a,last(X_a),Xs))) # label(fact_37_last__appendL) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 117 (all X_a all Xs all Ys_1 (Ys_1 != nil(X_a) -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),X_a,last(X_a),Ys_1))) # label(fact_38_last__appendR) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 118 (all X_a all Xs all Ys_1 ((Ys_1 = nil(X_a) -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),X_a,last(X_a),Xs)) & (Ys_1 != nil(X_a) -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),X_a,last(X_a),Ys_1)))) # label(fact_39_last__append) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 119 (all X_b all X_a all F all X_1 all Xs_1 hAPP(list(X_b),list(X_a),hAPP(fun(X_b,list(X_a)),fun(list(X_b),list(X_a)),maps(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X_1),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_b,list(X_a),F,X_1)),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,list(X_a)),fun(list(X_b),list(X_a)),maps(X_b,X_a),F),Xs_1))) # label(fact_40_maps__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 120 (all X_a all Xs all X hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a)))) = ti(X_a,X)) # label(fact_41_last__snoc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 121 (all X_a all X all Xs all Ys_1 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),Ys_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1))) # label(fact_42_append__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 122 (all X_a all Xs all Zs_2 all X all Xs1 all Ys_1 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs1) = Ys_1 -> (Xs = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs1),Zs_2) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs_2)))) # label(fact_43_Cons__eq__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 123 (all X_a all Ys_1 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),nil(X_a)),Ys_1) = Ys_1) # label(fact_44_append__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 124 (all X_a all Xs_1 all Ys (nil(X_a) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys) <-> Xs_1 = nil(X_a) & Ys = nil(X_a))) # label(fact_45_Nil__is__append__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 125 (all X_a all Xs hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),nil(X_a)) = Xs) # label(fact_46_append__Nil2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 126 (all X_a all Xs_1 all Ys (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys) <-> Ys = nil(X_a))) # label(fact_47_self__append__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 127 (all X_a all Ys all Xs_1 (Ys = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys) <-> Xs_1 = nil(X_a))) # label(fact_48_self__append__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 128 (all X_a all Xs_1 all Ys (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys) = nil(X_a) <-> Xs_1 = nil(X_a) & Ys = nil(X_a))) # label(fact_49_append__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 129 (all X_a all Xs_1 all Ys (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys) = Xs_1 <-> Ys = nil(X_a))) # label(fact_50_append__self__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 130 (all X_a all Xs_1 all Ys (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys) = Ys <-> Xs_1 = nil(X_a))) # label(fact_51_append__self__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 131 (all X_a all Xs all Ys_1 (Xs = Ys_1 -> Xs = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),nil(X_a)),Ys_1))) # label(fact_52_eq__Nil__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 132 (all X_a all Xs_1 all X_1 all Ys (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))) = Ys <-> Ys != nil(X_a) & hAPP(list(X_a),list(X_a),butlast(X_a),Ys) = Xs_1 & hAPP(list(X_a),X_a,last(X_a),Ys) = ti(X_a,X_1))) # label(fact_53_snoc__eq__iff__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 133 (all X_a all Xs (Xs != nil(X_a) -> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(list(X_a),X_a,last(X_a),Xs)),nil(X_a))) = Xs)) # label(fact_54_append__butlast__last__id) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 134 (all X_a all Ys all Zs_1 all X_1 all Xs_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),Zs_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1) <-> Ys = nil(X_a) & Zs_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1) | (exists Ys_4 (Ys = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Ys_4) & hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_4),Zs_1) = Xs_1)))) # label(fact_55_append__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 135 (all X_a all X_1 all Xs_1 all Ys all Zs_1 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),Zs_1) <-> Ys = nil(X_a) & hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1) = Zs_1 | (exists Ys_4 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Ys_4) = Ys & Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_4),Zs_1))))) # label(fact_56_Cons__eq__append__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 136 (all X_a all Xs_1 all X_1 all Ys all Y_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),nil(X_a))) <-> Xs_1 = Ys & ti(X_a,X_1) = ti(X_a,Y_1))) # label(fact_57_append1__eq__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 137 (all X_a all Xs all Ys_1 ((Ys_1 = nil(X_a) -> hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),list(X_a),butlast(X_a),Xs)) & (Ys_1 != nil(X_a) -> hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),butlast(X_a),Ys_1))))) # label(fact_58_butlast__append) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 138 (all X_a (linorder(X_a) -> (all Xs (Xs != nil(X_a) -> (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)))))))) # label(fact_59_sorted__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 139 (all X_a all X all Xs ((Xs = nil(X_a) -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = ti(X_a,X)) & (Xs != nil(X_a) -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = hAPP(list(X_a),X_a,last(X_a),Xs)))) # label(fact_60_last_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 140 (all X_a all X all Xs (Xs != nil(X_a) -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = hAPP(list(X_a),X_a,last(X_a),Xs))) # label(fact_61_last__ConsR) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 141 (all X_a all Xs_1 all P_1 (hBOOL(hAPP(list(X_a),bool,P_1,nil(X_a))) -> ((all X_2 all Xs_2 (hBOOL(hAPP(list(X_a),bool,P_1,Xs_2)) -> hBOOL(hAPP(list(X_a),bool,P_1,hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),nil(X_a))))))) -> hBOOL(hAPP(list(X_a),bool,P_1,Xs_1))))) # label(fact_62_rev__induct) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 142 (all X_a all Xs (Xs != nil(X_a) -> -(all Ys_3 all Y_2 Xs != hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),nil(X_a)))))) # label(fact_63_rev__cases) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 143 (all X_a all Xs_1 (hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),equal_equal(list(X_a)),Xs_1),nil(X_a))) <-> hBOOL(hAPP(list(X_a),bool,null(X_a),Xs_1)))) # label(fact_64_equal__Nil__null) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 144 (all X_b all X_a all X all Xs (hAPP(list(X_a),list(X_a),rotate1(X_a),nil(X_a)) = nil(X_a) & hAPP(list(X_b),list(X_b),rotate1(X_b),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X),Xs)) = hAPP(list(X_b),list(X_b),hAPP(list(X_b),fun(list(X_b),list(X_b)),append(X_b),Xs),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X),nil(X_b))))) # label(fact_65_rotate__simps) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 145 (all X_a all Ws (-hBOOL(hAPP(list(X_a),bool,distinct(X_a),Ws)) -> (exists Xs_2 exists Ys_3 exists Zs exists Y_2 Ws = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_2),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),nil(X_a))),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),nil(X_a))),Zs))))))) # label(fact_66_not__distinct__decomp) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 146 (all X_a all I_1 all X hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),I_1),X)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a))) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),I_1),X))) # label(fact_67_replicate__append__same) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 147 (all X_a all X all Xs hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a)))) # label(fact_68_rev_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 148 (all X_a all Xs_1 all Y_1 all Ys (hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys) <-> Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Ys)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),nil(X_a))))) # label(fact_69_rev__eq__Cons__iff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 149 (all X_a all Ys_1 all Xs (Xs != nil(X_a) -> hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),X_a,hd(X_a),Xs))) # label(fact_70_hd__append2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 150 (all X_a all Ys_1 all Xs ((Xs = nil(X_a) -> hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),X_a,hd(X_a),Ys_1)) & (Xs != nil(X_a) -> hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),X_a,hd(X_a),Xs)))) # label(fact_71_hd__append) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 151 (all X_a all Ys_1 all Xs (Xs != nil(X_a) -> hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),tl(X_a),Xs)),Ys_1))) # label(fact_72_tl__append2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 152 (all X_a all Xs_1 all Ys (hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) = hAPP(list(X_a),list(X_a),rev(X_a),Ys) <-> Xs_1 = Ys)) # label(fact_73_rev__is__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 153 (all X_a all Xs_1 all Ys (hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) = Ys <-> Xs_1 = hAPP(list(X_a),list(X_a),rev(X_a),Ys))) # label(fact_74_rev__swap) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 154 (all X_a all X_b all F all G ((all X_2 hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2)) -> ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G))) # label(fact_75_ext) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 155 (all X_a all X_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) <-> hBOOL(hAPP(X_a,bool,A_1,X_1)))) # label(fact_76_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 156 (all X_a all P_1 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1) = ti(fun(X_a,bool),P_1)) # label(fact_77_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 157 (all X_a all N_1 all X hAPP(list(X_a),list(X_a),rev(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)) # label(fact_78_rev__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 158 (all X_a all Xs hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs)) = Xs) # label(fact_79_rev__rev__ident) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 159 (all X_a all X_1 all Y_1 (hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),equal_equal(list(X_a)),X_1),Y_1)) <-> X_1 = Y_1)) # label(fact_80_equal__list__def) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 160 (all X_a all Xs_1 (hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) = nil(X_a) <-> Xs_1 = nil(X_a))) # label(fact_81_rev__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 161 (all X_a all Xs_1 (nil(X_a) = hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) <-> Xs_1 = nil(X_a))) # label(fact_82_Nil__is__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 162 (all X_a hAPP(list(X_a),list(X_a),rev(X_a),nil(X_a)) = nil(X_a)) # label(fact_83_rev_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 163 (all X_a all Xs all Ys_1 hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Ys_1)),hAPP(list(X_a),list(X_a),rev(X_a),Xs))) # label(fact_84_rev__append) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 164 (all X_a all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1))) <-> hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)))) # label(fact_85_distinct__rev) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 165 (all X_a all Xs (Xs != nil(X_a) -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs)) = hAPP(list(X_a),X_a,hd(X_a),Xs))) # label(fact_86_last__rev) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 166 (all X_a all Xs (Xs != nil(X_a) -> hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs)) = hAPP(list(X_a),X_a,last(X_a),Xs))) # label(fact_87_hd__rev) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.20 167 (all X_a all N_1 all X all K hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),K),X)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),K),X)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X))) # label(fact_88_append__replicate__commute) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 168 (all X_a all Xs (Xs != nil(X_a) -> hAPP(list(X_a),list(X_a),rotate1(X_a),Xs) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),tl(X_a),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(list(X_a),X_a,hd(X_a),Xs)),nil(X_a))))) # label(fact_89_rotate1__hd__tl) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 169 (all X_a all X all Xs hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = Xs) # label(fact_90_tl_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 170 (all X_a hAPP(list(X_a),list(X_a),tl(X_a),nil(X_a)) = nil(X_a)) # label(fact_91_tl_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 171 (all X_a all X all Xs hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = ti(X_a,X)) # label(fact_92_hd_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 172 (all X_a all Xs (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),tl(X_a),Xs))))) # label(fact_93_distinct__tl) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 173 (all X_a (linorder(X_a) -> (all Xs (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),tl(X_a),Xs))))))) # label(fact_94_sorted__tl) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 174 (all X_a all Xs_1 (hAPP(list(X_a),list(X_a),rotate1(X_a),Xs_1) = nil(X_a) <-> Xs_1 = nil(X_a))) # label(fact_95_rotate1__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 175 (all X_a all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),rotate1(X_a),Xs_1))) <-> hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)))) # label(fact_96_distinct1__rotate) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 176 (all X_a all X_1 all Xs_1 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)) = hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) <-> Xs_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)))) # label(fact_97_singleton__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 177 (all X_a all Xs_1 all X_1 (hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)) <-> Xs_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)))) # label(fact_98_rev__singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 178 (all X_a all N_1 all X all Xs hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)),Xs))) # label(fact_99_replicate__app__Cons__same) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 179 (all X_a (cl_HOL_Oequal(X_a) -> equal_equal(X_a) = fequal(X_a))) # label(fact_100_equal) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 180 (all X_a (cl_HOL_Oequal(X_a) -> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),equal_equal(X_a),X),X))))) # label(fact_101_equal__refl) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 181 (all X_a (cl_HOL_Oequal(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),equal_equal(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_102_equal__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 182 (all X_a (cl_HOL_Oequal(X_a) -> fequal(X_a) = equal_equal(X_a))) # label(fact_103_eq__equal) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 183 (all X_a all P_1 all Xs_1 (hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1) != nil(X_a) -> -hBOOL(hAPP(X_a,bool,P_1,hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1)))))) # label(fact_104_hd__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 184 (all X_a all P_1 -hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex1(X_a),P_1),nil(X_a)))) # label(fact_105_list__ex1__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 185 (all X_a all Y -hBOOL(hAPP(X_a,bool,hAPP(list(X_a),fun(X_a,bool),member_1(X_a),nil(X_a)),Y))) # label(fact_106_member__rec_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 186 (all X_a all Y all X all Xs (hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),X),Xs)) -> hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),X),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Xs))))) # label(fact_107_insert) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 187 (all X_a all X_1 all Xs_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(list(X_a),fun(X_a,bool),member_1(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1) | hBOOL(hAPP(X_a,bool,hAPP(list(X_a),fun(X_a,bool),member_1(X_a),Xs_1),Y_1)))) # label(fact_108_member__rec_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 188 (all X_a all X all Xs hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),X),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)))) # label(fact_109_elem) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 189 (all X_a all Xs_1 all P_1 all X_1 ((hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1)) & (-hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)))) # label(fact_110_dropWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 190 (all X_a all P_1 hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),nil(X_a)) = nil(X_a)) # label(fact_111_dropWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 191 (all X_a all P_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1))))) # label(fact_112_distinct__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 192 (all X_a (linorder(X_a) -> (all P_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1))))))) # label(fact_113_sorted__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 193 (all X_a all P_1 all Xs_1 all Y_1 all Ys (hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys) <-> Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys)) & -hBOOL(hAPP(X_a,bool,P_1,Y_1)))) # label(fact_114_dropWhile__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 194 (all X_a all A1 all A2 (hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),A1),A2)) <-> (exists X_2 exists Xs_2 (ti(X_a,A1) = ti(X_a,X_2) & A2 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2))) | (exists X_2 exists Xs_2 exists Y_2 (ti(X_a,A1) = ti(X_a,X_2) & A2 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Xs_2) & hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),X_2),Xs_2)))))) # label(fact_115_ListMem_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 195 (all X_a all P_1 all Xs_1 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1)) = Xs_1) # label(fact_116_takeWhile__dropWhile__id) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 196 (all X_a all X all N_1 (N_1 != zero_zero(nat) -> hAPP(list(X_a),X_a,hd(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)) = ti(X_a,X))) # label(fact_117_hd__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 197 (all X_a all X all N_1 (N_1 != zero_zero(nat) -> hAPP(list(X_a),X_a,last(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)) = ti(X_a,X))) # label(fact_118_last__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 198 (all X_b all X_a all Xs_1 all Ys all P_1 (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,nil(X_a)),nil(X_b))) -> ((all X_2 all Xs_2 hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2)),nil(X_b)))) -> ((all Y_2 all Ys_3 hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,nil(X_a)),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Y_2),Ys_3)))) -> ((all X_2 all Xs_2 all Y_2 all Ys_3 (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,Xs_2),Ys_3)) -> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2)),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Y_2),Ys_3))))) -> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,Xs_1),Ys))))))) # label(fact_119_list__induct2_H) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 199 (all X_b all X_a all F hAPP(list(X_b),list(X_a),hAPP(fun(X_b,option(X_a)),fun(list(X_b),list(X_a)),map_filter(X_b,X_a),F),nil(X_b)) = nil(X_a)) # label(fact_120_map__filter__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 200 (all X_a all R_1 hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),nil(X_a)),nil(X_a)))) # label(fact_121_listrelp_ONil) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 201 (all X_a all Xs_1 all Ys all R_1 all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,X_1),Y_1)) -> (hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),Xs_1),Ys)) -> hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys)))))) # label(fact_122_listrelp_OCons) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 202 (all X_a all P_1 hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),nil(X_a)) = nil(X_a)) # label(fact_123_takeWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 203 (all X_a all M all X_1 all N all Y_1 (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),M),X_1) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),Y_1) <-> M = N & (M != zero_zero(nat) -> ti(X_a,X_1) = ti(X_a,Y_1)))) # label(fact_124_replicate__eq__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 204 (all X_a all P_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))))) # label(fact_125_distinct__takeWhile) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 205 (all X_a (linorder(X_a) -> (all P_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))))))) # label(fact_126_sorted__takeWhile) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 206 (all X_a all X hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),zero_zero(nat)),X) = nil(X_a)) # label(fact_127_replicate__0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 207 (all X_a all N all X_1 (nil(X_a) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X_1) <-> N = zero_zero(nat))) # label(fact_128_empty__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 208 (all X_a all N all X_1 (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X_1) = nil(X_a) <-> N = zero_zero(nat))) # label(fact_129_replicate__empty) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 209 (all X_a all Xs_1 all P_1 all X_1 ((hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))) & (-hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)) = nil(X_a)))) # label(fact_130_takeWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 210 (all X_a all Xs_1 all L_2 all P_1 all X_1 (-hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),L_2))) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))) # label(fact_131_takeWhile__tail) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 211 (all X_a all X_1 all A_1 ((hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),A_1)) -> hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))),A_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))) & (-hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),A_1)) -> hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))),A_1) = nil(X_a)))) # label(fact_132_sublist__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 212 (all X_a all R_1 all A1 all A2 (hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),A1),A2)) <-> A1 = nil(X_a) & A2 = nil(X_a) | (exists X_2 exists Y_2 exists Xs_2 exists Ys_3 (A1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2) & A2 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_3) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,X_2),Y_2)) & hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),Xs_2),Ys_3)))))) # label(fact_133_listrelp_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 213 (all X_a all Fa hAPP(list(X_a),nat,hAPP(fun(X_a,nat),fun(list(X_a),nat),list_size(X_a),Fa),nil(X_a)) = zero_zero(nat)) # label(fact_134_list_Osize_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 214 (all X_a (zero(X_a) -> (all X_1 (zero_zero(X_a) = ti(X_a,X_1) <-> ti(X_a,X_1) = zero_zero(X_a))))) # label(fact_135_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 215 (all X_a all Xs (Xs != nil(X_a) -> hAPP(list(X_a),X_a,hd(X_a),Xs) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),zero_zero(nat)))) # label(fact_136_hd__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 216 (all X_a all X_b (linorder(X_b) -> (all F all X_1 hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),hAPP(fun(X_a,X_b),fun(X_a,fun(list(X_a),list(X_a))),linorder_insort_key(X_a,X_b),F),X_1),nil(X_a)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))))) # label(fact_137_insort__key_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 217 (all X_a all Xs_1 (Xs_1 != nil(X_a) -> (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),hAPP(list(X_a),X_a,last(X_a),Xs_1)))),Xs_1) = hAPP(list(X_a),list(X_a),butlast(X_a),Xs_1)))) # label(fact_138_takeWhile__not__last) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 218 (all X_a all X_1 all Xs_1 ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X_1),Xs_1) = Xs_1) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X_1),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)))) # label(fact_139_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 219 (all X_a all X_b (linorder(X_b) -> (all F all X_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),hAPP(fun(X_a,X_b),fun(X_a,fun(list(X_a),list(X_a))),linorder_insort_key(X_a,X_b),F),X_1),Xs_1))) <-> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)))))) # label(fact_140_distinct__insort) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 220 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Xs_1 hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),hAPP(fun(X_a,X_a),fun(X_a,fun(list(X_a),list(X_a))),linorder_insort_key(X_a,X_a),combi(X_a)),X_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),hAPP(fun(X_a,X_a),fun(X_a,fun(list(X_a),list(X_a))),linorder_insort_key(X_a,X_a),combi(X_a)),Y_1),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),hAPP(fun(X_a,X_a),fun(X_a,fun(list(X_a),list(X_a))),linorder_insort_key(X_a,X_a),combi(X_a)),Y_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),hAPP(fun(X_a,X_a),fun(X_a,fun(list(X_a),list(X_a))),linorder_insort_key(X_a,X_a),combi(X_a)),X_1),Xs_1))))) # label(fact_141_insort__left__comm) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 221 (all X_a all I_3 all X_1 all Xs_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),Xs_1),I_3)))))) # label(fact_142_notin__set__sublistI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 222 (all X_b all X_a (linorder(X_a) -> (all Xs_1 all F all X_1 all Y_1 (hAPP(X_b,X_a,F,X_1) != hAPP(X_b,X_a,F,Y_1) -> hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),hAPP(fun(X_b,X_a),fun(X_b,fun(list(X_b),list(X_b))),linorder_insort_key(X_b,X_a),F),Y_1),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),hAPP(fun(X_b,X_a),fun(X_b,fun(list(X_b),list(X_b))),linorder_insort_key(X_b,X_a),F),X_1),Xs_1)) = hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),hAPP(fun(X_b,X_a),fun(X_b,fun(list(X_b),list(X_b))),linorder_insort_key(X_b,X_a),F),X_1),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),hAPP(fun(X_b,X_a),fun(X_b,fun(list(X_b),list(X_b))),linorder_insort_key(X_b,X_a),F),Y_1),Xs_1)))))) # label(fact_143_insort__key__left__comm) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 223 (all X_a all X_1 all Xs_1 all I_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),Xs_1),I_3)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_144_in__set__sublistD) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 224 (all X_a (linorder(X_a) -> (all X_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),hAPP(fun(X_a,X_a),fun(X_a,fun(list(X_a),list(X_a))),linorder_insort_key(X_a,X_a),combi(X_a)),X_1),Xs_1))) <-> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)))))) # label(fact_145_sorted__insort) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 225 (all X_a all Xs_1 all Ys hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys)) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),list(X_a)),hAPP(list(X_a),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),list(X_a))),list_case(list(X_a),X_a),hAPP(list(X_a),list(X_a),tl(X_a),Ys)),hAPP(fun(list(X_a),list(X_a)),fun(X_a,fun(list(X_a),list(X_a))),combk(fun(list(X_a),list(X_a)),X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),hAPP(fun(list(X_a),fun(list(X_a),list(X_a))),fun(list(X_a),fun(list(X_a),list(X_a))),combc(list(X_a),list(X_a),list(X_a)),append(X_a)),Ys))),Xs_1)) # label(fact_146_tl__append) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 226 (all X_a all Y_1 all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)))) -> ti(X_a,Y_1) = ti(X_a,X_1) | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_147_set__ConsD) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 227 (all X_a all Xs_1 hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)) = hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)) # label(fact_148_set__rev) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 228 (all X_a all P_1 all Xs_1 (hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1) = Xs_1 <-> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,P_1,X_2)))))) # label(fact_149_takeWhile__eq__all__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 229 (all X_a all X_1 all P_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(X_a,bool,P_1,X_1)))) # label(fact_150_set__takeWhileD) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 230 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs_1)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_151_in__set__butlastD) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 231 (all X_a all X_b (linorder(X_b) -> (all F all Aa all Xs_1 hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),hAPP(fun(X_a,X_b),fun(X_a,fun(list(X_a),list(X_a))),linorder_insort_key(X_a,X_b),F),Aa),Xs_1) != nil(X_a)))) # label(fact_152_insort__not__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 232 (all X_a all Xs_1 hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),rotate1(X_a),Xs_1)) = hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)) # label(fact_153_set__rotate1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 233 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X_1),Xs_1) = Xs_1)) # label(fact_154_in__set__insert) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 234 (all X_a member_1(X_a) = set(X_a)) # label(fact_155_member__set) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 235 (all X_a all P_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex1(X_a),P_1),Xs_1)) <-> (exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(X_a,bool,P_1,X_2)) & (all Y_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(X_a,bool,P_1,Y_2)) -> ti(X_a,Y_2) = ti(X_a,X_2))))))) # label(fact_156_list__ex1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 236 (all X_a all Xs_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(list(X_a),fun(X_a,bool),member_1(X_a),Xs_1),X_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_157_List_Omember__def) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 237 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),X_1),Xs_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_158_ListMem__iff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 238 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(list(X_a),fun(X_a,bool),member_1(X_a),Xs_1),X_1)))) # label(fact_159_in__set__member) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 239 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_1))),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_1))),Xs_1)))))) # label(fact_160_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 240 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_1))),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)) = hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_1))),Xs_1)))))) # label(fact_161_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 241 (all X_a all A_1 hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),nil(X_a)),A_1) = nil(X_a)) # label(fact_162_sublist__nil) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 242 (all X_a all I_3 all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),Xs_1),I_3))))) # label(fact_163_distinct__sublistI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 243 (all X_a all Xs_1 hAPP(list(X_a),list(X_a),rotate1(X_a),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),list(X_a)),hAPP(list(X_a),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),list(X_a))),list_case(list(X_a),X_a),nil(X_a)),hAPP(fun(X_a,list(X_a)),fun(X_a,fun(list(X_a),list(X_a))),hAPP(fun(list(X_a),fun(list(X_a),list(X_a))),fun(fun(X_a,list(X_a)),fun(X_a,fun(list(X_a),list(X_a)))),combb(list(X_a),fun(list(X_a),list(X_a)),X_a),hAPP(fun(list(X_a),fun(list(X_a),list(X_a))),fun(list(X_a),fun(list(X_a),list(X_a))),combc(list(X_a),list(X_a),list(X_a)),append(X_a))),hAPP(list(X_a),fun(X_a,list(X_a)),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),fun(X_a,list(X_a))),combc(X_a,list(X_a),list(X_a)),cons(X_a)),nil(X_a)))),Xs_1)) # label(fact_164_rotate1__def) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 244 (all X_a all X all Xs hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),zero_zero(nat)) = ti(X_a,X)) # label(fact_165_nth__Cons__0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 245 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))) <-> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)))) # label(fact_166_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 246 (all X_a all X_1 all N all Y_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),Y_1)))) <-> ti(X_a,X_1) = ti(X_a,Y_1) & N != zero_zero(nat))) # label(fact_167_in__set__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 247 (all X_a all P_1 all N all Aa ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),Aa)))) & hBOOL(hAPP(X_a,bool,P_1,X_2)))) <-> hBOOL(hAPP(X_a,bool,P_1,Aa)) & N != zero_zero(nat))) # label(fact_168_Bex__set__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 248 (all X_a all P_1 all N all Aa ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),Aa)))) -> hBOOL(hAPP(X_a,bool,P_1,X_2)))) <-> hBOOL(hAPP(X_a,bool,P_1,Aa)) | N = zero_zero(nat))) # label(fact_169_Ball__set__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 249 (all X_a (linorder(X_a) -> (all Ys all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) -> (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Ys)) -> (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Ys)) -> (hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1) = hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys) -> Xs_1 = Ys)))))))) # label(fact_170_sorted__distinct__set__unique) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 250 (all X_a all Ys all P_1 all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (-hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys)) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)))) # label(fact_171_takeWhile__append1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 251 (all X_a all As (As != nil(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(list(X_a),X_a,last(X_a),As)),hAPP(list(X_a),fun(X_a,bool),set(X_a),As))))) # label(fact_172_last__in__set) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 252 (all X_a all P_1 all Xs_1 (hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1) = nil(X_a) <-> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,P_1,X_2)))))) # label(fact_173_dropWhile__eq__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 253 (all X_a all Ys all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs_1)))) | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Ys)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys))))))) # label(fact_174_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 254 (all X_a all Xs_1 (Xs_1 != nil(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(list(X_a),X_a,hd(X_a),Xs_1)),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_175_hd__in__set) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 255 (all X_a all Ys all P_1 all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (-hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1)),Ys)))) # label(fact_176_dropWhile__append1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 256 (all X_a all X_1 all Xs_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X_1),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))) # label(fact_177_not__in__set__insert) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 257 (all X_a all Ys all P_1 all Xs_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,P_1,X_2)))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys)) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Ys))) # label(fact_178_dropWhile__append2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 258 (all X_a all Ys all P_1 all Xs_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,P_1,X_2)))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Ys)))) # label(fact_179_takeWhile__append2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 259 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) <-> (exists Ys_3 exists Zs Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs))))) # label(fact_180_in__set__conv__decomp) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 260 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) <-> (exists Ys_3 exists Zs (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs)) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Zs))))))) # label(fact_181_in__set__conv__decomp__last) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 261 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) <-> (exists Ys_3 exists Zs (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs)) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys_3))))))) # label(fact_182_in__set__conv__decomp__first) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 262 (all X_a all P_1 all Xs_1 ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(X_a,bool,P_1,X_2)))) -> -(all Ys_3 all X_2 ((exists Zs Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs))) -> -hBOOL(hAPP(X_a,bool,P_1,X_2)))))) # label(fact_183_split__list__propE) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 263 (all X_a all Q_1 all P_1 all L_2 all K_1 (L_2 = K_1 -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),L_2))) -> (hBOOL(hAPP(X_a,bool,P_1,X_2)) <-> hBOOL(hAPP(X_a,bool,Q_1,X_2))))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),L_2) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Q_1),K_1)))) # label(fact_184_dropWhile__cong) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 264 (all X_a all Q_1 all P_1 all L_2 all K_1 (L_2 = K_1 -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),L_2))) -> (hBOOL(hAPP(X_a,bool,P_1,X_2)) <-> hBOOL(hAPP(X_a,bool,Q_1,X_2))))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),L_2) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Q_1),K_1)))) # label(fact_185_takeWhile__cong) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 265 (all X_b all X_a all F all X_1 all Xs_1 hAPP(list(X_b),list(X_a),hAPP(fun(X_b,option(X_a)),fun(list(X_b),list(X_a)),map_filter(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X_1),Xs_1)) = hAPP(option(X_a),list(X_a),hAPP(fun(X_a,list(X_a)),fun(option(X_a),list(X_a)),hAPP(list(X_a),fun(fun(X_a,list(X_a)),fun(option(X_a),list(X_a))),option_case(list(X_a),X_a),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,option(X_a)),fun(list(X_b),list(X_a)),map_filter(X_b,X_a),F),Xs_1)),hAPP(list(X_a),fun(X_a,list(X_a)),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),fun(X_a,list(X_a))),combc(X_a,list(X_a),list(X_a)),cons(X_a)),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,option(X_a)),fun(list(X_b),list(X_a)),map_filter(X_b,X_a),F),Xs_1))),hAPP(X_b,option(X_a),F,X_1))) # label(fact_186_map__filter__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 266 (all X_a all P_1 all Xs_1 ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(X_a,bool,P_1,X_2)))) -> -(all Ys_3 all X_2 ((exists Zs Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs))) -> (hBOOL(hAPP(X_a,bool,P_1,X_2)) -> -(all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys_3))) -> -hBOOL(hAPP(X_a,bool,P_1,Xa))))))))) # label(fact_187_split__list__first__propE) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 267 (all X_a all P_1 all Xs_1 ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(X_a,bool,P_1,X_2)))) -> -(all Ys_3 all X_2 all Zs (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs)) -> (hBOOL(hAPP(X_a,bool,P_1,X_2)) -> -(all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Zs))) -> -hBOOL(hAPP(X_a,bool,P_1,Xa))))))))) # label(fact_188_split__list__last__propE) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 268 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (exists Ys_3 exists Zs (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs)) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys_3))))))) # label(fact_189_split__list__first) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 269 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (exists Ys_3 exists Zs (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs)) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Zs))))))) # label(fact_190_split__list__last) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 270 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (exists Ys_3 exists Zs Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs))))) # label(fact_191_split__list) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 271 (all X_a all P_1 all Xs_1 ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(X_a,bool,P_1,X_2)))) <-> (exists Ys_3 exists X_2 ((exists Zs Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs))) & hBOOL(hAPP(X_a,bool,P_1,X_2)) & (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys_3))) -> -hBOOL(hAPP(X_a,bool,P_1,Xa)))))))) # label(fact_192_split__list__first__prop__iff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 272 (all X_a all P_1 all Xs_1 ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(X_a,bool,P_1,X_2)))) <-> (exists Ys_3 exists X_2 exists Zs (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs)) & hBOOL(hAPP(X_a,bool,P_1,X_2)) & (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Zs))) -> -hBOOL(hAPP(X_a,bool,P_1,Xa)))))))) # label(fact_193_split__list__last__prop__iff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 273 (all X_a all X_1 all L_2 all A_1 hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),L_2)),A_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),hAPP(bool,fun(list(X_a),fun(list(X_a),list(X_a))),if(list(X_a)),hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),A_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))),nil(X_a))),hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),L_2),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),A_1))))) # label(fact_194_sublist__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 274 (all X_a all X all Xs all N_1 hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),hAPP(nat,nat,suc,N_1)) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),N_1)) # label(fact_195_nth__Cons__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 275 (all X_a all N_1 all X hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(nat,nat,suc,N_1)),X) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X))) # label(fact_196_replicate__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 276 (all M_1 hAPP(nat,nat,suc,M_1) != zero_zero(nat)) # label(fact_197_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 277 (all M_1 zero_zero(nat) != hAPP(nat,nat,suc,M_1)) # label(fact_198_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 278 (all Nat_5 hAPP(nat,nat,suc,Nat_5) != zero_zero(nat)) # label(fact_199_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 279 (all M_1 hAPP(nat,nat,suc,M_1) != zero_zero(nat)) # label(fact_200_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 280 (all Nat_4 zero_zero(nat) != hAPP(nat,nat,suc,Nat_4)) # label(fact_201_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 281 (all M_1 zero_zero(nat) != hAPP(nat,nat,suc,M_1)) # label(fact_202_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 282 (all X_a all X_1 all Xs_1 all N hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),N) = hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),X_1),hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1)),N)) # label(fact_203_nth_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 283 (all X_a all F1 all F2 hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),F1),F2),zero_zero(nat)) = ti(X_a,F1)) # label(fact_204_nat__case__0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 284 (all X_a all F1 all F2 all Nat_3 hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),F1),F2),hAPP(nat,nat,suc,Nat_3)) = hAPP(nat,X_a,F2,Nat_3)) # label(fact_205_nat__case__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 285 (all N_1 N_1 != hAPP(nat,nat,suc,N_1)) # label(fact_206_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 286 (all N_1 hAPP(nat,nat,suc,N_1) != N_1) # label(fact_207_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 287 (all Nat_3 all Nat_2 (hAPP(nat,nat,suc,Nat_3) = hAPP(nat,nat,suc,Nat_2) <-> Nat_3 = Nat_2)) # label(fact_208_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 288 (all X all Y (hAPP(nat,nat,suc,X) = hAPP(nat,nat,suc,Y) -> X = Y)) # label(fact_209_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 289 (all N_1 (N_1 != zero_zero(nat) -> (exists M_2 N_1 = hAPP(nat,nat,suc,M_2)))) # label(fact_210_not0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 290 (all N all P_1 (hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> ((all N_2 (hBOOL(hAPP(nat,bool,P_1,N_2)) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_2))))) -> hBOOL(hAPP(nat,bool,P_1,N))))) # label(fact_211_nat__induct) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 291 (all P_1 all K_1 (hBOOL(hAPP(nat,bool,P_1,K_1)) -> ((all N_2 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_2))) -> hBOOL(hAPP(nat,bool,P_1,N_2)))) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))))) # label(fact_212_zero__induct) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 292 (all Y (Y != zero_zero(nat) -> -(all Nat_1 Y != hAPP(nat,nat,suc,Nat_1)))) # label(fact_213_nat_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 293 (all X_a all N_1 all Xs (Xs != nil(X_a) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N_1)),Xs) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(list(X_a),X_a,hd(X_a),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),hAPP(list(X_a),list(X_a),tl(X_a),Xs))))) # label(fact_214_take__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 294 (all X_a (linorder(X_a) -> (all X_1 all Xs_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),hAPP(fun(X_a,X_a),fun(X_a,fun(list(X_a),list(X_a))),linord2118332866rt_key(X_a,X_a),combi(X_a)),X_1),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),hAPP(fun(X_a,X_a),fun(X_a,fun(list(X_a),list(X_a))),linorder_insort_key(X_a,X_a),combi(X_a)),X_1),Xs_1))))) # label(fact_215_insort__insert__insort) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.21 295 (all X_a all P_1 all X_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex1(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))) <-> (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_all(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),P_1))),hAPP(X_a,fun(X_a,bool),fequal(X_a),X_1))),Xs_1))) & (-hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex1(X_a),P_1),Xs_1))))) # label(fact_216_list__ex1__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 296 (all X_a (linorder(X_a) -> (all Aa all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),hAPP(fun(X_a,X_a),fun(X_a,fun(list(X_a),list(X_a))),linorder_insort_key(X_a,X_a),combi(X_a)),Aa),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),Aa),Xs_1)) = Xs_1))))) # label(fact_217_insort__remove1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 297 (all X_a all X all Y all Zs_2 hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),X),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),Y),Zs_2)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),Y),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),X),Zs_2))) # label(fact_218_remove1__commute) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 298 (all X_a all N_1 hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),nil(X_a)) = nil(X_a)) # label(fact_219_take__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 299 (all X_a all X_1 all N all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs_1)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_220_in__set__takeD) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 300 (all X_a all I_1 all Xs (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_1),Xs))))) # label(fact_221_distinct__take) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 301 (all X_a (linorder(X_a) -> (all N_1 all Xs (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs))))))) # label(fact_222_sorted__take) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 302 (all X_a all Xs all X all Y ((ti(X_a,X) = ti(X_a,Y) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),X),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Xs)) = Xs) & (ti(X_a,X) != ti(X_a,Y) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),X),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Xs)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),X),Xs))))) # label(fact_223_remove1_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 303 (all X_a all X hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),X),nil(X_a)) = nil(X_a)) # label(fact_224_remove1_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 304 (all X_a all Xs_1 all Aa all Ba (ti(X_a,Aa) != ti(X_a,Ba) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),Ba),Xs_1)))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)))))) # label(fact_225_in__set__remove1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 305 (all X_a all Y_1 all X_1 all Xs_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),Y_1),Xs_1)))))) # label(fact_226_notin__set__remove1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 306 (all X_a all X_1 all Xs_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),X_1),Xs_1) = Xs_1)) # label(fact_227_remove1__idem) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 307 (all X_a all X all Xs (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),X),Xs))))) # label(fact_228_distinct__remove1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 308 (all X_a (linorder(X_a) -> (all A_2 all Xs (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),A_2),Xs))))))) # label(fact_229_sorted__remove1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 309 (all X_a all P_1 all X_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_all(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))) <-> hBOOL(hAPP(X_a,bool,P_1,X_1)) & hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_all(X_a),P_1),Xs_1)))) # label(fact_230_list__all__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 310 (all X_a all P_1 hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_all(X_a),P_1),nil(X_a)))) # label(fact_231_list__all__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 311 (all X_a all P_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_all(X_a),P_1),Xs_1)) <-> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,P_1,X_2)))))) # label(fact_232_list__all__iff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 312 (all X_a all P_1 all Xs_1 all Ys (hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_all(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys))) <-> hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_all(X_a),P_1),Xs_1)) & hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_all(X_a),P_1),Ys)))) # label(fact_233_list__all__append) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 313 (all X_a all P_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_all(X_a),P_1),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1))) <-> hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_all(X_a),P_1),Xs_1)))) # label(fact_234_list__all__rev) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 314 (all X_a all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),zero_zero(nat)),Xs) = nil(X_a)) # label(fact_235_take__0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 315 (all X_a all N all Xs_1 (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs_1) = nil(X_a) <-> N = zero_zero(nat) | Xs_1 = nil(X_a))) # label(fact_236_take__eq__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 316 (all X_a all N_1 all X all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs))) # label(fact_237_take__Suc__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 317 (all X_a (linorder(X_a) -> (all X_1 all Xs_1 hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),X_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),hAPP(fun(X_a,X_a),fun(X_a,fun(list(X_a),list(X_a))),linorder_insort_key(X_a,X_a),combi(X_a)),X_1),Xs_1)) = Xs_1))) # label(fact_238_remove1__insort) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 318 (all X_a all N_1 all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),hAPP(list(X_a),list(X_a),tl(X_a),Xs)) = hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N_1)),Xs))) # label(fact_239_take__tl) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 319 (all X_a all N all X_1 all Xs_1 hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)) = hAPP(nat,list(X_a),hAPP(fun(nat,list(X_a)),fun(nat,list(X_a)),hAPP(list(X_a),fun(fun(nat,list(X_a)),fun(nat,list(X_a))),nat_case(list(X_a)),nil(X_a)),hAPP(fun(nat,list(X_a)),fun(nat,list(X_a)),hAPP(fun(list(X_a),list(X_a)),fun(fun(nat,list(X_a)),fun(nat,list(X_a))),combb(list(X_a),list(X_a),nat),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1)),hAPP(list(X_a),fun(nat,list(X_a)),hAPP(fun(nat,fun(list(X_a),list(X_a))),fun(list(X_a),fun(nat,list(X_a))),combc(nat,list(X_a),list(X_a)),take(X_a)),Xs_1))),N)) # label(fact_240_take__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 320 (all X_a all X_b (linorder(X_b) -> (all F all X_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),hAPP(fun(X_a,X_b),fun(X_a,fun(list(X_a),list(X_a))),linord2118332866rt_key(X_a,X_b),F),X_1),Xs_1))))))) # label(fact_241_distinct__insort__insert) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 321 (all X_a all Ys all X_1 all Xs_1 ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),X_1),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),X_1),Xs_1)),Ys)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),X_1),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),X_1),Ys))))) # label(fact_242_remove1__append) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 322 (all X_a (linorder(X_a) -> (all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),hAPP(fun(X_a,X_a),fun(X_a,fun(list(X_a),list(X_a))),linord2118332866rt_key(X_a,X_a),combi(X_a)),X_1),Xs_1) = Xs_1)))) # label(fact_243_insort__insert__triv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 323 (all X_a (linorder(X_a) -> (all X_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),hAPP(fun(X_a,X_a),fun(X_a,fun(list(X_a),list(X_a))),linord2118332866rt_key(X_a,X_a),combi(X_a)),X_1),Xs_1))))))) # label(fact_244_sorted__insort__insert) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 324 (all X_a all G all F all Xs_1 all Ys (Xs_1 = Ys -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys))) -> (hBOOL(hAPP(X_a,bool,F,X_2)) <-> hBOOL(hAPP(X_a,bool,G,X_2))))) -> (hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_all(X_a),F),Xs_1)) <-> hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_all(X_a),G),Ys)))))) # label(fact_245_list__all__cong) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 325 (all X_a all Xs all Ys_1 ((all I_2 hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_2),Xs) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_2),Ys_1)) -> Xs = Ys_1)) # label(fact_246_take__equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 326 (all X_a all Fa all Aa all List_1 hAPP(list(X_a),nat,hAPP(fun(X_a,nat),fun(list(X_a),nat),list_size(X_a),Fa),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Aa),List_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(X_a,nat,Fa,Aa)),hAPP(list(X_a),nat,hAPP(fun(X_a,nat),fun(list(X_a),nat),list_size(X_a),Fa),List_1))),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_247_list_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 327 (all X_a all P_1 all Xs_1 ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(X_a,bool,P_1,X_2)))) -> (exists Ys_3 exists X_2 ((exists Zs Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs))) & hBOOL(hAPP(X_a,bool,P_1,X_2)))))) # label(fact_248_split__list__prop) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 328 (all X_a all P_1 all Xs_1 ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(X_a,bool,P_1,X_2)))) -> (exists Ys_3 exists X_2 exists Zs (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs)) & hBOOL(hAPP(X_a,bool,P_1,X_2)) & (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Zs))) -> -hBOOL(hAPP(X_a,bool,P_1,Xa)))))))) # label(fact_249_split__list__last__prop) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 329 (all X_a all P_1 all Xs_1 ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(X_a,bool,P_1,X_2)))) -> (exists Ys_3 exists X_2 ((exists Zs Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs))) & hBOOL(hAPP(X_a,bool,P_1,X_2)) & (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys_3))) -> -hBOOL(hAPP(X_a,bool,P_1,Xa)))))))) # label(fact_250_split__list__first__prop) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 330 (all X_a all Xs_1 hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),hAPP(fun(list(X_a),fun(X_a,list(X_a))),fun(list(X_a),fun(list(X_a),list(X_a))),foldl(list(X_a),X_a),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),fun(X_a,list(X_a))),combc(X_a,list(X_a),list(X_a)),cons(X_a))),nil(X_a)),Xs_1)) # label(fact_251_rev__foldl__cons) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 331 (all X_a (monoid_add(X_a) -> (all X_1 all Zs_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),hAPP(list(X_a),X_a,hAPP(X_a,fun(list(X_a),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(list(X_a),X_a)),foldl(X_a,X_a),plus_plus(X_a)),zero_zero(X_a)),Zs_1)) = hAPP(list(X_a),X_a,hAPP(X_a,fun(list(X_a),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(list(X_a),X_a)),foldl(X_a,X_a),plus_plus(X_a)),X_1),Zs_1)))) # label(fact_252_foldl__absorb0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 332 (all X_a (cancel_semigroup_add(X_a) -> (all B_2 all A_2 all C_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_2),A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),A_2) -> ti(X_a,B_2) = ti(X_a,C_2))))) # label(fact_253_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 333 (all X_a (cancel146912293up_add(X_a) -> (all A_2 all B_2 all C_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2) -> ti(X_a,B_2) = ti(X_a,C_2))))) # label(fact_254_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 334 (all X_a (cancel_semigroup_add(X_a) -> (all A_2 all B_2 all C_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2) -> ti(X_a,B_2) = ti(X_a,C_2))))) # label(fact_255_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 335 (all X_a (cancel_semigroup_add(X_a) -> (all Ba all Aa all C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa) <-> ti(X_a,Ba) = ti(X_a,C_1))))) # label(fact_256_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 336 (all X_a (cancel_semigroup_add(X_a) -> (all Aa all Ba all C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1) <-> ti(X_a,Ba) = ti(X_a,C_1))))) # label(fact_257_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 337 (all X_a (ab_semigroup_add(X_a) -> (all A_2 all B_2 all C_2 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_2),B_2)),C_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_2),C_2))))) # label(fact_258_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 338 (all X_a (semigroup_add(X_a) -> (all X_1 all Y_1 all Zs_1 hAPP(list(X_a),X_a,hAPP(X_a,fun(list(X_a),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(list(X_a),X_a)),foldl(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),X_1),Y_1)),Zs_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),hAPP(list(X_a),X_a,hAPP(X_a,fun(list(X_a),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(list(X_a),X_a)),foldl(X_a,X_a),plus_plus(X_a)),Y_1),Zs_1))))) # label(fact_259_foldl__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 339 (all M all K_1 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_1) <-> M = N)) # label(fact_260_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 340 (all K_1 all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N) <-> M = N)) # label(fact_261_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 341 (all M_1 all N_1 all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K))) # label(fact_262_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 342 (all X all Y all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Z_1))) # label(fact_263_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 343 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M_1)) # label(fact_264_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 344 (all X_a (comm_monoid_add(X_a) -> (all A_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),zero_zero(X_a)) = ti(X_a,A_2)))) # label(fact_265_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 345 (all X_a (monoid_add(X_a) -> (all A_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),zero_zero(X_a)) = ti(X_a,A_2)))) # label(fact_266_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 346 (all X_a (linord219039673up_add(X_a) -> (all Aa (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_267_double__zero__sym) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 347 (all X_a (comm_monoid_add(X_a) -> (all A_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_2) = ti(X_a,A_2)))) # label(fact_268_add__0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 348 (all X_a (monoid_add(X_a) -> (all A_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_2) = ti(X_a,A_2)))) # label(fact_269_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 349 (all M_1 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1) = M_1 -> N_1 = zero_zero(nat))) # label(fact_270_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 350 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = zero_zero(nat) <-> M = zero_zero(nat) & N = zero_zero(nat))) # label(fact_271_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 351 (all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),zero_zero(nat)) = M_1) # label(fact_272_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 352 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N_1) = N_1) # label(fact_273_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 353 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_1)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,suc,N_1))) # label(fact_274_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 354 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_1)),N_1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1))) # label(fact_275_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 355 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1))) # label(fact_276_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 356 (all X_b all X_a all F all Aa all X_1 all Xs_1 hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),Aa),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X_1),Xs_1)) = hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),F,Aa),X_1)),Xs_1)) # label(fact_277_foldl__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 357 (all X_b all X_a all F all Aa hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),Aa),nil(X_b)) = ti(X_a,Aa)) # label(fact_278_foldl__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 358 (all X_b all X_a all F all Aa all Xs_1 all Ys hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),Aa),hAPP(list(X_b),list(X_b),hAPP(list(X_b),fun(list(X_b),list(X_b)),append(X_b),Xs_1),Ys)) = hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),Aa),Xs_1)),Ys)) # label(fact_279_foldl__append) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 359 (all M all N (hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) <-> M = hAPP(nat,nat,suc,zero_zero(nat)) & N = zero_zero(nat) | M = zero_zero(nat) & N = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_280_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 360 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = hAPP(nat,nat,suc,zero_zero(nat)) <-> M = hAPP(nat,nat,suc,zero_zero(nat)) & N = zero_zero(nat) | M = zero_zero(nat) & N = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_281_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 361 (all X_a all N_1 all M_1 all X hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M_1)),X) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),M_1),X))) # label(fact_282_replicate__add) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 362 (all X_a all X_b all S all Xs_1 all F ((all X_2 all Y_2 all S_3 hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,S_3),X_2)),Y_2) = hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,S_3),Y_2)),X_2)) -> hAPP(list(X_a),X_b,hAPP(X_b,fun(list(X_a),X_b),hAPP(fun(X_b,fun(X_a,X_b)),fun(X_b,fun(list(X_a),X_b)),foldl(X_b,X_a),F),S),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)) = hAPP(list(X_a),X_b,hAPP(X_b,fun(list(X_a),X_b),hAPP(fun(X_b,fun(X_a,X_b)),fun(X_b,fun(list(X_a),X_b)),foldl(X_b,X_a),F),S),Xs_1))) # label(fact_283_foldl__rev) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 363 (all X_b all X_a all F all G all L_2 all K_1 all Aa all Ba (ti(X_a,Aa) = ti(X_a,Ba) -> (L_2 = K_1 -> ((all A_3 all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(list(X_b),fun(X_b,bool),set(X_b),L_2))) -> hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),F,A_3),X_2) = hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),G,A_3),X_2))) -> hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),Aa),L_2) = hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),G),Ba),K_1))))) # label(fact_284_foldl__cong) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 364 (all X_b all X_a all F all Xs_1 all P_1 all S (hBOOL(hAPP(X_a,bool,P_1,S)) -> ((all S_3 all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(list(X_b),fun(X_b,bool),set(X_b),Xs_1))) -> (hBOOL(hAPP(X_a,bool,P_1,S_3)) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),F,S_3),X_2)))))) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),S),Xs_1)))))) # label(fact_285_foldl__weak__invariant) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 365 (all X_a (linorder(X_a) -> (all Xs_1 hAPP(list(X_a),list(X_a),hAPP(fun(X_a,X_a),fun(list(X_a),list(X_a)),linorder_sort_key(X_a,X_a),combi(X_a)),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),hAPP(fun(list(X_a),fun(X_a,list(X_a))),fun(list(X_a),fun(list(X_a),list(X_a))),foldl(list(X_a),X_a),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),fun(X_a,list(X_a))),combc(X_a,list(X_a),list(X_a)),hAPP(fun(X_a,X_a),fun(X_a,fun(list(X_a),list(X_a))),linorder_insort_key(X_a,X_a),combi(X_a)))),nil(X_a)),Xs_1)))) # label(fact_286_sort__foldl__insort) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 366 (all X_a (comm_semiring_1(X_a) -> (all A_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_2) = ti(X_a,A_2)))) # label(fact_287_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 367 (all X_a (comm_semiring_1(X_a) -> (all A_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),zero_zero(X_a)) = ti(X_a,A_2)))) # label(fact_288_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 368 (all X_a (semiri456707255roduct(X_a) -> (all Ba all Aa (ti(X_a,Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_289_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 369 (all X_a all X_b (linorder(X_b) -> (all F hAPP(list(X_a),list(X_a),hAPP(fun(X_a,X_b),fun(list(X_a),list(X_a)),linorder_sort_key(X_a,X_b),F),nil(X_a)) = nil(X_a)))) # label(fact_290_sort__key__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 370 (all X_a all X_b (linorder(X_b) -> (all F all Xs_1 hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,X_b),fun(list(X_a),list(X_a)),linorder_sort_key(X_a,X_b),F),Xs_1)) = hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)))) # label(fact_291_set__sort) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 371 (all X_a all X_b (linorder(X_b) -> (all F all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,X_b),fun(list(X_a),list(X_a)),linorder_sort_key(X_a,X_b),F),Xs_1))) <-> hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)))))) # label(fact_292_distinct__sort) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 372 (all M all Ns (hAPP(list(nat),nat,hAPP(nat,fun(list(nat),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(list(nat),nat)),foldl(nat,nat),plus_plus(nat)),M),Ns) = zero_zero(nat) <-> M = zero_zero(nat) & (all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),hAPP(list(nat),fun(nat,bool),set(nat),Ns))) -> X_2 = zero_zero(nat))))) # label(fact_293_sum__eq__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 373 (all X_a (linorder(X_a) -> (all Xs_1 hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,X_a),fun(list(X_a),list(X_a)),linorder_sort_key(X_a,X_a),combi(X_a)),Xs_1)))))) # label(fact_294_sorted__sort) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 374 (all X_a (comm_semiring_1(X_a) -> (all A_2 all B_2 all C_2 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_2),B_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),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_2),C_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_2),D_1))))) # label(fact_295_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 375 (all X_a (comm_semiring_1(X_a) -> (all A_2 all B_2 all C_2 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_2),B_2)),C_2) = 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_2),C_2)),B_2)))) # label(fact_296_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 376 (all X_a (comm_semiring_1(X_a) -> (all A_2 all B_2 all C_2 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_2),B_2)),C_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_2),C_2))))) # label(fact_297_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 377 (all X_a (comm_semiring_1(X_a) -> (all A_2 all C_2 all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),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_2),C_2)),D_1)))) # label(fact_298_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 378 (all X_a (comm_semiring_1(X_a) -> (all A_2 all C_2 all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),D_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),D_1))))) # label(fact_299_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 379 (all X_a (comm_semiring_1(X_a) -> (all A_2 all C_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),A_2)))) # label(fact_300_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 380 (all X_a all X_b (linorder(X_b) -> (all F all X_1 all Xs_1 hAPP(list(X_a),list(X_a),hAPP(fun(X_a,X_b),fun(list(X_a),list(X_a)),linorder_sort_key(X_a,X_b),F),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),hAPP(fun(X_a,X_b),fun(X_a,fun(list(X_a),list(X_a))),linorder_insort_key(X_a,X_b),F),X_1),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,X_b),fun(list(X_a),list(X_a)),linorder_sort_key(X_a,X_b),F),Xs_1))))) # label(fact_301_sort__key__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 381 (all X_a (linord219039673up_add(X_a) -> (all Aa (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa) = zero_zero(X_a) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_302_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 382 (all X_a all X_b all S all Xs_1 all X_1 all F ((all X_2 all Y_2 all S_3 hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,S_3),X_2)),Y_2) = hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,S_3),Y_2)),X_2)) -> hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,hAPP(list(X_a),X_b,hAPP(X_b,fun(list(X_a),X_b),hAPP(fun(X_b,fun(X_a,X_b)),fun(X_b,fun(list(X_a),X_b)),foldl(X_b,X_a),F),S),Xs_1)),X_1) = hAPP(list(X_a),X_b,hAPP(X_b,fun(list(X_a),X_b),hAPP(fun(X_b,fun(X_a,X_b)),fun(X_b,fun(list(X_a),X_b)),foldl(X_b,X_a),F),hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,S),X_1)),Xs_1))) # label(fact_303_foldl__fun__comm) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 383 (all Nat hAPP(nat,nat,nat_size,hAPP(nat,nat,suc,Nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,nat_size,Nat)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_304_nat_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 384 (all X_a (monoid_add(X_a) -> (all Xs_1 hAPP(list(X_a),X_a,hAPP(X_a,fun(list(X_a),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(list(X_a),X_a)),foldl(X_a,X_a),plus_plus(X_a)),zero_zero(X_a)),Xs_1) = hAPP(X_a,X_a,hAPP(list(X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(list(X_a),fun(X_a,X_a)),foldr(X_a,X_a),plus_plus(X_a)),Xs_1),zero_zero(X_a))))) # label(fact_305_foldl__foldr1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 385 (all X_a (monoid_add(X_a) -> (all Aa all Xs_1 hAPP(list(X_a),X_a,hAPP(X_a,fun(list(X_a),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(list(X_a),X_a)),foldl(X_a,X_a),plus_plus(X_a)),Aa),Xs_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),hAPP(X_a,X_a,hAPP(list(X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(list(X_a),fun(X_a,X_a)),foldr(X_a,X_a),plus_plus(X_a)),Xs_1),zero_zero(X_a)))))) # label(fact_306_foldl__foldr1__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 386 (all X_b all X_a all F all P_1 all Xs_1 all Q_1 all X_1 (hBOOL(hAPP(X_a,bool,Q_1,X_1)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(list(X_b),fun(X_b,bool),set(X_b),Xs_1))) -> hBOOL(hAPP(X_b,bool,P_1,X_2)))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,P_1,X_2)) & hBOOL(hAPP(X_a,bool,Q_1,Y_2)) -> hBOOL(hAPP(X_a,bool,Q_1,hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),F,Y_2),X_2))))) -> hBOOL(hAPP(X_a,bool,Q_1,hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),X_1),Xs_1))))))) # label(fact_307_foldl__invariant) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 387 (all X_a all X_b all F all X_1 all Xs_1 all Aa hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X_1),Xs_1)),Aa) = hAPP(X_a,X_a,hAPP(X_b,fun(X_a,X_a),F,X_1),hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),Xs_1),Aa))) # label(fact_309_foldr_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 388 (all X_a all X_b all F all Aa hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),nil(X_b)),Aa) = ti(X_a,Aa)) # label(fact_310_foldr_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 389 (all X_a all X_b all F all Xs_1 all Ys all Aa hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(list(X_b),fun(list(X_b),list(X_b)),append(X_b),Xs_1),Ys)),Aa) = hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),Xs_1),hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),Ys),Aa))) # label(fact_311_foldr__append) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 390 (all X_a (ab_semigroup_add(X_a) -> (all Xs_1 all Aa hAPP(X_a,X_a,hAPP(list(X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(list(X_a),fun(X_a,X_a)),foldr(X_a,X_a),plus_plus(X_a)),Xs_1),Aa) = hAPP(list(X_a),X_a,hAPP(X_a,fun(list(X_a),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(list(X_a),X_a)),foldl(X_a,X_a),plus_plus(X_a)),Aa),Xs_1)))) # label(fact_312_foldr__conv__foldl) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 391 (all X_a all X_b all F all Xs_1 all Aa hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),Xs_1),Aa) = hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),F)),Aa),hAPP(list(X_b),list(X_b),rev(X_b),Xs_1))) # label(fact_313_foldr__foldl) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 392 (all X_b all X_a all F all Aa all Xs_1 hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),Aa),Xs_1) = hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_b,fun(X_a,X_a)),combc(X_a,X_b,X_a),F)),hAPP(list(X_b),list(X_b),rev(X_b),Xs_1)),Aa)) # label(fact_314_foldl__foldr) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 393 (all X_b all X_a all F all G all L_2 all K_1 all Aa all Ba (ti(X_a,Aa) = ti(X_a,Ba) -> (L_2 = K_1 -> ((all A_3 all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(list(X_b),fun(X_b,bool),set(X_b),L_2))) -> hAPP(X_a,X_a,hAPP(X_b,fun(X_a,X_a),F,X_2),A_3) = hAPP(X_a,X_a,hAPP(X_b,fun(X_a,X_a),G,X_2),A_3))) -> hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),L_2),Aa) = hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),G),K_1),Ba))))) # label(fact_315_foldr__cong) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 394 (all Nat hAPP(nat,nat,size_size(nat),hAPP(nat,nat,suc,Nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,size_size(nat),Nat)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_316_nat_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 395 (all X_a (linorder(X_a) -> (all Y_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1))) -> (Xs_1 = nil(X_a) -> hAPP(X_a,X_a,hAPP(list(X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(list(X_a),fun(X_a,X_a)),foldr(X_a,X_a),ord_max(X_a)),Xs_1),Y_1) = ti(X_a,Y_1)) & (Xs_1 != nil(X_a) -> hAPP(X_a,X_a,hAPP(list(X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(list(X_a),fun(X_a,X_a)),foldr(X_a,X_a),ord_max(X_a)),Xs_1),Y_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),zero_zero(nat))),Y_1)))))) # label(fact_317_foldr__max__sorted) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 396 (all N all Ns (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),N),hAPP(list(nat),fun(nat,bool),set(nat),Ns))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(list(nat),nat,hAPP(nat,fun(list(nat),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(list(nat),nat)),foldl(nat,nat),plus_plus(nat)),zero_zero(nat)),Ns))))) # label(fact_318_elem__le__sum) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 397 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N_1))) # label(fact_321_le0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 398 (all N_1 hAPP(nat,nat,size_size(nat),N_1) = N_1) # label(fact_322_nat__size) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 399 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_1))) # label(fact_323_le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 400 (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),N_1),M_1)))) # label(fact_324_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 401 (all M_1 all N_1 (M_1 = N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))) # label(fact_325_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 402 (all K all I_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),K))))) # label(fact_326_le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 403 (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),N_1),M_1)) -> M_1 = N_1))) # label(fact_327_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 404 (all X_a (ordere236663937imp_le(X_a) -> (all X all Y all Z_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),ord_max(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z_1))))) # label(fact_328_max__add__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 405 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N_1),zero_zero(nat)) = N_1) # label(fact_329_max__0R) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 406 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),zero_zero(nat)),N_1) = N_1) # label(fact_330_max__0L) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 407 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),M_1),N_1))) # label(fact_331_max__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 408 (all X_a (ordere236663937imp_le(X_a) -> (all Aa all C_1 all Ba (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),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)))))) # label(fact_332_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 409 (all X_a (ordere236663937imp_le(X_a) -> (all C_1 all Aa all Ba (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_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)))))) # label(fact_333_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 410 (all X_a (ordere779506340up_add(X_a) -> (all C_2 all A_2 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_2),C_2))))))) # label(fact_334_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 411 (all X_a (ordere779506340up_add(X_a) -> (all C_2 all A_2 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),B_2))))))) # label(fact_335_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 412 (all X_a (ordere779506340up_add(X_a) -> (all C_2 all D_1 all A_2 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_2),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_2),C_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_2),D_1)))))))) # label(fact_336_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 413 (all X_a (ordere236663937imp_le(X_a) -> (all A_2 all C_2 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_2),C_2))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_2)))))) # label(fact_337_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 414 (all X_a (ordere236663937imp_le(X_a) -> (all C_2 all A_2 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),B_2))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_2)))))) # label(fact_338_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 415 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N_1))) # label(fact_339_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 416 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),zero_zero(nat))) <-> N = zero_zero(nat))) # label(fact_340_le__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 417 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),N_1))) # label(fact_341_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 418 (all M all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),M)))) # label(fact_342_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 419 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) | M = hAPP(nat,nat,suc,N))) # label(fact_343_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 420 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),hAPP(nat,nat,suc,M))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)))) # label(fact_344_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 421 (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),M_1),hAPP(nat,nat,suc,N_1))))) # label(fact_345_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 422 (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_346_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 423 (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_eq(nat),M_1),N_1)))) # label(fact_347_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 424 (all N_1 all M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)))) # label(fact_348_le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 425 (all N_1 all M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M_1)))) # label(fact_349_le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 426 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) <-> (exists K_2 N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)))) # label(fact_350_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 427 (all K_1 all M all N (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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_351_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 428 (all M_1 all I_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M_1))))) # label(fact_352_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 429 (all M_1 all I_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),J))))) # label(fact_353_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 430 (all K all I_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J)) -> 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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))))) # label(fact_354_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 431 (all K all L all I_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),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_1),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L)))))) # label(fact_355_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 432 (all M_1 all K 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),M_1),K)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)))) # label(fact_356_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 433 (all M_1 all K 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),M_1),K)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))) # label(fact_357_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 434 (all M_1 all K 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),M_1),K)),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),K),N_1))))) # label(fact_358_add__leE) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 435 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,suc,N)),M) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),hAPP(nat,nat,suc,N)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),ord_max(nat),N))),M)) # label(fact_359_max__Suc1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 436 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),M),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),hAPP(nat,nat,suc,N)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),ord_max(nat)),N))),M)) # label(fact_360_max__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 437 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)) <-> 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)),N)))) # label(fact_361_less__eq__nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 438 (all X_a (ordere216010020id_add(X_a) -> (all B_2 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),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_2),B_2)),zero_zero(X_a)))))))) # label(fact_362_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 439 (all X_a (ordere216010020id_add(X_a) -> (all B_2 all A_2 all C_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)))))))) # label(fact_363_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 440 (all X_a (ordere216010020id_add(X_a) -> (all B_2 all C_2 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),C_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)))))))) # label(fact_364_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 441 (all X_a (ordere216010020id_add(X_a) -> (all Y_1 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_1)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_1) = zero_zero(X_a) <-> ti(X_a,X_1) = zero_zero(X_a) & ti(X_a,Y_1) = zero_zero(X_a))))))) # label(fact_365_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 442 (all X_a (ordere216010020id_add(X_a) -> (all B_2 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_2)) -> 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_2),B_2)))))))) # label(fact_366_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 443 (all X_a (linord219039673up_add(X_a) -> (all Aa (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),Aa),Aa)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))))))) # label(fact_367_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 444 (all X_a (linord219039673up_add(X_a) -> (all Aa (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),Aa),Aa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)))))) # label(fact_368_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 445 (all X_a (linorder(X_a) -> (all Zs_2 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Zs_2))) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Zs_2))))))))) # label(fact_369_sorted__many) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.22 446 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Zs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Zs_1)))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Zs_1))))))) # label(fact_370_sorted__many__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 447 (all X_b all X_a (linorder(X_a) -> (all Ys all F all X_1 all Y_1 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_1)),hAPP(X_b,X_a,F,Y_1))) -> hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),hAPP(fun(X_b,X_a),fun(X_b,fun(list(X_b),list(X_b))),linorder_insort_key(X_b,X_a),F),X_1),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Y_1),Ys)) = hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X_1),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Y_1),Ys))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_1)),hAPP(X_b,X_a,F,Y_1))) -> hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),hAPP(fun(X_b,X_a),fun(X_b,fun(list(X_b),list(X_b))),linorder_insort_key(X_b,X_a),F),X_1),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Y_1),Ys)) = hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Y_1),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),hAPP(fun(X_b,X_a),fun(X_b,fun(list(X_b),list(X_b))),linorder_insort_key(X_b,X_a),F),X_1),Ys))))))) # label(fact_371_insort__key_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 448 (all X_a all Y_1 all F all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Y_1),hAPP(X_a,nat,F,X_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Y_1),hAPP(list(X_a),nat,hAPP(fun(X_a,nat),fun(list(X_a),nat),list_size(X_a),F),Xs_1)))))) # label(fact_372_list__size__estimation_H) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 449 (all Ns all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(list(nat),nat,hAPP(nat,fun(list(nat),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(list(nat),nat)),foldl(nat,nat),plus_plus(nat)),N),Ns))))) # label(fact_374_start__le__sum) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 450 (all X_a (linorder(X_a) -> (all X_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))) <-> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) & (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),X_2)))))))) # label(fact_375_sorted__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 451 (all X_a (linorder(X_a) -> (all Xs_1 all Ys (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys))) <-> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) & hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Ys)) & (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Xa)))))))))) # label(fact_376_sorted__append) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 452 (all X_a (linorder(X_a) -> (all Aa (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Aa)) <-> Aa = nil(X_a) | (exists Xs_2 exists X_2 (Aa = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2) & (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_2))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Xa)))) & hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_2)))))))) # label(fact_377_sorted_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 453 (all X_a all X_b (linorder(X_b) -> (all F all Aa all Xs_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Aa)),hAPP(X_a,X_b,F,X_2))))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),hAPP(fun(X_a,X_b),fun(X_a,fun(list(X_a),list(X_a))),linorder_insort_key(X_a,X_b),F),Aa),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Aa),Xs_1))))) # label(fact_378_insort__is__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 454 (all X_a (linorder(X_a) -> (all X_1 all Xs_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),X_2)))) -> (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)))))))) # label(fact_379_sorted_OCons) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 455 (all X_a (order(X_a) -> (all N all N_3 all F ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,N)),hAPP(nat,X_a,F,N_3)))))))) # label(fact_380_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 456 (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)) -> (exists M_2 M_3 = hAPP(nat,nat,suc,M_2)))) # label(fact_381_Suc__le__D) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 457 (all X_a (preorder(X_a) -> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),X))))) # label(fact_382_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 458 (all X_a all Xs_1 all X_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))))) # label(fact_383_set__subset__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 459 (all X_a all N all Xs_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs_1))),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)))) # label(fact_384_set__take__subset) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 460 (all X_a all X_1 all Xs_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),X_1),Xs_1))),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)))) # label(fact_385_set__remove1__subset) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 461 (all X_a all Xs_1 all I_3 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),Xs_1),I_3))),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)))) # label(fact_386_set__sublist__subset) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 462 (all X_a all X_b (ord(X_b) -> (all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) <-> (all X_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2)))))))) # label(fact_387_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 463 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_388_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 464 (all X_a (order(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) = ti(X_a,Y_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)))))) # label(fact_389_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 465 (all X_a (preorder(X_a) -> (all X all Y (X = Y -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_390_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 466 (all X_a all X_b (ord(X_b) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))))) # label(fact_391_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 467 (all X_a (order(X_a) -> (all Y_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_392_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 468 (all X_a (ord(X_a) -> (all C_2 all A_2 all B_2 (ti(X_a,A_2) = ti(X_a,B_2) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),C_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C_2))))))) # label(fact_393_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 469 (all X_a (order(X_a) -> (all C_2 all A_2 all B_2 (ti(X_a,A_2) = ti(X_a,B_2) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_2),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_2),A_2))))))) # label(fact_394_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 470 (all X_a (ord(X_a) -> (all C_2 all A_2 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_2)) -> (ti(X_a,B_2) = ti(X_a,C_2) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C_2))))))) # label(fact_395_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 471 (all X_a (order(X_a) -> (all C_2 all B_2 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),A_2)) -> (ti(X_a,B_2) = ti(X_a,C_2) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_2),A_2))))))) # label(fact_396_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 472 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> ti(X_a,X) = ti(X_a,Y)))))) # label(fact_397_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 473 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z_1))))))) # label(fact_398_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 474 (all X_a (order(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> ti(X_a,X) = ti(X_a,Y)))))) # label(fact_399_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 475 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),X))))))) # label(fact_400_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 476 (all X_a all X_b (ord(X_b) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))))) # label(fact_401_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 477 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_402_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 478 (all X_a all Xs_1 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),M),Xs_1))),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs_1)))))) # label(fact_403_set__take__subset__set__take) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 479 (all X_a (linorder(X_a) -> (all Z_2 all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_2),X_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_2),Y_1)))))) # label(fact_404_le__max__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 480 (all X_a (order(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Least) = ti(X_a,X))))) # label(fact_405_max__leastR) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 481 (all X_a (ord(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Least),X) = ti(X_a,X))))) # label(fact_406_max__leastL) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 482 (all X_a (ord(X_a) -> ord_max(X_a) = hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),max(X_a),ord_less_eq(X_a)))) # label(fact_407_max__ord__max) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 483 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_408_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 484 (all Y all X all Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_409_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 485 (all X_a all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1)) -> ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)))) # label(fact_410_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 486 (all X_a all C_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B))))) # label(fact_411_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 487 (all X_a all X_b (ord(X_b) -> (all F all G ((all X_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2)))) -> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)))))) # label(fact_412_le__funI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 488 (all X_a (linorder(X_a) -> (all A_2 all B_2 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_2)),X)) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),X)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),X))))))) # label(fact_413_min__max_Ole__supE) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 489 (all X_a (linorder(X_a) -> (all B_2 all D_1 all A_2 all C_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),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),ord_max(X_a),A_2),B_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),C_2),D_1)))))))) # label(fact_414_min__max_Osup__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 490 (all X_a all A_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),A_1))) # label(fact_415_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 491 (all X_a all A_1 all B (ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1)))) # label(fact_416_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 492 (all X_a all A_1 all B (ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)))) # label(fact_417_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 493 (all X_a all A_1 all B (ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1)))) # label(fact_418_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 494 (all X_a all X_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B))))) # label(fact_419_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 495 (all X_a all B all X_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B))))) # label(fact_420_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 496 (all X_a all X_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B))))) # label(fact_421_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 497 (all X_a all C_3 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),C_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C_3))))) # label(fact_422_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 498 (all X_a all A_1 all B (ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))))) # label(fact_423_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 499 (all X_a (linorder(X_a) -> (all A_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),A_2) = ti(X_a,A_2)))) # label(fact_424_min__max_Osup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 500 (all X_a (linorder(X_a) -> (all A_2 all B_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_2),A_2)))) # label(fact_425_min__max_Osup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 501 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),X)))) # label(fact_426_min__max_Osup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 502 (all X_a (linorder(X_a) -> (all A_2 all B_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_2)))) # label(fact_427_min__max_Osup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 503 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))) # label(fact_428_min__max_Osup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 504 (all X_a (linorder(X_a) -> (all B_2 all A_2 all C_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),C_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_2),C_2))))) # label(fact_429_min__max_Osup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 505 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z_1))))) # label(fact_430_min__max_Osup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 506 (all X_a (linorder(X_a) -> (all A_2 all B_2 all C_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_2)),C_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_2),C_2))))) # label(fact_431_min__max_Osup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 507 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1))))) # label(fact_432_min__max_Osup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 508 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))))) # label(fact_433_le__maxI1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 509 (all X_a (linorder(X_a) -> (all Y all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))))) # label(fact_434_le__maxI2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 510 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1) = ti(X_a,Y_1))))) # label(fact_435_min__max_Ole__iff__sup) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 511 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1)),Z_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),Z_2)))))) # label(fact_436_min__max_Ole__sup__iff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 512 (all X_a (linorder(X_a) -> (all B_2 all X all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_2))))))) # label(fact_437_min__max_Ole__supI1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 513 (all X_a (linorder(X_a) -> (all A_2 all X all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_2))))))) # label(fact_438_min__max_Ole__supI2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 514 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y) = ti(X_a,Y))))) # label(fact_439_min__max_Osup__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 515 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y) = ti(X_a,X))))) # label(fact_440_min__max_Osup__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 516 (all X_a (linorder(X_a) -> (all B_2 all A_2 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_2)),X))))))) # label(fact_441_min__max_Ole__supI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 517 (all X_a (linorder(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1)),X))))))) # label(fact_442_min__max_Osup__least) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 518 (all X_a all B all A_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)))) # label(fact_443_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 519 (all F ((all I_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,hAPP(nat,nat,suc,I_2))),hAPP(nat,nat,F,I_2)))) -> (exists I_2 all K_2 hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_2)) = hAPP(nat,nat,F,I_2)))) # label(fact_444_weak__decr__stable) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 520 (all X_a (linorder(X_a) -> (all X_1 all Xs_1 hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))) = hAPP(list(X_a),X_a,hAPP(X_a,fun(list(X_a),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(list(X_a),X_a)),foldl(X_a,X_a),ord_max(X_a)),X_1),Xs_1)))) # label(fact_445_Max__fin__set__fold) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 521 (all X_a all Q_1 all P_1 ((all X_2 (hBOOL(hAPP(X_a,bool,P_1,X_2)) -> hBOOL(hAPP(X_a,bool,Q_1,X_2)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1))))) # label(fact_446_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 522 (all X_a all R_2 all S_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S_2))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),R_2),S_2)))) # label(fact_447_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 523 (all X_a all X_1 all P_1 all Q_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),P_1),Q_1)) -> (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(hAPP(X_a,bool,Q_1,X_1))))) # label(fact_448_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 524 (all X_a all Q_1 all P_1 all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),P_1),Q_1)) -> hBOOL(hAPP(X_a,bool,Q_1,X_1))))) # label(fact_449_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 525 (all X_a all Q_1 all P_1 ((all X_2 (hBOOL(hAPP(X_a,bool,P_1,X_2)) -> hBOOL(hAPP(X_a,bool,Q_1,X_2)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),P_1),Q_1)))) # label(fact_450_predicate1I) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 526 (all X_a (linorder(X_a) -> (all X_1 all Xs_1 hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))) = hAPP(list(X_a),X_a,hAPP(X_a,fun(list(X_a),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(list(X_a),X_a)),foldl(X_a,X_a),ord_max(X_a)),X_1),Xs_1)))) # label(fact_451_min__max_OSup__fin__set__fold) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 527 (all X_b all X_a (order(X_a) & ord(X_b) -> (all C_1 all F all Ba all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Ba)),Aa)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),Ba)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,C_1)),Aa)))))))) # label(fact_452_xt2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 528 (all X_a (order(X_a) -> (all C_1 all Aa all F all Ba (ti(X_a,Aa) = hAPP(X_a,X_a,F,Ba) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),Ba)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,F,Y_2)),hAPP(X_a,X_a,F,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,F,C_1)),Aa)))))))) # label(fact_453_xt1_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 529 (all X_b all X_a (order(X_a) & order(X_b) -> (all C_1 all F all Ba all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Aa)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),hAPP(X_a,X_b,F,Ba))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),hAPP(X_a,X_b,F,Aa))))))))) # label(fact_454_xt3) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 530 (all X_a (order(X_a) -> (all F all C_1 all Ba all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Aa)) -> (hAPP(X_a,X_a,F,Ba) = ti(X_a,C_1) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,F,Y_2)),hAPP(X_a,X_a,F,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),hAPP(X_a,X_a,F,Aa))))))))) # label(fact_455_xt1_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 531 (all X_a all X_b (ord(X_b) & ord(X_a) -> (all F all C_1 all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) -> (hAPP(X_a,X_b,F,Ba) = ti(X_b,C_1) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Aa)),C_1)))))))) # label(fact_456_ord__le__eq__subst) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 532 (all X_a all X_b (order(X_b) & order(X_a) -> (all F all C_1 all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Ba)),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Aa)),C_1)))))))) # label(fact_457_order__subst2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 533 (all X_a all X_b (order(X_b) & order(X_a) -> (all C_1 all Aa all F all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),hAPP(X_b,X_a,F,Ba))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),hAPP(X_b,X_a,F,C_1))))))))) # label(fact_458_order__subst1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 534 (all X_a all X_b (ord(X_b) & ord(X_a) -> (all C_1 all Aa all F all Ba (ti(X_a,Aa) = hAPP(X_b,X_a,F,Ba) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),hAPP(X_b,X_a,F,C_1))))))))) # label(fact_459_ord__eq__le__subst) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 535 (all X_b all X_a all F all P_1 all Xs_1 all Q_1 all X_1 (hBOOL(hAPP(X_a,bool,Q_1,X_1)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(list(X_b),fun(X_b,bool),set(X_b),Xs_1))) -> hBOOL(hAPP(X_b,bool,P_1,X_2)))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,P_1,X_2)) & hBOOL(hAPP(X_a,bool,Q_1,Y_2)) -> hBOOL(hAPP(X_a,bool,Q_1,hAPP(X_a,X_a,hAPP(X_b,fun(X_a,X_a),F,X_2),Y_2))))) -> hBOOL(hAPP(X_a,bool,Q_1,hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),Xs_1),X_1))))))) # label(fact_460_foldr__invariant) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 536 (all N all P_1 ((all N_2 ((all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_2)),N_2)) -> hBOOL(hAPP(nat,bool,P_1,M_2)))) -> hBOOL(hAPP(nat,bool,P_1,N_2)))) -> hBOOL(hAPP(nat,bool,P_1,N)))) # label(fact_461_full__nat__induct) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 537 (all X_a (linorder(X_a) -> hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),min(X_a),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),ord_less_eq(X_a))) = ord_max(X_a))) # label(fact_462_dual__min) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 538 (all X_a all A_2 all List hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_2),List)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),List)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_463_list_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 539 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,N)) = 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),N))) # label(fact_464_diff__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 540 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),M),hAPP(nat,nat,suc,N)) = 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)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),ord_min(nat)),N))),M)) # label(fact_465_min__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 541 (all X_a (linorder(X_a) -> (all X all A_2 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_2),B_2))) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_2)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_2))))))) # label(fact_466_min__max_Ole__infE) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 542 (all X_a (linorder(X_a) -> (all B_2 all D_1 all A_2 all C_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),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),ord_min(X_a),A_2),B_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),C_2),D_1)))))))) # label(fact_467_min__max_Oinf__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 543 (all X_a (linorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1)))))))) # label(fact_468_min__max_Oinf__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 544 (all X_a (linorder(X_a) -> (all B_2 all X all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_2),B_2)))))))) # label(fact_469_min__max_Ole__infI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 545 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y) = ti(X_a,Y))))) # label(fact_470_min__max_Oinf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 546 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y) = ti(X_a,X))))) # label(fact_471_min__max_Oinf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 547 (all X_a (linorder(X_a) -> (all A_2 all B_2 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_2),B_2)),X)))))) # label(fact_472_min__max_Ole__infI2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 548 (all X_a (linorder(X_a) -> (all B_2 all A_2 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_2),B_2)),X)))))) # label(fact_473_min__max_Ole__infI1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 549 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z_2 (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),ord_min(X_a),Y_1),Z_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z_2)))))) # label(fact_474_min__max_Ole__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 550 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1) = ti(X_a,X_1))))) # label(fact_475_min__max_Ole__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 551 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Y))))) # label(fact_476_min__max_Oinf__le2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 552 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),X))))) # label(fact_477_min__max_Oinf__le1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 553 (all X_a (linorder(X_a) -> (all A_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_2),A_2) = ti(X_a,A_2)))) # label(fact_478_min__max_Oinf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 554 (all X_a all X_b (minus(X_b) -> (all A_1 all B all X_2 hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),minus_minus(fun(X_a,X_b)),A_1),B),X_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,A_1,X_2)),hAPP(X_a,X_b,B,X_2))))) # label(fact_479_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 555 (all X_a (linorder(X_a) -> (all A_2 all B_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_2),B_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B_2),A_2)))) # label(fact_480_min__max_Oinf_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 556 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),X)))) # label(fact_481_min__max_Oinf__commute) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 557 (all X_a (linorder(X_a) -> (all A_2 all B_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_2),B_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_2),B_2)))) # label(fact_482_min__max_Oinf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 558 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)))) # label(fact_483_min__max_Oinf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 559 (all X_a (linorder(X_a) -> (all B_2 all A_2 all C_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_2),C_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B_2),C_2))))) # label(fact_484_min__max_Oinf_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 560 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z_1))))) # label(fact_485_min__max_Oinf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 561 (all X_a (linorder(X_a) -> (all A_2 all B_2 all C_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_2),B_2)),C_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B_2),C_2))))) # label(fact_486_min__max_Oinf_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 562 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1))))) # label(fact_487_min__max_Oinf__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 563 (all X_b all X_a (minus(X_a) -> (all A_1 all B all X_1 hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),minus_minus(fun(X_b,X_a)),A_1),B),X_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_b,X_a,A_1,X_1)),hAPP(X_b,X_a,B,X_1))))) # label(fact_488_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 564 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)) = ti(X_a,X)))) # label(fact_489_min__max_Osup__inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 565 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)) = ti(X_a,X)))) # label(fact_490_min__max_Oinf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 566 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z_1))))) # label(fact_491_min__max_Osup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 567 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z_1))))) # label(fact_492_min__max_Oinf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 568 (all X_a (linorder(X_a) -> (all Y all Z_1 all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Z_1),X))))) # label(fact_493_min__max_Osup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 569 (all X_a (linorder(X_a) -> (all Y all Z_1 all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Z_1),X))))) # label(fact_494_min__max_Oinf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 570 (all X_a all Xs hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),rev(X_a),Xs)) = hAPP(list(X_a),nat,size_size(list(X_a)),Xs)) # label(fact_495_length__rev) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 571 (all X_a all N_1 all Xs all Ys_1 hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))),Ys_1))) # label(fact_496_take__append) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 572 (all X_a (group_add(X_a) -> (all Aa all Ba (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba) = zero_zero(X_a) <-> ti(X_a,Aa) = ti(X_a,Ba))))) # label(fact_497_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 573 (all X_a (ab_group_add(X_a) -> (all Aa all Ba (ti(X_a,Aa) = ti(X_a,Ba) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba) = zero_zero(X_a))))) # label(fact_498_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 574 (all X_a (group_add(X_a) -> (all A_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),A_2) = zero_zero(X_a)))) # label(fact_499_diff__self) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 575 (all X_a (group_add(X_a) -> (all A_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),zero_zero(X_a)) = ti(X_a,A_2)))) # label(fact_500_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 576 (all X_a (group_add(X_a) -> (all A_2 all B_2 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_2),B_2)),B_2) = ti(X_a,A_2)))) # label(fact_501_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 577 (all X_a (group_add(X_a) -> (all A_2 all B_2 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_2),B_2)),B_2) = ti(X_a,A_2)))) # label(fact_502_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 578 (all X_a (ordere236663937imp_le(X_a) -> (all X all Y all Z_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),ord_min(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z_1))))) # label(fact_503_min__add__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 579 (all X_a (ordered_ab_group_add(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z_1))))) # label(fact_504_max__diff__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 580 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),zero_zero(nat)),N_1) = zero_zero(nat)) # label(fact_505_min__0L) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 581 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),N_1),zero_zero(nat)) = zero_zero(nat)) # label(fact_506_min__0R) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 582 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),M_1),N_1))) # label(fact_507_min__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 583 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N_1) = zero_zero(nat)) # label(fact_508_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 584 (all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),zero_zero(nat)) = M_1) # label(fact_509_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 585 (all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),M_1) = zero_zero(nat)) # label(fact_510_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 586 (all M_1 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1) = zero_zero(nat) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M_1) = zero_zero(nat) -> M_1 = N_1))) # label(fact_511_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 587 (all M_1 all N_1 all K 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_1)),N_1)),hAPP(nat,nat,suc,K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)),K)) # label(fact_512_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 588 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)) # label(fact_513_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 589 (all M_1 all K all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)) # label(fact_514_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 590 (all K all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)) # label(fact_515_diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 591 (all I_1 all J all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))) # label(fact_516_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 592 (all N_1 all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M_1)),N_1) = M_1) # label(fact_517_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 593 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)),N_1) = M_1) # label(fact_518_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 594 (all I_1 all J all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),K)),J)) # label(fact_519_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 595 (all M_1 all I_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),I_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),I_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),M_1),N_1)),I_1)) # label(fact_520_min__diff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 596 (all X_a (linorder(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),X) = ti(X_a,X)))) # label(fact_521_Min_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 597 (all X_a (ordered_ab_group_add(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z_1))))) # label(fact_522_min__diff__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 598 (all X_a (ab_group_add(X_a) -> (all Aa all Ba all C_1 all D_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_2) -> (ti(X_a,Aa) = ti(X_a,Ba) <-> ti(X_a,C_1) = ti(X_a,D_2)))))) # label(fact_523_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 599 (all X_a all N_1 all Xs hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),N_1)) # label(fact_524_length__take) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 600 (all X_a all Xs all Ys_1 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs) != hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1) -> Xs != Ys_1)) # label(fact_525_neq__if__length__neq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 601 (all X_a all N_1 all M_1 all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),M_1),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),N_1),M_1)),Xs)) # label(fact_526_take__take) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 602 (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),minus_minus(nat),M_1),N_1)),M_1))) # label(fact_527_diff__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.23 603 (all L 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,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M_1))))) # label(fact_528_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 604 (all L 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,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),L)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),L))))) # label(fact_529_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 605 (all I_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),I_1)) = I_1)) # label(fact_530_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 606 (all N all K_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K_1) <-> M = N)))) # label(fact_531_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 607 (all N_1 all K all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)))) # label(fact_532_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 608 (all N all K_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N)) -> (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),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))))) # label(fact_533_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 609 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba all C_1 all D_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_2) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D_2))))))) # label(fact_534_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 610 (all X_a (ord(X_a) -> ord_min(X_a) = hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),min(X_a),ord_less_eq(X_a)))) # label(fact_535_min__ord__min) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 611 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1)),Z_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),Z_2)))))) # label(fact_536_min__le__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 612 (all X_a all N_1 all X hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)) = N_1) # label(fact_537_length__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 613 (all X_a all Xs hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),rotate1(X_a),Xs)) = hAPP(list(X_a),nat,size_size(list(X_a)),Xs)) # label(fact_538_length__rotate1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 614 (all X_a all X_b (linorder(X_b) -> (all F all Xs_1 hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,X_b),fun(list(X_a),list(X_a)),linorder_sort_key(X_a,X_b),F),Xs_1)) = hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))) # label(fact_539_length__sort) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 615 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) <-> 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),minus_minus(X_a),Aa),Ba)),zero_zero(X_a))))))) # label(fact_540_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 616 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1))))))) # label(fact_541_min__max_Odistrib__inf__le) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 617 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z_1))))))) # label(fact_542_min__max_Odistrib__sup__le) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 618 (all N_1 all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M_1)) = zero_zero(nat)) # label(fact_543_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 619 (all X_a hAPP(list(X_a),nat,size_size(list(X_a)),nil(X_a)) = zero_zero(nat)) # label(fact_544_list_Osize_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 620 (all X_a all Xs_1 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = zero_zero(nat) <-> Xs_1 = nil(X_a))) # label(fact_545_length__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 621 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_546_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 622 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1) = zero_zero(nat))) # label(fact_547_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 623 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),N_1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)))) # label(fact_548_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 624 (all X_a all X all Xs all Ys_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1))) -> Xs != hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Ys_1))) # label(fact_549_impossible__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 625 (all I_1 all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K)),J))) # label(fact_550_diff__diff__right) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 626 (all J_1 all K_1 all I (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_1),K_1)),I)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_1))))) # label(fact_551_le__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 627 (all M_1 all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),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),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M_1)),K))))) # label(fact_552_le__add__diff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 628 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)) = M_1)) # label(fact_553_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 629 (all I_1 all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J)),K))) # label(fact_554_add__diff__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 630 (all I all K_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),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),K_1)),J_1))))) # label(fact_555_le__diff__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 631 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)),N_1) = M_1)) # label(fact_556_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 632 (all K_1 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),J_1),I) = K_1 <-> J_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),I)))) # label(fact_557_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 633 (all I_1 all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)))) # label(fact_558_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 634 (all I_1 all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)),I_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_1)),K))) # label(fact_559_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 635 (all I_1 all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_1)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)),I_1))) # label(fact_560_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 636 (all X_a all Xs all Ys_1 hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1))) # label(fact_561_length__append) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 637 (all X_a all Xs all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),N_1)) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs) = Xs)) # label(fact_562_take__all) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 638 (all X_a all I_1 all K all X hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_1),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),K),X)) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),I_1),K)),X)) # label(fact_563_take__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 639 (all X_a all P_1 all Xs_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))) # label(fact_564_length__takeWhile__le) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 640 (all X_a all X_b (linorder(X_b) -> (all F all X_1 all Xs_1 hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),hAPP(fun(X_a,X_b),fun(X_a,fun(list(X_a),list(X_a))),linorder_insort_key(X_a,X_b),F),X_1),Xs_1)) = hAPP(nat,nat,suc,hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))))) # label(fact_565_length__insort) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 641 (all X_a all P_1 all Xs_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))) # label(fact_566_length__dropWhile__le) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 642 (all N_1 all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M_1)),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N_1),M_1)) # label(fact_567_nat__minus__add__max) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 643 (all X_a all P_1 all Xs_1 hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))),Xs_1)) # label(fact_568_takeWhile__eq__take) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 644 (all X_a (linorder(X_a) -> hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),max(X_a),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),ord_less_eq(X_a))) = ord_min(X_a))) # label(fact_569_dual__max) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 645 (all X_a all Xs all Ys_1 hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),Xs),Ys_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1))) # label(fact_570_length__splice) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 646 (all M_1 all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> 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),K))),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,J)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M_1)))) # label(fact_571_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 647 (all M_1 all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K)),hAPP(nat,nat,suc,J)))) # label(fact_572_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 648 (all X_a all Xs all X all Ys_1 hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Ys_1))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)) = ti(X_a,X)) # label(fact_573_nth__append__length) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 649 (all X_a all Xs all Ys_1 all N_1 hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),N_1)) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys_1),N_1)) # label(fact_574_nth__append__length__plus) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 650 (all X_a (linorder(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),X) = ti(X_a,X)))) # label(fact_575_Max_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 651 (all X_a all L_2 all L_1 all A_1 hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),L_2),L_1)),A_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),L_2),A_1)),hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),L_1),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),hAPP(list(X_a),nat,size_size(list(X_a)),L_2)))),A_1))))) # label(fact_576_sublist__append) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 652 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,suc,N)),M) = 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)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),ord_min(nat),N))),M)) # label(fact_577_min__Suc1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 653 (all X_a all X_b all P_1 all Xs_1 all Ys (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(list(X_b),nat,size_size(list(X_b)),Ys) -> (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,nil(X_a)),nil(X_b))) -> ((all X_2 all Xs_2 all Y_2 all Ys_3 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_2) = hAPP(list(X_b),nat,size_size(list(X_b)),Ys_3) -> (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,Xs_2),Ys_3)) -> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2)),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Y_2),Ys_3)))))) -> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,Xs_1),Ys)))))) # label(fact_578_list__induct2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 654 (all X_a all N all Xs_1 (hAPP(nat,nat,suc,N) = hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) <-> (exists Y_2 exists Ys_3 (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_3) & hAPP(list(X_a),nat,size_size(list(X_a)),Ys_3) = N)))) # label(fact_579_Suc__length__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 655 (all X_a all Xs_1 all N (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(nat,nat,suc,N) <-> (exists Y_2 exists Ys_3 (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_3) & hAPP(list(X_a),nat,size_size(list(X_a)),Ys_3) = N)))) # label(fact_580_length__Suc__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 656 (all X_a (linorder(X_a) -> (all X all Y all Z_1 ((all X_2 all Y_2 all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y_2),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),Y_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),Z))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z_1)))))) # label(fact_581_min__max_Odistrib__imp2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 657 (all X_a all C_3 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),C_3)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),C_3),A_1)) = ti(fun(X_a,bool),A_1)))) # label(fact_582_double__diff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 658 (all X_a all D_3 all B all A_1 all C_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),D_3),B)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),C_3),D_3)))))) # label(fact_583_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 659 (all X_a all A_1 all B hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)),A_1))) # label(fact_584_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 660 (all X_a (linorder(X_a) -> (all X all Y all Z_1 ((all X_2 all Y_2 all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y_2),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),Y_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),Z))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z_1)))))) # label(fact_585_min__max_Odistrib__imp1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 661 (all I all P_1 all K_1 (hBOOL(hAPP(nat,bool,P_1,K_1)) -> ((all N_2 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_2))) -> hBOOL(hAPP(nat,bool,P_1,N_2)))) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K_1),I)))))) # label(fact_586_zero__induct__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 662 (all X_a (ord(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Least),X) = ti(X_a,Least))))) # label(fact_587_min__leastL) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 663 (all X_a all B all C_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)))))) # label(fact_588_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 664 (all X_a all C_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B))) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B))))) # label(fact_589_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 665 (all X_a all A_1 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B))))) # label(fact_590_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 666 (all X_a all C_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B)))) # label(fact_591_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 667 (all X_a all A_1 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)),B) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)) # label(fact_592_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 668 (all X_a all C_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)))) # label(fact_593_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 669 (all X_a all C_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B)))) # label(fact_594_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 670 (all X_a (order(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Least) = ti(X_a,Least))))) # label(fact_595_min__leastR) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 671 (all X_a all I_1 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,I_1)),Xs) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_1),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_1)),nil(X_a))))) # label(fact_596_take__Suc__conv__app__nth) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 672 (all X_a (linorder(X_a) -> (all I_1 all J all Xs (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),J)),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_1))))))))) # label(fact_597_sorted__rev__nth__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 673 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))) # label(fact_598_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 674 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,N_1)))) # label(fact_599_lessI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 675 (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),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_1))))) # label(fact_600_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 676 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1)))) # label(fact_601_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 677 (all N_1 all J all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),N_1)),K)))) # label(fact_602_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 678 (all L 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),M_1),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_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M_1)))))) # label(fact_603_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 679 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba all C_1 all D_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_2) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_2))))))) # label(fact_604_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 680 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))))))) # label(fact_605_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 681 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))))))) # label(fact_606_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 682 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))))))) # label(fact_607_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 683 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))))))) # label(fact_608_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 684 (all X_a (order(X_a) -> (all B_2 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),A_2)) -> (ti(X_a,A_2) != ti(X_a,B_2) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_2))))))) # label(fact_609_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 685 (all X_a (order(X_a) -> (all A_2 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_2)) -> (ti(X_a,A_2) != ti(X_a,B_2) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_2))))))) # label(fact_610_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 686 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) | ti(X_a,X) = ti(X_a,Y))))) # label(fact_611_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 687 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_612_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 688 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)))) # label(fact_613_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 689 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_614_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 690 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_615_leD) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 691 (all X_a (order(X_a) -> (all A_2 all B_2 (ti(X_a,A_2) != ti(X_a,B_2) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_2))))))) # label(fact_616_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 692 (all X_a (order(X_a) -> (all A_2 all B_2 (ti(X_a,A_2) != ti(X_a,B_2) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_2))))))) # label(fact_617_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 693 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_618_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 694 (all X_a (linorder(X_a) -> (all Y all X (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_619_not__leE) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 695 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_620_leI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 696 (all X_a (order(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) | ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_621_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 697 (all X_a (preorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)))))) # label(fact_622_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 698 (all X_a (order(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & ti(X_a,X_1) != ti(X_a,Y_1))))) # label(fact_623_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 699 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_624_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 700 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)))))) # label(fact_625_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 701 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)))))) # label(fact_626_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 702 (all Y all X all Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_627_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 703 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_628_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 704 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))) # label(fact_629_not__less0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 705 (all N (N != zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_630_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 706 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))) # label(fact_631_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 707 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> N_1 != zero_zero(nat))) # label(fact_632_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 708 (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_633_gr0I) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 709 (all M all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M))))) # label(fact_634_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 710 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) | M = N)) # label(fact_635_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 711 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_636_Suc__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 712 (all N all M (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M))) <-> N = M))) # label(fact_637_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 713 (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))) -> M_1 = N_1))) # label(fact_638_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 714 (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),M_1),hAPP(nat,nat,suc,N_1))))) # label(fact_639_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 715 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> (hAPP(nat,nat,suc,M_1) != N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),N_1))))) # label(fact_640_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 716 (all K all I_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_1)),K))))) # label(fact_641_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 717 (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_642_less__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 718 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_643_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 719 (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_644_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 720 (all I_1 all J -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),J)),I_1))) # label(fact_645_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 721 (all J all I_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_1)),I_1))) # label(fact_646_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 722 (all K_1 all M all N (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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_647_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 723 (all M_1 all I_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M_1))))) # label(fact_648_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 724 (all M_1 all I_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),J))))) # label(fact_649_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 725 (all K all I_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J)) -> 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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))))) # label(fact_650_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 726 (all K all L all I_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),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_1),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L)))))) # label(fact_651_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 727 (all M_1 all N_1 all K all L (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),L) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))))) # label(fact_652_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 728 (all I_1 all J all K (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),J)),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K)))) # label(fact_653_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 729 (all X_a (linorder(X_a) -> (all Z_2 all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),Y_1)))))) # label(fact_654_less__max__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 730 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z_2 (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),ord_max(X_a),X_1),Y_1)),Z_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),Z_2)))))) # label(fact_655_max__less__iff__conj) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 731 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) & M != N)) # label(fact_656_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 732 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) | M = N)) # label(fact_657_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 733 (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)))) # label(fact_658_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 734 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> (M_1 != N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))))) # label(fact_659_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 735 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) | M_1 = N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))) # label(fact_660_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 736 (all P_1 all M all N ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N),M))) -> ((M = N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N),M))) -> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N),M))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N),M)))))) # label(fact_661_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 737 (all S_1 all T_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S_1),T_4)) -> S_1 != T_4)) # label(fact_662_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 738 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1)) -> M_1 != N_1)) # label(fact_663_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 739 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))) # label(fact_664_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 740 (all X all Y (X != Y -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X))))) # label(fact_665_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 741 (all M all N (M != N <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)))) # label(fact_666_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 742 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))) # label(fact_667_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 743 (all X_a (ordere236663937imp_le(X_a) -> (all Aa all C_1 all Ba (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),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)))))) # label(fact_668_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 744 (all X_a (ordere236663937imp_le(X_a) -> (all C_1 all Aa all Ba (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_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)))))) # label(fact_669_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 745 (all X_a (ordere223160158up_add(X_a) -> (all C_2 all A_2 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_2)) -> 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_2),C_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_2),C_2))))))) # label(fact_670_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 746 (all X_a (ordere223160158up_add(X_a) -> (all C_2 all A_2 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_2)) -> 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_2),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),B_2))))))) # label(fact_671_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 747 (all X_a (ordere223160158up_add(X_a) -> (all C_2 all D_1 all A_2 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_2),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_2),C_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_2),D_1)))))))) # label(fact_672_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 748 (all X_a (ordere236663937imp_le(X_a) -> (all A_2 all C_2 all B_2 (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_2),C_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_2),C_2))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_2)))))) # label(fact_673_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 749 (all X_a (ordere236663937imp_le(X_a) -> (all C_2 all A_2 all B_2 (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_2),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),B_2))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_2)))))) # label(fact_674_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 750 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (ti(X_a,X) != ti(X_a,Y) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_675_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 751 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_676_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 752 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))))))) # label(fact_677_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 753 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))))))) # label(fact_678_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 754 (all X_a (order(X_a) -> (all C_2 all B_2 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_2)) -> (ti(X_a,B_2) = ti(X_a,C_2) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_2),A_2))))))) # label(fact_679_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 755 (all X_a (ord(X_a) -> (all C_2 all A_2 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_2)) -> (ti(X_a,B_2) = ti(X_a,C_2) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C_2))))))) # label(fact_680_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 756 (all X_a (order(X_a) -> (all C_2 all A_2 all B_2 (ti(X_a,A_2) = ti(X_a,B_2) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_2),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_2),A_2))))))) # label(fact_681_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 757 (all X_a (ord(X_a) -> (all C_2 all A_2 all B_2 (ti(X_a,A_2) = ti(X_a,B_2) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),C_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C_2))))))) # label(fact_682_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 758 (all X_a (order(X_a) -> (all B_2 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_2)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_2)))))) # label(fact_683_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 759 (all X_a (preorder(X_a) -> (all A_2 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_2)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_2)))))) # label(fact_684_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 760 (all X_a (preorder(X_a) -> (all P_1 all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) -> hBOOL(P_1)))))) # label(fact_685_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 761 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ti(X_a,Y) != ti(X_a,X))))) # label(fact_686_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 762 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ti(X_a,X) != ti(X_a,Y))))) # label(fact_687_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 763 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_688_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 764 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_689_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 765 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ti(X_a,X) != ti(X_a,Y))))) # label(fact_690_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 766 (all X_a (linorder(X_a) -> (all X all Y (ti(X_a,X) != ti(X_a,Y) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_691_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 767 (all X_a (linorder(X_a) -> (all Y_1 all X_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_692_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 768 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) | ti(X_a,X) = ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_693_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 769 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) | ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_694_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 770 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) != ti(X_a,Y_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)))))) # label(fact_695_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 771 (all X_a (preorder(X_a) -> (all X -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),X))))) # label(fact_696_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 772 (all X_a (linorder(X_a) -> (all A_2 all X all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_2))))))) # label(fact_697_min__max_Oless__supI2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 773 (all X_a (linorder(X_a) -> (all B_2 all X all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_2))))))) # label(fact_698_min__max_Oless__supI1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 774 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z_2 (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),ord_min(X_a),X_1),Y_1)),Z_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),Z_2)))))) # label(fact_699_min__less__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 775 (all X_a (linorder(X_a) -> (all Z_2 all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),Y_1)))))) # label(fact_700_min__less__iff__conj) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 776 (all X_a (linorder(X_a) -> (all A_2 all B_2 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),X)) -> 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),ord_min(X_a),A_2),B_2)),X)))))) # label(fact_701_min__max_Oless__infI2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 777 (all X_a (linorder(X_a) -> (all B_2 all A_2 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),X)) -> 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),ord_min(X_a),A_2),B_2)),X)))))) # label(fact_702_min__max_Oless__infI1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 778 (all X_a (ordere223160158up_add(X_a) -> (all C_2 all D_1 all A_2 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_2),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_2),C_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_2),D_1)))))))) # label(fact_703_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 779 (all X_a (ordere223160158up_add(X_a) -> (all C_2 all D_1 all A_2 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_2),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_2),C_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_2),D_1)))))))) # label(fact_704_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 780 (all X_a (linordered_idom(X_a) -> (all Aa (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),Aa),Aa)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))))))) # label(fact_705_even__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 781 (all X_a (linord219039673up_add(X_a) -> (all Aa (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),Aa),Aa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa)))))) # label(fact_706_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 782 (all X_a (linord219039673up_add(X_a) -> (all Aa (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),Aa),Aa)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))))))) # label(fact_707_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 783 (all X_a (ordere216010020id_add(X_a) -> (all B_2 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_2)) -> 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_2),B_2)))))))) # label(fact_708_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 784 (all X_a (ordere216010020id_add(X_a) -> (all B_2 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),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_2),B_2)),zero_zero(X_a)))))))) # label(fact_709_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 785 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) <-> 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),minus_minus(X_a),Aa),Ba)),zero_zero(X_a))))))) # label(fact_710_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 786 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) <-> (exists M_2 N = hAPP(nat,nat,suc,M_2)))) # label(fact_711_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 787 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))) <-> N = zero_zero(nat))) # label(fact_712_less__Suc0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 788 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))) <-> M = zero_zero(nat) | (exists J_2 (M = hAPP(nat,nat,suc,J_2) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),N)))))) # label(fact_713_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 789 (all M all N (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),N))) <-> 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),zero_zero(nat)),N)))) # label(fact_714_add__gr__0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 790 (all I_1 all M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),M_1))))) # label(fact_715_less__add__Suc1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 791 (all I_1 all M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),I_1))))) # label(fact_716_less__add__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 792 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) <-> (exists K_2 N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2))))) # label(fact_717_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 793 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),M)))) # label(fact_718_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 794 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_719_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 795 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_720_Suc__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 796 (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),hAPP(nat,nat,suc,N_1))))) # label(fact_721_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 797 (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),hAPP(nat,nat,suc,M_1)),N_1)))) # label(fact_722_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 798 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M))) <-> N = M))) # label(fact_723_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 799 (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_724_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 800 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)),M_1))))) # label(fact_725_diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 801 (all N all M (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),M))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_726_zero__less__diff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 802 (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),minus_minus(nat),M_1),N_1)),hAPP(nat,nat,suc,M_1)))) # label(fact_727_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 803 (all M_1 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)) = M_1)) # label(fact_728_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 804 (all I all J_1 all K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),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),K_1)),J_1)))) # label(fact_729_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 805 (all C_2 all A_2 all B_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C_2),A_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),C_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B_2),C_2)))))) # label(fact_730_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 806 (all N all K_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))))) # label(fact_731_less__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 807 (all X_a all Xs_1 all Ys (Xs_1 = Ys <-> hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(list(X_a),nat,size_size(list(X_a)),Ys) & (all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I_2) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys),I_2))))) # label(fact_732_list__eq__iff__nth__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 808 (all X_a all Xs all I_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),N_1)) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs)),I_1) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_1))) # label(fact_733_nth__take) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 809 (all X_a all X all I_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),N_1)) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)),I_1) = ti(X_a,X))) # label(fact_734_nth__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 810 (all X_a all Y_1 all F all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y_1),hAPP(X_a,nat,F,X_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y_1),hAPP(list(X_a),nat,hAPP(fun(X_a,nat),fun(list(X_a),nat),list_size(X_a),F),Xs_1)))))) # label(fact_735_list__size__estimation) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 811 (all X_2 hAPP(nat,fun(nat,bool),ord_less(nat),X_2) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X_2))) # label(fact_736_less__eq__Suc__le__raw) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 812 (all X_a (ordere216010020id_add(X_a) -> (all B_2 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),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_2),B_2)),zero_zero(X_a)))))))) # label(fact_737_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 813 (all X_a (ordere216010020id_add(X_a) -> (all B_2 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),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_2),B_2)),zero_zero(X_a)))))))) # label(fact_738_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 814 (all X_a (ordere216010020id_add(X_a) -> (all B_2 all C_2 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),C_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)))))))) # label(fact_739_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 815 (all X_a (ordere216010020id_add(X_a) -> (all B_2 all C_2 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),C_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)))))))) # label(fact_740_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 816 (all X_a (ordere216010020id_add(X_a) -> (all B_2 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_2)) -> 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_2),B_2)))))))) # label(fact_741_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 817 (all X_a (ordere216010020id_add(X_a) -> (all B_2 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_2)) -> 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_2),B_2)))))))) # label(fact_742_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 818 (all X_a all Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) <-> Xs_1 != nil(X_a))) # label(fact_743_length__greater__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 819 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))))) # label(fact_744_length__pos__if__in__set) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 820 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))) = N_1)) # label(fact_745_Suc__pred) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 821 (all I_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),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),N_1),hAPP(nat,nat,suc,I_1))),N_1)))) # label(fact_746_diff__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 822 (all P_1 all Aa all Ba (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba))) <-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba)) & -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) | (exists D (Aa = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),D) & -hBOOL(hAPP(nat,bool,P_1,D))))))) # label(fact_747_nat__diff__split__asm) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 823 (all P_1 all Aa all Ba (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba))) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba)) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))) & (all D (Aa = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),D) -> hBOOL(hAPP(nat,bool,P_1,D)))))) # label(fact_748_nat__diff__split) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 824 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) <-> (exists I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) & hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I_2) = ti(X_a,X_1))))) # label(fact_749_in__set__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 825 (all X_a all P_1 all Xs_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,P_1,X_2)))) <-> (all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I_2))))))) # label(fact_750_all__set__conv__all__nth) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 826 (all X_a all N all Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),N)),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_751_nth__mem) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 827 (all X_a all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) <-> (all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> (all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> (I_2 != J_2 -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I_2) != hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),J_2)))))))) # label(fact_752_distinct__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 828 (all X_a all J_1 all I all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> (hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),J_1) <-> I = J_1))))) # label(fact_753_nth__eq__iff__index__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 829 (all X_a all P_1 all Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> -hBOOL(hAPP(X_a,bool,P_1,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))))))) # label(fact_754_nth__length__takeWhile) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 830 (all X_a all J_1 all P_1 all Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)))) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)),J_1) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),J_1))) # label(fact_755_takeWhile__nth) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 831 (all X_a all N_1 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs))) # label(fact_756_take__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 832 (all X_a all P_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_all(X_a),P_1),Xs_1)) <-> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),N_2))))))) # label(fact_757_list__all__length) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 833 (all X_a all Ys_1 all N_1 all Xs ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)),N_1) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),N_1)) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)),N_1) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))))) # label(fact_758_nth__append) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 834 (all X_a (linorder(X_a) -> (all I_1 all J all Xs (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_1)),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),J))))))))) # label(fact_759_sorted__nth__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 835 (all X_a (linorder(X_a) -> (all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) <-> (all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> (all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I_2)),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),J_2))))))))))) # label(fact_760_sorted__equals__nth__mono) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 836 (all X_a all N_1 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs)),N_1) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),hAPP(nat,nat,suc,N_1))))) # label(fact_761_rev__nth) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 837 (all X_a all J_1 all P_1 all Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1)))) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1)),J_1) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)))))) # label(fact_762_dropWhile__nth) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 838 (all X_a (linorder(X_a) -> (all Xs ((all I_2 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_2)),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),J_2)))))) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs)))))) # label(fact_763_sorted__nth__monoI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 839 (all X_a all P_1 all Xs_1 all N ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I_2)))))) -> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> -hBOOL(hAPP(X_a,bool,P_1,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),N)))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs_1)))) # label(fact_764_takeWhile__eq__take__P__nth) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 840 (all X_a all P_1 all Xs_1 all J_1 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1)) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))))))) # label(fact_765_length__takeWhile__less__P__nth) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 841 (all X_a all X_b (ord(X_b) -> (all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G)) <-> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) & -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),G),F)))))) # label(fact_766_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 842 (all X_a all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) & ti(fun(X_a,bool),A_1) != ti(fun(X_a,bool),B))) # label(fact_767_psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 843 (all X_a all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) | ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B))) # label(fact_768_subset__iff__psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 844 (all X_a all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)))) # label(fact_769_psubset__imp__subset) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 845 (all X_a all C_3 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),C_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),C_3))))) # label(fact_770_psubset__subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 846 (all X_a all C_3 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B),C_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),C_3))))) # label(fact_771_subset__psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 847 (all X_a all Ys_1 all K all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1))) -> ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K)) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_2) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys_1),I_2))) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),K),Xs) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),K),Ys_1))))) # label(fact_772_nth__take__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 848 (all X_a all F all G all Xs_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X_a,nat,F,X_2)),hAPP(X_a,nat,G,X_2))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,hAPP(fun(X_a,nat),fun(list(X_a),nat),list_size(X_a),F),Xs_1)),hAPP(list(X_a),nat,hAPP(fun(X_a,nat),fun(list(X_a),nat),list_size(X_a),G),Xs_1))))) # label(fact_773_list__size__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 849 (all X_a all C_3 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B),C_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),C_3))))) # label(fact_774_psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 850 (all X_a all C_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B))))) # label(fact_775_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 851 (all X_a all X_1 all P_1 all Xs_1 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I_2))))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,P_1,X_1))))) # label(fact_776_all__nth__imp__all__set) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 852 (all X_a all P_1 all N all Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,P_1,X_2)))) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),N)))))) # label(fact_777_list__ball__nth) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 853 (all X_a all Xs all Ys_1 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs) = hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1) -> ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_2) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys_1),I_2))) -> Xs = Ys_1))) # label(fact_778_nth__equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 854 (all X_a all P_1 all K_1 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1)) -> (exists X1 hBOOL(hAPP(X_a,bool,hAPP(nat,fun(X_a,bool),P_1,I_2),X1))))) <-> (exists Xs_2 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_2) = K_1 & (all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1)) -> hBOOL(hAPP(X_a,bool,hAPP(nat,fun(X_a,bool),P_1,I_2),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_2),I_2))))))))) # label(fact_779_Skolem__list__nth) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 855 (all M all K_1 all F ((all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M_2)),hAPP(nat,nat,F,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),hAPP(nat,nat,F,M)),K_1)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_1)))))) # label(fact_780_mono__nat__linear__lb) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.25 856 (all P_1 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,P_1,J_1)) -> ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1)) -> (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,I_2))) -> hBOOL(hAPP(nat,bool,P_1,I_2))))) -> hBOOL(hAPP(nat,bool,P_1,I)))))) # label(fact_781_inc__induct) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 857 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> (exists K_2 N_1 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2))))) # label(fact_782_less__imp__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 858 (all N all P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> (hBOOL(hAPP(nat,bool,P_1,N)) -> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),N)) & (all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_2)) -> -hBOOL(hAPP(nat,bool,P_1,I_2)))) & hBOOL(hAPP(nat,bool,P_1,K_2))))))) # label(fact_783_ex__least__nat__le) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 859 (all I_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J)) -> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2)) & hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_2) = J)))) # label(fact_784_less__imp__add__positive) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 860 (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_785_gr0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 861 (all X_a (order(X_a) -> (all N all N_3 all F ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N)),hAPP(nat,X_a,F,N_3)))))))) # label(fact_786_lift__Suc__mono__less) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 862 (all X_a (order(X_a) -> (all N all M all F ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N)),hAPP(nat,X_a,F,M))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M))))))) # label(fact_787_lift__Suc__mono__less__iff) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 863 (all X_a (linordered_semidom(X_a) -> (all B_2 all C_2 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),C_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)))))))) # label(fact_788_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 864 (all X_a all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) -> (exists B_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B),A_1)))))) # label(fact_789_psubset__imp__ex__mem) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 865 (all X_a (linordered_idom(X_a) -> (all X all Y (ti(X_a,X) != ti(X_a,Y) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_790_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 866 (all I all J_1 all F ((all I_2 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I_2)),hAPP(nat,nat,F,J_2))))) -> (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,F,I)),hAPP(nat,nat,F,J_1)))))) # label(fact_791_less__mono__imp__le__mono) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 867 (all X_a all N_1 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs))),nil(X_a))) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N_1)),Xs))) # label(fact_792_take__hd__drop) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 868 (all X_a all N_1 all X all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,N_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs)) # label(fact_793_drop__Suc__Cons) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 869 (all X_a all N all Xs_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs_1))),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)))) # label(fact_794_set__drop__subset) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 870 (all X_a all N_1 all Xs hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),N_1)) # label(fact_795_length__drop) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 871 (all X_a all N_1 all Xs all Y all Ys_1 (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Ys_1) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),N_1) = ti(X_a,Y))) # label(fact_796_nth__via__drop) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 872 (all X_a all N_1 all M_1 all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),M_1),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),M_1),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M_1)),Xs))) # label(fact_797_take__drop) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 873 (all X_a all N_1 all M_1 all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),M_1),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs))) # label(fact_798_drop__take) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 874 (all X_a all N_1 all Xs hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs)) = Xs) # label(fact_799_append__take__drop__id) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 875 (all X_a all I_1 all K all X hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),I_1),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),K),X)) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K),I_1)),X)) # label(fact_800_drop__replicate) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 876 (all X_a all N_1 all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,N_1)),Xs) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),hAPP(list(X_a),list(X_a),tl(X_a),Xs))) # label(fact_801_drop__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 877 (all X_a all N_1 all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)) = hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs))) # label(fact_802_drop__butlast) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 878 (all X_a all N_1 all Xs hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),hAPP(list(X_a),list(X_a),butlast(X_a),Xs))) # label(fact_803_butlast__drop) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 879 (all X_a all I_1 all Xs (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),I_1),Xs))))) # label(fact_804_distinct__drop) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 880 (all X_a (linorder(X_a) -> (all N_1 all Xs (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs))))))) # label(fact_805_sorted__drop) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 881 (all X_a all N_1 hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),nil(X_a)) = nil(X_a)) # label(fact_806_drop__Nil) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 882 (all X_a all X_1 all N all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs_1)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_807_in__set__dropD) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 883 (all X_a all N_1 all M_1 all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),M_1),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M_1)),Xs)) # label(fact_808_drop__drop) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 884 (all X_a all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),zero_zero(nat)),Xs) = Xs) # label(fact_809_drop__0) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 885 (all X_a all N_1 all Xs hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),hAPP(list(X_a),list(X_a),tl(X_a),Xs))) # label(fact_810_tl__drop) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 886 (all X_a all N_1 all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),hAPP(list(X_a),list(X_a),tl(X_a),Xs)) = hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs))) # label(fact_811_drop__tl) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 887 (all X_a all Xs_1 all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),M),Xs_1))),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs_1)))))) # label(fact_812_set__drop__subset__set__drop) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 888 (all X_a all N all Xs_1 (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs_1) = nil(X_a) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)),N)))) # label(fact_813_drop__eq__Nil) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 889 (all X_a all Xs all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),N_1)) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs) = nil(X_a))) # label(fact_814_drop__all) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 890 (all X_a all N_1 all Xs all Ys_1 hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))),Ys_1))) # label(fact_815_drop__append) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 891 (all X_a all Xs_1 all Ys all Zs_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys) = Zs_1 <-> Xs_1 = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)),Zs_1) & Ys = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)),Zs_1))) # label(fact_816_append__eq__conv__conj) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 892 (all X_a all I_1 all J all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J)),Xs) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_1),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),J),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),I_1),Xs)))) # label(fact_817_take__add) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 893 (all X_a all N_1 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs)) = hAPP(list(X_a),X_a,last(X_a),Xs))) # label(fact_818_last__drop) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 894 (all X_a all N all X_1 all Xs_1 hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)) = hAPP(nat,list(X_a),hAPP(fun(nat,list(X_a)),fun(nat,list(X_a)),hAPP(list(X_a),fun(fun(nat,list(X_a)),fun(nat,list(X_a))),nat_case(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),hAPP(list(X_a),fun(nat,list(X_a)),hAPP(fun(nat,fun(list(X_a),list(X_a))),fun(list(X_a),fun(nat,list(X_a))),combc(nat,list(X_a),list(X_a)),drop(X_a)),Xs_1)),N)) # label(fact_819_drop__Cons) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 895 (all X_a all P_1 all Xs_1 hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))),Xs_1)) # label(fact_820_dropWhile__eq__drop) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 896 (all X_a all N_1 all I_1 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),I_1)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs)),I_1) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),I_1)))) # label(fact_821_nth__drop) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 897 (all X_a all Xs_1_1 all Xs_2_1 all Ys_1_1 all Ys_2 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1_1),Xs_2_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1_1),Ys_2) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1_1)),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1_1))) -> Xs_1_1 = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1_1)),Ys_1_1) & Xs_2_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1_1)),Ys_1_1)),Ys_2)) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1_1)),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1_1))) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1_1)),Xs_1_1) = Ys_1_1 & hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1_1)),Xs_1_1)),Xs_2_1) = Ys_2))) # label(fact_822_append__eq__append__conv__if) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 898 (all X_a all I_1 all Xs hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),I_1),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),I_1)),hAPP(list(X_a),list(X_a),rev(X_a),Xs))) # label(fact_823_rev__drop) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 899 (all X_a all I_1 all Xs hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_1),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),I_1)),hAPP(list(X_a),list(X_a),rev(X_a),Xs))) # label(fact_824_rev__take) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 900 (all X_a all I_1 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_1)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,I_1)),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),I_1),Xs))) # label(fact_825_nth__drop_H) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 901 (all X_a all N_1 all Xs (Xs != nil(X_a) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs)) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),N_1)))) # label(fact_826_hd__drop__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 902 (all X_a all I_1 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> Xs = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_1),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_1)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,I_1)),Xs))))) # label(fact_827_id__take__nth__drop) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 903 (all I_1 all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K)) -> (K != hAPP(nat,nat,suc,I_1) -> -(all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> K != hAPP(nat,nat,suc,J_2)))))) # label(fact_828_lessE) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 904 (all I_1 all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_1)),K)) -> -(all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> K != hAPP(nat,nat,suc,J_2))))) # label(fact_829_Suc__lessE) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 905 (all X_a (dense_linorder(X_a) -> (all Z_1 all Y ((all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z_1)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)))))) # label(fact_830_dense__le) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 906 (all X_a (dense_linorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ((all W (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W),Z_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1))))))) # label(fact_831_dense__le__bounded) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 907 (all X_b all X_a (order(X_a) & ord(X_b) -> (all C_1 all F all Ba all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Ba)),Aa)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),Ba)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C_1)),Aa)))))))) # label(fact_832_xt6) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 908 (all X_b all X_a (order(X_a) & order(X_b) -> (all C_1 all F all Ba all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Ba)),Aa)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),Ba)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C_1)),Aa)))))))) # label(fact_833_xt4) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 909 (all X_b all X_a (order(X_a) & order(X_b) -> (all C_1 all F all Ba all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),hAPP(X_a,X_b,F,Ba))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Aa))))))))) # label(fact_834_xt5) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 910 (all X_b all X_a (order(X_a) & order(X_b) -> (all C_1 all F all Ba all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Aa)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Ba))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Aa))))))))) # label(fact_835_xt7) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.25 911 (all X_a all X_b (order(X_b) & order(X_a) -> (all C_1 all Aa all F all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),hAPP(X_b,X_a,F,Ba))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,C_1))))))))) # label(fact_836_order__le__less__subst1) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 912 (all X_a all X_b (order(X_b) & order(X_a) -> (all C_1 all Aa all F all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,Ba))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,C_1))))))))) # label(fact_837_order__less__le__subst1) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 913 (all X_a all X_b (order(X_b) & order(X_a) -> (all F all C_1 all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Ba)),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),C_1)))))))) # label(fact_838_order__less__le__subst2) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 914 (all X_a all X_b (order(X_b) & order(X_a) -> (all F all C_1 all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Ba)),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),C_1)))))))) # label(fact_839_order__le__less__subst2) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 915 (all X_a all A_2 all I_1 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),A_2) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_1),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_2),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,I_1)),Xs))))) # label(fact_840_upd__conv__take__nth__drop) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 916 (all X_a (linordered_field(X_a) -> (all X all Y ((all E (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),E)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),E))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_841_field__le__epsilon) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 917 (all X_a all Xs all I_1 all X all Y hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),I_1),Y) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),Y)) # label(fact_842_list__update__overwrite) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 918 (all X_a all Xs all X all X_3 all I_1 all I_4 (I_1 != I_4 -> hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),I_4),X_3) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_4),X_3)),I_1),X))) # label(fact_843_list__update__swap) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 919 (all X_a all Xs all X all I_1 all J (I_1 != J -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),J) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),J))) # label(fact_844_nth__list__update__neq) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 920 (all X_a all Xs all I_1 hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_1)) = Xs) # label(fact_845_list__update__id) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 921 (all X_a all I_1 all Y hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),nil(X_a)),I_1),Y) = nil(X_a)) # label(fact_846_list__update__code_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 922 (all X_a all I_1 all V_1 hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),nil(X_a)),I_1),V_1) = nil(X_a)) # label(fact_847_list__update_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 923 (all X_a all Xs_1 all K_1 all X_1 (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs_1),K_1),X_1) = nil(X_a) <-> Xs_1 = nil(X_a))) # label(fact_848_list__update__nonempty) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 924 (all X_a all Xs all I_1 all X hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)) = hAPP(list(X_a),nat,size_size(list(X_a)),Xs)) # label(fact_849_length__list__update) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 925 (all X_a all X all Xs all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),I_1)) -> hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X) = Xs)) # label(fact_850_list__update__beyond) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 926 (all X_a all I all X_1 all Xs_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs_1),I),X_1))),A_1))))) # label(fact_851_set__update__subsetI) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 927 (all X_a all X all Xs all I_1 all Y hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),hAPP(nat,nat,suc,I_1)),Y) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),Y))) # label(fact_852_list__update__code_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 928 (all X_a all X all Xs all Y hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),zero_zero(nat)),Y) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Xs)) # label(fact_853_list__update__code_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 929 (all X_a all X_1 all N all Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs_1),N),X_1)))))) # label(fact_854_set__update__memI) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 930 (all X_a all Ys_1 all X all I_1 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)),I_1),X) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),Ys_1))) # label(fact_855_list__update__append1) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 931 (all X_a all Xs all X all Ys_1 all Y hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Ys_1))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),Y) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Ys_1))) # label(fact_856_list__update__length) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 932 (all X_a all X all J all I_1 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> (I_1 = J -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),J) = ti(X_a,X)) & (I_1 != J -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),J) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),J)))) # label(fact_857_nth__list__update) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 933 (all X_a all X_1 all I all Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs_1),I),X_1) = Xs_1 <-> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I) = ti(X_a,X_1)))) # label(fact_858_list__update__same__conv) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 934 (all X_a all X all I_1 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),I_1) = ti(X_a,X))) # label(fact_859_nth__list__update__eq) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 935 (all X_a all X_1 all Xs_1 all I all V hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),I),V) = hAPP(nat,list(X_a),hAPP(fun(nat,list(X_a)),fun(nat,list(X_a)),hAPP(list(X_a),fun(fun(nat,list(X_a)),fun(nat,list(X_a))),nat_case(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),V),Xs_1)),hAPP(fun(nat,list(X_a)),fun(nat,list(X_a)),hAPP(fun(list(X_a),list(X_a)),fun(fun(nat,list(X_a)),fun(nat,list(X_a))),combb(list(X_a),list(X_a),nat),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1)),hAPP(X_a,fun(nat,list(X_a)),hAPP(fun(nat,fun(X_a,list(X_a))),fun(X_a,fun(nat,list(X_a))),combc(nat,X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs_1)),V))),I)) # label(fact_860_list__update_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 936 (all X_a all Ys_1 all X all N_1 all Xs ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)),N_1),X) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),N_1),X)),Ys_1)) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)),N_1),X) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Ys_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))),X))))) # label(fact_861_list__update__append) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 937 (all X_a all X_b all Xs_1 all Xss hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,suc,hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))),hAPP(nat,nat,hAPP(list(list(X_b)),fun(nat,nat),hAPP(fun(list(X_b),fun(nat,nat)),fun(list(list(X_b)),fun(nat,nat)),foldr(list(X_b),nat),hAPP(fun(list(X_b),nat),fun(list(X_b),fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(list(X_b),nat),fun(list(X_b),fun(nat,nat))),combb(nat,fun(nat,nat),list(X_b)),ord_max(nat)),size_size(list(X_b)))),Xss),zero_zero(nat))) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)),hAPP(nat,nat,hAPP(list(list(X_b)),fun(nat,nat),hAPP(fun(list(X_b),fun(nat,nat)),fun(list(list(X_b)),fun(nat,nat)),foldr(list(X_b),nat),hAPP(fun(list(X_b),nat),fun(list(X_b),fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(list(X_b),nat),fun(list(X_b),fun(nat,nat))),combb(nat,fun(nat,nat),list(X_b)),ord_max(nat)),hAPP(nat,fun(list(X_b),nat),hAPP(fun(list(X_b),fun(nat,nat)),fun(nat,fun(list(X_b),nat)),combc(list(X_b),nat,nat),hAPP(fun(list(X_b),nat),fun(list(X_b),fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(list(X_b),nat),fun(list(X_b),fun(nat,nat))),combb(nat,fun(nat,nat),list(X_b)),minus_minus(nat)),size_size(list(X_b)))),hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(list(list(X_b)),list(list(X_b)),hAPP(fun(list(X_b),bool),fun(list(list(X_b)),list(list(X_b))),filter(list(X_b)),hAPP(fun(list(X_b),bool),fun(list(X_b),bool),hAPP(fun(bool,bool),fun(fun(list(X_b),bool),fun(list(X_b),bool)),combb(bool,bool,list(X_b)),fNot),hAPP(list(X_b),fun(list(X_b),bool),hAPP(fun(list(X_b),fun(list(X_b),bool)),fun(list(X_b),fun(list(X_b),bool)),combc(list(X_b),list(X_b),bool),fequal(list(X_b))),nil(X_b)))),Xss)),zero_zero(nat))))) # label(fact_862_transpose__aux__max) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 938 (all X_a all Xs_1 all I_3 hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),Xs_1),I_3)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,fun(nat,bool)),fun(X_a,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(X_a,fun(nat,bool)),fun(X_a,bool)),combb(fun(nat,bool),bool,X_a),fEx(nat)),hAPP(fun(nat,bool),fun(X_a,fun(nat,bool)),hAPP(fun(X_a,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(X_a,fun(nat,bool))),combc(X_a,fun(nat,bool),fun(nat,bool)),hAPP(fun(X_a,fun(nat,fun(bool,bool))),fun(X_a,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(X_a,fun(nat,fun(bool,bool))),fun(X_a,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),X_a),combs(nat,bool,bool)),hAPP(fun(X_a,fun(nat,bool)),fun(X_a,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(X_a,fun(nat,bool)),fun(X_a,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),X_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),hAPP(fun(nat,X_a),fun(X_a,fun(nat,bool)),hAPP(fun(X_a,fun(fun(nat,X_a),fun(nat,bool))),fun(fun(nat,X_a),fun(X_a,fun(nat,bool))),combc(X_a,fun(nat,X_a),fun(nat,bool)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(nat,X_a),fun(nat,bool))),hAPP(fun(fun(X_a,bool),fun(fun(nat,X_a),fun(nat,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(nat,X_a),fun(nat,bool)))),combb(fun(X_a,bool),fun(fun(nat,X_a),fun(nat,bool)),X_a),combb(X_a,bool,nat)),fequal(X_a))),hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1))))),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),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),I_3)))))) # label(fact_863_set__sublist) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 939 (all X_a all X_1 all Xs_1 hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),hAPP(X_a,fun(X_a,bool),fequal(X_a),X_1)),Xs_1))),X_1) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),hAPP(X_a,fun(X_a,bool),fequal(X_a),X_1)),Xs_1)) # label(fact_864_replicate__length__filter) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 940 (all X_a all P_1 all Xs_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Xs_1))),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)))) # label(fact_865_filter__is__subset) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 941 (all X_a all P_1 all Xs_1 (hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Xs_1) = nil(X_a) <-> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> -hBOOL(hAPP(X_a,bool,P_1,X_2)))))) # label(fact_866_filter__empty__conv) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 942 (all X_a all P_1 all Xs_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Xs_1))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))) # label(fact_867_length__filter__le) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 943 (all X_a all N all P_1 all X_1 ((hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X_1)) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X_1)) & (-hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X_1)) = nil(X_a)))) # label(fact_868_filter__replicate) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 944 (all X_a all Q_1 all X_1 all Xs_1 hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),Q_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),X_1),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),X_1),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),Q_1),Xs_1))) # label(fact_869_filter__remove1) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 945 (all X_a all Xs_1 all P_1 all X_1 (-hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),X_1),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Xs_1))) # label(fact_870_remove1__filter__not) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 946 (all X_a all X_b (linorder(X_b) -> (all F all Xs_1 all P_1 all X_1 (-hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),hAPP(fun(X_a,X_b),fun(X_a,fun(list(X_a),list(X_a))),linorder_insort_key(X_a,X_b),F),X_1),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Xs_1))))) # label(fact_871_filter__insort__triv) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 947 (all X_a all P_1 all Xs_1 all Ys hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Ys))) # label(fact_872_filter__append) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 948 (all X_a all P_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Xs_1))))) # label(fact_873_distinct__filter) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 949 (all X_a all P_1 all Q_1 all Xs_1 hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),Q_1),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),Q_1)),P_1)),Xs_1)) # label(fact_874_filter__filter) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 950 (all X_a all P_1 all Xs_1 hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Xs_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)))),P_1))) # label(fact_875_set__filter) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 951 (all X_a all P_1 all Xs_1 (hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Xs_1) = Xs_1 <-> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,P_1,X_2)))))) # label(fact_876_filter__id__conv) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 952 (all X_a all P_1 hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),nil(X_a)) = nil(X_a)) # label(fact_877_filter_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 953 (all X_a all Xs_1 all P_1 all X_1 ((hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Xs_1))) & (-hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Xs_1)))) # label(fact_878_filter_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 954 (all X_a all P_1 all Xs_1 hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1))) # label(fact_879_rev__filter) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 955 (all X_a (linorder(X_a) -> (all G all Xs_1 hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),hAPP(list(X_a),X_a,G,Xs_1))),Xs_1)))))) # label(fact_880_sorted__same) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 956 (all X_a all X_b (linorder(X_b) -> (all P_1 all F all Xs_1 hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,X_b),fun(list(X_a),list(X_a)),linorder_sort_key(X_a,X_b),F),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,X_b),fun(list(X_a),list(X_a)),linorder_sort_key(X_a,X_b),F),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Xs_1))))) # label(fact_881_filter__sort) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 957 (all X_a all P_1 all Xs_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Xs_1))),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),P_1)),Xs_1))) = hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)) # label(fact_882_sum__length__filter__compl) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 958 (all X_a all P_1 all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (-hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Xs_1))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))))) # label(fact_883_length__filter__less) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 959 (all X_a all S all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),Xs_1),S)))),Xs_1) = hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),Xs_1),S))) # label(fact_884_filter__in__sublist) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 960 (all X_a all Xs_1 hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,fun(nat,bool)),fun(X_a,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(X_a,fun(nat,bool)),fun(X_a,bool)),combb(fun(nat,bool),bool,X_a),fEx(nat)),hAPP(fun(nat,bool),fun(X_a,fun(nat,bool)),hAPP(fun(X_a,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(X_a,fun(nat,bool))),combc(X_a,fun(nat,bool),fun(nat,bool)),hAPP(fun(X_a,fun(nat,fun(bool,bool))),fun(X_a,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(X_a,fun(nat,fun(bool,bool))),fun(X_a,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),X_a),combs(nat,bool,bool)),hAPP(fun(X_a,fun(nat,bool)),fun(X_a,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(X_a,fun(nat,bool)),fun(X_a,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),X_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),hAPP(fun(nat,X_a),fun(X_a,fun(nat,bool)),hAPP(fun(X_a,fun(fun(nat,X_a),fun(nat,bool))),fun(fun(nat,X_a),fun(X_a,fun(nat,bool))),combc(X_a,fun(nat,X_a),fun(nat,bool)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(nat,X_a),fun(nat,bool))),hAPP(fun(fun(X_a,bool),fun(fun(nat,X_a),fun(nat,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(nat,X_a),fun(nat,bool)))),combb(fun(X_a,bool),fun(fun(nat,X_a),fun(nat,bool)),X_a),combb(X_a,bool,nat)),fequal(X_a))),hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1))))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))))) # label(fact_885_set__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 961 (all X_a all P_1 all Xs_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1)))) -> -hBOOL(hAPP(X_a,bool,P_1,X_2)))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Xs_1))) # label(fact_886_takeWhile__eq__filter) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 962 (all X_a all P_1 all Ys all X_1 all Xs_1 (hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Ys) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1) <-> (exists Us exists Vs (Ys = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Vs)) & (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Us))) -> -hBOOL(hAPP(X_a,bool,P_1,X_2)))) & hBOOL(hAPP(X_a,bool,P_1,X_1)) & Xs_1 = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Vs))))) # label(fact_887_filter__eq__Cons__iff) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 963 (all X_a all X_1 all Xs_1 all P_1 all Ys (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Ys) <-> (exists Us exists Vs (Ys = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Vs)) & (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Us))) -> -hBOOL(hAPP(X_a,bool,P_1,X_2)))) & hBOOL(hAPP(X_a,bool,P_1,X_1)) & Xs_1 = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Vs))))) # label(fact_888_Cons__eq__filter__iff) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 964 (all X_a all P_1 all Xs_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> -hBOOL(hAPP(X_a,bool,P_1,X_2)))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Xs_1) = nil(X_a))) # label(fact_889_filter__False) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 965 (all X_a all Xs_1 hAPP(nat,nat,hAPP(list(list(X_a)),fun(nat,nat),hAPP(fun(list(X_a),fun(nat,nat)),fun(list(list(X_a)),fun(nat,nat)),foldr(list(X_a),nat),hAPP(fun(list(X_a),nat),fun(list(X_a),fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(list(X_a),nat),fun(list(X_a),fun(nat,nat))),combb(nat,fun(nat,nat),list(X_a)),ord_max(nat)),size_size(list(X_a)))),hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),Xs_1)),zero_zero(nat)) = hAPP(list(list(X_a)),nat,size_size(list(list(X_a))),hAPP(list(list(X_a)),list(list(X_a)),hAPP(fun(list(X_a),bool),fun(list(list(X_a)),list(list(X_a))),filter(list(X_a)),hAPP(fun(list(X_a),bool),fun(list(X_a),bool),hAPP(fun(bool,bool),fun(fun(list(X_a),bool),fun(list(X_a),bool)),combb(bool,bool,list(X_a)),fNot),hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(list(X_a),fun(list(X_a),bool)),fun(list(X_a),fun(list(X_a),bool)),combc(list(X_a),list(X_a),bool),fequal(list(X_a))),nil(X_a)))),Xs_1))) # label(fact_890_transpose__max__length) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 966 (all X_a all P_1 all Xs_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,P_1,X_2)))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Xs_1) = Xs_1)) # label(fact_891_filter__True) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 967 (all X_a all Xss_1 hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),hAPP(list(list(X_a)),list(list(X_a)),hAPP(list(X_a),fun(list(list(X_a)),list(list(X_a))),cons(list(X_a)),nil(X_a)),Xss_1)) = hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),Xss_1)) # label(fact_892_transpose_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 968 (all X_a all Xs_1 (hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),Xs_1) = nil(list(X_a)) <-> (all X_2 (hBOOL(hAPP(fun(list(X_a),bool),bool,hAPP(list(X_a),fun(fun(list(X_a),bool),bool),member(list(X_a)),X_2),hAPP(list(list(X_a)),fun(list(X_a),bool),set(list(X_a)),Xs_1))) -> X_2 = nil(X_a))))) # label(fact_893_transpose__empty) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 969 (all X_a hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),nil(list(X_a))) = nil(list(X_a))) # label(fact_894_transpose_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 970 (all X_a all Xs_1 hAPP(list(list(X_a)),nat,size_size(list(list(X_a))),hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),Xs_1)) = hAPP(nat,nat,hAPP(list(list(X_a)),fun(nat,nat),hAPP(fun(list(X_a),fun(nat,nat)),fun(list(list(X_a)),fun(nat,nat)),foldr(list(X_a),nat),hAPP(fun(list(X_a),nat),fun(list(X_a),fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(list(X_a),nat),fun(list(X_a),fun(nat,nat))),combb(nat,fun(nat,nat),list(X_a)),ord_max(nat)),size_size(list(X_a)))),Xs_1),zero_zero(nat))) # label(fact_895_length__transpose) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 971 (all X_a all Q_1 all P_1 all Xs_1 all Ys (Xs_1 = Ys -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys))) -> (hBOOL(hAPP(X_a,bool,P_1,X_2)) <-> hBOOL(hAPP(X_a,bool,Q_1,X_2))))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),Q_1),Ys)))) # label(fact_896_filter__cong) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 972 (all X_a all X_1 all Xs_1 all P_1 all Ys (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Ys) -> (exists Us exists Vs (Ys = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Vs)) & (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Us))) -> -hBOOL(hAPP(X_a,bool,P_1,X_2)))) & hBOOL(hAPP(X_a,bool,P_1,X_1)) & Xs_1 = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Vs))))) # label(fact_897_Cons__eq__filterD) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 973 (all X_a all P_1 all Ys all X_1 all Xs_1 (hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Ys) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1) -> (exists Us exists Vs (Ys = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Vs)) & (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Us))) -> -hBOOL(hAPP(X_a,bool,P_1,X_2)))) & hBOOL(hAPP(X_a,bool,P_1,X_1)) & Xs_1 = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_1),Vs))))) # label(fact_898_filter__eq__ConsD) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 974 (all X_a all A_1 all XS hAPP(fun(list(X_a),bool),fun(list(X_a),bool),hAPP(fun(X_a,bool),fun(fun(list(X_a),bool),fun(list(X_a),bool)),set_Cons(X_a),A_1),XS) = hAPP(fun(list(X_a),bool),fun(list(X_a),bool),collect(list(X_a)),hAPP(fun(list(X_a),fun(X_a,bool)),fun(list(X_a),bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(list(X_a),fun(X_a,bool)),fun(list(X_a),bool)),combb(fun(X_a,bool),bool,list(X_a)),fEx(X_a)),hAPP(fun(list(X_a),fun(X_a,fun(list(X_a),bool))),fun(list(X_a),fun(X_a,bool)),hAPP(fun(fun(X_a,fun(list(X_a),bool)),fun(X_a,bool)),fun(fun(list(X_a),fun(X_a,fun(list(X_a),bool))),fun(list(X_a),fun(X_a,bool))),combb(fun(X_a,fun(list(X_a),bool)),fun(X_a,bool),list(X_a)),hAPP(fun(fun(list(X_a),bool),bool),fun(fun(X_a,fun(list(X_a),bool)),fun(X_a,bool)),combb(fun(list(X_a),bool),bool,X_a),fEx(list(X_a)))),hAPP(fun(X_a,fun(list(X_a),bool)),fun(list(X_a),fun(X_a,fun(list(X_a),bool))),hAPP(fun(list(X_a),fun(fun(X_a,fun(list(X_a),bool)),fun(X_a,fun(list(X_a),bool)))),fun(fun(X_a,fun(list(X_a),bool)),fun(list(X_a),fun(X_a,fun(list(X_a),bool)))),combc(list(X_a),fun(X_a,fun(list(X_a),bool)),fun(X_a,fun(list(X_a),bool))),hAPP(fun(list(X_a),fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool)))),fun(list(X_a),fun(fun(X_a,fun(list(X_a),bool)),fun(X_a,fun(list(X_a),bool)))),hAPP(fun(fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool))),fun(fun(X_a,fun(list(X_a),bool)),fun(X_a,fun(list(X_a),bool)))),fun(fun(list(X_a),fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool)))),fun(list(X_a),fun(fun(X_a,fun(list(X_a),bool)),fun(X_a,fun(list(X_a),bool))))),combb(fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool))),fun(fun(X_a,fun(list(X_a),bool)),fun(X_a,fun(list(X_a),bool))),list(X_a)),combs(X_a,fun(list(X_a),bool),fun(list(X_a),bool))),hAPP(fun(list(X_a),fun(X_a,fun(list(X_a),fun(bool,bool)))),fun(list(X_a),fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool)))),hAPP(fun(fun(X_a,fun(list(X_a),fun(bool,bool))),fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool)))),fun(fun(list(X_a),fun(X_a,fun(list(X_a),fun(bool,bool)))),fun(list(X_a),fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool))))),combb(fun(X_a,fun(list(X_a),fun(bool,bool))),fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool))),list(X_a)),hAPP(fun(fun(list(X_a),fun(bool,bool)),fun(fun(list(X_a),bool),fun(list(X_a),bool))),fun(fun(X_a,fun(list(X_a),fun(bool,bool))),fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool)))),combb(fun(list(X_a),fun(bool,bool)),fun(fun(list(X_a),bool),fun(list(X_a),bool)),X_a),combs(list(X_a),bool,bool))),hAPP(fun(list(X_a),fun(X_a,fun(list(X_a),bool))),fun(list(X_a),fun(X_a,fun(list(X_a),fun(bool,bool)))),hAPP(fun(fun(X_a,fun(list(X_a),bool)),fun(X_a,fun(list(X_a),fun(bool,bool)))),fun(fun(list(X_a),fun(X_a,fun(list(X_a),bool))),fun(list(X_a),fun(X_a,fun(list(X_a),fun(bool,bool))))),combb(fun(X_a,fun(list(X_a),bool)),fun(X_a,fun(list(X_a),fun(bool,bool))),list(X_a)),hAPP(fun(fun(list(X_a),bool),fun(list(X_a),fun(bool,bool))),fun(fun(X_a,fun(list(X_a),bool)),fun(X_a,fun(list(X_a),fun(bool,bool)))),combb(fun(list(X_a),bool),fun(list(X_a),fun(bool,bool)),X_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(list(X_a),bool),fun(list(X_a),fun(bool,bool))),combb(bool,fun(bool,bool),list(X_a)),fconj))),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),fun(X_a,fun(list(X_a),bool))),hAPP(fun(list(X_a),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(X_a,fun(list(X_a),bool)))),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),fun(X_a,fun(list(X_a),bool)))),combc(list(X_a),fun(X_a,fun(list(X_a),list(X_a))),fun(X_a,fun(list(X_a),bool))),hAPP(fun(list(X_a),fun(fun(list(X_a),list(X_a)),fun(list(X_a),bool))),fun(list(X_a),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(X_a,fun(list(X_a),bool)))),hAPP(fun(fun(fun(list(X_a),list(X_a)),fun(list(X_a),bool)),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(X_a,fun(list(X_a),bool)))),fun(fun(list(X_a),fun(fun(list(X_a),list(X_a)),fun(list(X_a),bool))),fun(list(X_a),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(X_a,fun(list(X_a),bool))))),combb(fun(fun(list(X_a),list(X_a)),fun(list(X_a),bool)),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(X_a,fun(list(X_a),bool))),list(X_a)),combb(fun(list(X_a),list(X_a)),fun(list(X_a),bool),X_a)),hAPP(fun(list(X_a),fun(list(X_a),bool)),fun(list(X_a),fun(fun(list(X_a),list(X_a)),fun(list(X_a),bool))),hAPP(fun(fun(list(X_a),bool),fun(fun(list(X_a),list(X_a)),fun(list(X_a),bool))),fun(fun(list(X_a),fun(list(X_a),bool)),fun(list(X_a),fun(fun(list(X_a),list(X_a)),fun(list(X_a),bool)))),combb(fun(list(X_a),bool),fun(fun(list(X_a),list(X_a)),fun(list(X_a),bool)),list(X_a)),combb(list(X_a),bool,list(X_a))),fequal(list(X_a))))),cons(X_a)))))),hAPP(fun(list(X_a),bool),fun(X_a,fun(list(X_a),bool)),hAPP(fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool))),fun(fun(list(X_a),bool),fun(X_a,fun(list(X_a),bool))),combc(X_a,fun(list(X_a),bool),fun(list(X_a),bool)),hAPP(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool))),hAPP(fun(fun(bool,bool),fun(fun(list(X_a),bool),fun(list(X_a),bool))),fun(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool)))),combb(fun(bool,bool),fun(fun(list(X_a),bool),fun(list(X_a),bool)),X_a),combb(bool,bool,list(X_a))),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1)))),hAPP(fun(list(X_a),bool),fun(list(X_a),bool),hAPP(fun(list(X_a),fun(fun(list(X_a),bool),bool)),fun(fun(list(X_a),bool),fun(list(X_a),bool)),combc(list(X_a),fun(list(X_a),bool),bool),member(list(X_a))),XS))))))) # label(fact_899_set__Cons__def) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 975 (all X_a all J_1 all I all Xs_1 (hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),rev(nat),hAPP(list(list(X_a)),list(nat),hAPP(fun(list(X_a),nat),fun(list(list(X_a)),list(nat)),map(list(X_a),nat),size_size(list(X_a))),Xs_1)))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(list(list(X_a)),nat,size_size(list(list(X_a))),hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),Xs_1)))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),hAPP(list(list(X_a)),nat,size_size(list(list(X_a))),hAPP(list(list(X_a)),list(list(X_a)),hAPP(fun(list(X_a),bool),fun(list(list(X_a)),list(list(X_a))),filter(list(X_a)),hAPP(fun(list(X_a),nat),fun(list(X_a),bool),hAPP(fun(nat,bool),fun(fun(list(X_a),nat),fun(list(X_a),bool)),combb(nat,bool,list(X_a)),hAPP(nat,fun(nat,bool),ord_less(nat),I)),size_size(list(X_a)))),Xs_1)))) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(nat,list(X_a),hAPP(list(list(X_a)),fun(nat,list(X_a)),nth(list(X_a)),hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),Xs_1)),I)),J_1) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(nat,list(X_a),hAPP(list(list(X_a)),fun(nat,list(X_a)),nth(list(X_a)),Xs_1),J_1)),I))))) # label(fact_900_nth__nth__transpose__sorted) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 976 (all X_a all I all Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(list(list(X_a)),nat,size_size(list(list(X_a))),hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),Xs_1)))) -> hAPP(nat,list(X_a),hAPP(list(list(X_a)),fun(nat,list(X_a)),nth(list(X_a)),hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),Xs_1)),I) = hAPP(list(list(X_a)),list(X_a),hAPP(fun(list(X_a),X_a),fun(list(list(X_a)),list(X_a)),map(list(X_a),X_a),hAPP(nat,fun(list(X_a),X_a),hAPP(fun(list(X_a),fun(nat,X_a)),fun(nat,fun(list(X_a),X_a)),combc(list(X_a),nat,X_a),nth(X_a)),I)),hAPP(list(list(X_a)),list(list(X_a)),hAPP(fun(list(X_a),bool),fun(list(list(X_a)),list(list(X_a))),filter(list(X_a)),hAPP(fun(list(X_a),nat),fun(list(X_a),bool),hAPP(fun(nat,bool),fun(fun(list(X_a),nat),fun(list(X_a),bool)),combb(nat,bool,list(X_a)),hAPP(nat,fun(nat,bool),ord_less(nat),I)),size_size(list(X_a)))),Xs_1)))) # label(fact_901_nth__transpose) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 977 (all X_b all X_a all F all N all Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> hAPP(nat,X_b,hAPP(list(X_b),fun(nat,X_b),nth(X_b),hAPP(list(X_a),list(X_b),hAPP(fun(X_a,X_b),fun(list(X_a),list(X_b)),map(X_a,X_b),F),Xs_1)),N) = hAPP(X_a,X_b,F,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),N)))) # label(fact_902_nth__map) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 978 (all X_a all X_b all F all Xs_1 hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),hAPP(list(list(X_b)),list(list(X_a)),hAPP(fun(list(X_b),list(X_a)),fun(list(list(X_b)),list(list(X_a))),map(list(X_b),list(X_a)),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F)),Xs_1)) = hAPP(list(list(X_b)),list(list(X_a)),hAPP(fun(list(X_b),list(X_a)),fun(list(list(X_b)),list(list(X_a))),map(list(X_b),list(X_a)),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F)),hAPP(list(list(X_b)),list(list(X_b)),transpose(X_b),Xs_1))) # label(fact_903_transpose__map__map) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 979 (all X_a all Xs_1 hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),rev(nat),hAPP(list(list(X_a)),list(nat),hAPP(fun(list(X_a),nat),fun(list(list(X_a)),list(nat)),map(list(X_a),nat),size_size(list(X_a))),hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),Xs_1)))))) # label(fact_904_sorted__transpose) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 980 (all X_a all X_b all F all Xs_1 hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1)) = hAPP(list(X_b),nat,size_size(list(X_b)),Xs_1)) # label(fact_905_length__map) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 981 (all X_b all X_a all X_c all F all Xs_1 all G all Ys (hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1) = hAPP(list(X_c),list(X_a),hAPP(fun(X_c,X_a),fun(list(X_c),list(X_a)),map(X_c,X_a),G),Ys) -> hAPP(list(X_b),nat,size_size(list(X_b)),Xs_1) = hAPP(list(X_c),nat,size_size(list(X_c)),Ys))) # label(fact_906_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 982 (all X_b all X_a all K_1 all Lst hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),K_1)),Lst) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(list(X_b),nat,size_size(list(X_b)),Lst)),K_1)) # label(fact_907_map__replicate__const) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 983 (all X_b all X_a (linorder(X_a) -> (all P_1 all F all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1))) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(fun(X_b,bool),fun(list(X_b),list(X_b)),filter(X_b),P_1),Xs_1)))))))) # label(fact_908_sorted__filter) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 984 (all X_b all X_a (linorder(X_a) -> (all F all G all Xs_1 hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(fun(X_b,bool),fun(list(X_b),list(X_b)),filter(X_b),hAPP(X_a,fun(X_b,bool),hAPP(fun(X_b,fun(X_a,bool)),fun(X_a,fun(X_b,bool)),combc(X_b,X_a,bool),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,bool)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,bool))),combb(X_a,fun(X_a,bool),X_b),fequal(X_a)),F)),hAPP(list(X_b),X_a,G,Xs_1))),Xs_1))))))) # label(fact_909_sorted__map__same) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 985 (all X_b all X_a all F all Xs_1 all K_1 all Y_1 hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),hAPP(X_b,list(X_b),hAPP(nat,fun(X_b,list(X_b)),hAPP(list(X_b),fun(nat,fun(X_b,list(X_b))),list_update(X_b),Xs_1),K_1),Y_1)) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1)),K_1),hAPP(X_b,X_a,F,Y_1))) # label(fact_910_map__update) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 986 (all X_b all X_a (linorder(X_a) -> (all X_1 all F all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1))) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),remove1(X_b),X_1),Xs_1)))))))) # label(fact_911_sorted__map__remove1) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 987 (all X_b all X_a (linorder(X_a) -> (all F all X_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),hAPP(fun(X_b,X_a),fun(X_b,fun(list(X_b),list(X_b))),linorder_insort_key(X_b,X_a),F),X_1),Xs_1)))) <-> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1))))))) # label(fact_912_sorted__insort__key) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 988 (all X_b all X_a (linorder(X_a) -> (all F all Xs_1 hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_b)),linorder_sort_key(X_b,X_a),F),Xs_1))))))) # label(fact_913_sorted__sort__key) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 989 (all X_b all X_a (linorder(X_a) -> (all X_1 all F all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1))) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),hAPP(fun(X_b,X_a),fun(X_b,fun(list(X_b),list(X_b))),linord2118332866rt_key(X_b,X_a),F),X_1),Xs_1)))))))) # label(fact_914_sorted__insort__insert__key) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 990 (all X_b all X_a all F all Xs_1 hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),hAPP(list(X_b),list(X_b),butlast(X_b),Xs_1)) = hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1))) # label(fact_915_map__butlast) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 991 (all X_b all X_a all F all Xs_1 hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),hAPP(list(X_b),list(X_b),tl(X_b),Xs_1)) = hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1))) # label(fact_916_map__tl) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 992 (all X_a all X_2 hAPP(list(X_a),list(X_a),hAPP(fun(X_a,X_a),fun(list(X_a),list(X_a)),map(X_a,X_a),combi(X_a)),X_2) = X_2) # label(fact_917_map__ident) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.26 993 (all X_b all X_a all F all N all X_1 hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),hAPP(X_b,list(X_b),hAPP(nat,fun(X_b,list(X_b)),replicate(X_b),N),X_1)) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),hAPP(X_b,X_a,F,X_1))) # label(fact_918_map__replicate) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 994 (all X_a all X_b all F all Xs_1 hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1)) = hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),hAPP(list(X_b),list(X_b),rev(X_b),Xs_1))) # label(fact_919_rev__map) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 995 (all X_a all X_b all N all F all Xs_1 hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1)) = hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(nat,fun(list(X_b),list(X_b)),take(X_b),N),Xs_1))) # label(fact_920_take__map) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 996 (all X_b all X_a all F all Xs_1 all Ys hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(list(X_b),fun(list(X_b),list(X_b)),append(X_b),Xs_1),Ys)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1)),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Ys))) # label(fact_921_map__append) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 997 (all X_b all X_a all X_c all G all Aa all F all Xs_1 hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),G),Aa),hAPP(list(X_c),list(X_b),hAPP(fun(X_c,X_b),fun(list(X_c),list(X_b)),map(X_c,X_b),F),Xs_1)) = hAPP(list(X_c),X_a,hAPP(X_a,fun(list(X_c),X_a),hAPP(fun(X_a,fun(X_c,X_a)),fun(X_a,fun(list(X_c),X_a)),foldl(X_a,X_c),hAPP(fun(X_c,X_b),fun(X_a,fun(X_c,X_a)),hAPP(fun(X_a,fun(fun(X_c,X_b),fun(X_c,X_a))),fun(fun(X_c,X_b),fun(X_a,fun(X_c,X_a))),combc(X_a,fun(X_c,X_b),fun(X_c,X_a)),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(fun(X_c,X_b),fun(X_c,X_a))),hAPP(fun(fun(X_b,X_a),fun(fun(X_c,X_b),fun(X_c,X_a))),fun(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(fun(X_c,X_b),fun(X_c,X_a)))),combb(fun(X_b,X_a),fun(fun(X_c,X_b),fun(X_c,X_a)),X_a),combb(X_b,X_a,X_c)),G)),F)),Aa),Xs_1)) # label(fact_922_foldl__map) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 998 (all X_a all X_b all N all F all Xs_1 hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1)) = hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(nat,fun(list(X_b),list(X_b)),drop(X_b),N),Xs_1))) # label(fact_923_drop__map) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 999 (all X_b all X_a all F all X_1 all Xs_1 hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X_1),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(X_b,X_a,F,X_1)),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1))) # label(fact_924_map_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1000 (all X_b all X_a all F all Xs_1 (hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1) = nil(X_a) <-> Xs_1 = nil(X_b))) # label(fact_925_map__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1001 (all X_b all X_a all F hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),nil(X_b)) = nil(X_a)) # label(fact_926_map_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1002 (all X_a all X_b all F all Xs_1 (nil(X_a) = hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1) <-> Xs_1 = nil(X_b))) # label(fact_927_Nil__is__map__conv) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1003 (all X_b all X_a all F all Xs_1 all G (hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1) = hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),G),Xs_1) <-> (all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(list(X_b),fun(X_b,bool),set(X_b),Xs_1))) -> hAPP(X_b,X_a,F,X_2) = hAPP(X_b,X_a,G,X_2))))) # label(fact_928_map__eq__conv) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1004 (all X_b all X_a all F all Xs_1 (Xs_1 != nil(X_a) -> hAPP(list(X_b),X_b,hd(X_b),hAPP(list(X_a),list(X_b),hAPP(fun(X_a,X_b),fun(list(X_a),list(X_b)),map(X_a,X_b),F),Xs_1)) = hAPP(X_a,X_b,F,hAPP(list(X_a),X_a,hd(X_a),Xs_1)))) # label(fact_929_hd__map) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1005 (all X_b all X_a all F all Xs_1 (Xs_1 != nil(X_a) -> hAPP(list(X_b),X_b,last(X_b),hAPP(list(X_a),list(X_b),hAPP(fun(X_a,X_b),fun(list(X_a),list(X_b)),map(X_a,X_b),F),Xs_1)) = hAPP(X_a,X_b,F,hAPP(list(X_a),X_a,last(X_a),Xs_1)))) # label(fact_930_last__map) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1006 (all X_b all X_a (linorder(X_a) -> (all P_1 all X_1 all F all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1))) -> (hBOOL(hAPP(X_b,bool,P_1,X_1)) -> hAPP(list(X_b),list(X_b),hAPP(fun(X_b,bool),fun(list(X_b),list(X_b)),filter(X_b),P_1),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),hAPP(fun(X_b,X_a),fun(X_b,fun(list(X_b),list(X_b))),linorder_insort_key(X_b,X_a),F),X_1),Xs_1)) = hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),hAPP(fun(X_b,X_a),fun(X_b,fun(list(X_b),list(X_b))),linorder_insort_key(X_b,X_a),F),X_1),hAPP(list(X_b),list(X_b),hAPP(fun(X_b,bool),fun(list(X_b),list(X_b)),filter(X_b),P_1),Xs_1))))))) # label(fact_931_filter__insort) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1007 (all X_a all I all Xs_1 (hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),rev(nat),hAPP(list(list(X_a)),list(nat),hAPP(fun(list(X_a),nat),fun(list(list(X_a)),list(nat)),map(list(X_a),nat),size_size(list(X_a))),Xs_1)))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(list(list(X_a)),nat,size_size(list(list(X_a))),Xs_1))) -> hAPP(list(list(X_a)),list(X_a),hAPP(fun(list(X_a),X_a),fun(list(list(X_a)),list(X_a)),map(list(X_a),X_a),hAPP(nat,fun(list(X_a),X_a),hAPP(fun(list(X_a),fun(nat,X_a)),fun(nat,fun(list(X_a),X_a)),combc(list(X_a),nat,X_a),nth(X_a)),I)),hAPP(list(list(X_a)),list(list(X_a)),hAPP(fun(list(X_a),bool),fun(list(list(X_a)),list(list(X_a))),filter(list(X_a)),hAPP(fun(list(X_a),nat),fun(list(X_a),bool),hAPP(fun(nat,bool),fun(fun(list(X_a),nat),fun(list(X_a),bool)),combb(nat,bool,list(X_a)),hAPP(nat,fun(nat,bool),ord_less(nat),I)),size_size(list(X_a)))),hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),Xs_1))) = hAPP(nat,list(X_a),hAPP(list(list(X_a)),fun(nat,list(X_a)),nth(list(X_a)),Xs_1),I)))) # label(fact_932_transpose__column) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1008 (all X_a all Xs_1 (hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),rev(nat),hAPP(list(list(X_a)),list(nat),hAPP(fun(list(X_a),nat),fun(list(list(X_a)),list(nat)),map(list(X_a),nat),size_size(list(X_a))),Xs_1)))) -> hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),Xs_1)) = hAPP(list(list(X_a)),list(list(X_a)),hAPP(fun(list(X_a),bool),fun(list(list(X_a)),list(list(X_a))),takeWhile(list(X_a)),hAPP(fun(list(X_a),bool),fun(list(X_a),bool),hAPP(fun(bool,bool),fun(fun(list(X_a),bool),fun(list(X_a),bool)),combb(bool,bool,list(X_a)),fNot),hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(list(X_a),fun(list(X_a),bool)),fun(list(X_a),fun(list(X_a),bool)),combc(list(X_a),list(X_a),bool),fequal(list(X_a))),nil(X_a)))),Xs_1))) # label(fact_933_transpose__transpose) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1009 (all X_a all Xs_1 (hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),rev(nat),hAPP(list(list(X_a)),list(nat),hAPP(fun(list(X_a),nat),fun(list(list(X_a)),list(nat)),map(list(X_a),nat),size_size(list(X_a))),Xs_1)))) -> (Xs_1 = nil(list(X_a)) -> hAPP(list(list(X_a)),nat,size_size(list(list(X_a))),hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),Xs_1)) = zero_zero(nat)) & (Xs_1 != nil(list(X_a)) -> hAPP(list(list(X_a)),nat,size_size(list(list(X_a))),hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),Xs_1)) = hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(nat,list(X_a),hAPP(list(list(X_a)),fun(nat,list(X_a)),nth(list(X_a)),Xs_1),zero_zero(nat)))))) # label(fact_934_length__transpose__sorted) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1010 (all X_b all X_a (linorder(X_a) -> (all T_3 all F all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1)))) -> hAPP(list(X_b),list(X_b),hAPP(fun(X_b,bool),fun(list(X_b),list(X_b)),filter(X_b),hAPP(fun(X_b,X_a),fun(X_b,bool),hAPP(fun(X_a,bool),fun(fun(X_b,X_a),fun(X_b,bool)),combb(X_a,bool,X_b),hAPP(X_a,fun(X_a,bool),ord_less(X_a),T_3)),F)),Xs_1) = hAPP(list(X_b),list(X_b),hAPP(fun(X_b,bool),fun(list(X_b),list(X_b)),takeWhile(X_b),hAPP(fun(X_b,X_a),fun(X_b,bool),hAPP(fun(X_a,bool),fun(fun(X_b,X_a),fun(X_b,bool)),combb(X_a,bool,X_b),hAPP(X_a,fun(X_a,bool),ord_less(X_a),T_3)),F)),Xs_1))))) # label(fact_935_filter__equals__takeWhile__sorted__rev) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1011 (all X_a all I all Xs_1 (hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),rev(nat),hAPP(list(list(X_a)),list(nat),hAPP(fun(list(X_a),nat),fun(list(list(X_a)),list(nat)),map(list(X_a),nat),size_size(list(X_a))),Xs_1)))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(list(list(X_a)),nat,size_size(list(list(X_a))),Xs_1))) -> hAPP(list(list(X_a)),nat,size_size(list(list(X_a))),hAPP(list(list(X_a)),list(list(X_a)),hAPP(fun(list(X_a),bool),fun(list(list(X_a)),list(list(X_a))),filter(list(X_a)),hAPP(fun(list(X_a),nat),fun(list(X_a),bool),hAPP(fun(nat,bool),fun(fun(list(X_a),nat),fun(list(X_a),bool)),combb(nat,bool,list(X_a)),hAPP(nat,fun(nat,bool),ord_less(nat),I)),size_size(list(X_a)))),hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),Xs_1))) = hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(nat,list(X_a),hAPP(list(list(X_a)),fun(nat,list(X_a)),nth(list(X_a)),Xs_1),I))))) # label(fact_936_transpose__column__length) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1012 (all X_a all X_b (linorder(X_b) -> (all F all Aa all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (hBOOL(hAPP(list(X_b),bool,linorder_sorted(X_b),hAPP(list(X_a),list(X_b),hAPP(fun(X_a,X_b),fun(list(X_a),list(X_b)),map(X_a,X_b),F),Xs_1))) -> (hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),hAPP(fun(X_a,X_b),fun(X_a,bool),hAPP(fun(X_b,bool),fun(fun(X_a,X_b),fun(X_a,bool)),combb(X_b,bool,X_a),hAPP(X_b,fun(X_b,bool),fequal(X_b),hAPP(X_a,X_b,F,Aa))),F)),Xs_1)) = ti(X_a,Aa) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),hAPP(fun(X_a,X_b),fun(X_a,fun(list(X_a),list(X_a))),linorder_insort_key(X_a,X_b),F),Aa),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),remove1(X_a),Aa),Xs_1)) = Xs_1)))))) # label(fact_937_insort__key__remove1) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1013 (all X_a all Xss hAPP(list(list(X_a)),list(X_a),concat(X_a),hAPP(list(list(X_a)),list(list(X_a)),hAPP(fun(list(X_a),list(X_a)),fun(list(list(X_a)),list(list(X_a))),map(list(X_a),list(X_a)),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),list(X_a)),hAPP(list(X_a),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),list(X_a))),list_case(list(X_a),X_a),nil(X_a)),hAPP(fun(X_a,list(X_a)),fun(X_a,fun(list(X_a),list(X_a))),hAPP(fun(list(X_a),fun(list(X_a),list(X_a))),fun(fun(X_a,list(X_a)),fun(X_a,fun(list(X_a),list(X_a)))),combb(list(X_a),fun(list(X_a),list(X_a)),X_a),combk(list(X_a),list(X_a))),hAPP(list(X_a),fun(X_a,list(X_a)),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),fun(X_a,list(X_a))),combc(X_a,list(X_a),list(X_a)),cons(X_a)),nil(X_a))))),Xss)) = hAPP(list(list(X_a)),list(X_a),hAPP(fun(list(X_a),X_a),fun(list(list(X_a)),list(X_a)),map(list(X_a),X_a),hd(X_a)),hAPP(list(list(X_a)),list(list(X_a)),hAPP(fun(list(X_a),bool),fun(list(list(X_a)),list(list(X_a))),filter(list(X_a)),hAPP(fun(list(X_a),bool),fun(list(X_a),bool),hAPP(fun(bool,bool),fun(fun(list(X_a),bool),fun(list(X_a),bool)),combb(bool,bool,list(X_a)),fNot),hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(list(X_a),fun(list(X_a),bool)),fun(list(X_a),fun(list(X_a),bool)),combc(list(X_a),list(X_a),bool),fequal(list(X_a))),nil(X_a)))),Xss))) # label(fact_938_transpose__aux__filter__head) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1014 (all X_a all X_b all Ys all F ((exists Xs_2 Ys = hAPP(list(X_a),list(X_b),hAPP(fun(X_a,X_b),fun(list(X_a),list(X_b)),map(X_a,X_b),F),Xs_2)) <-> (all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(list(X_b),fun(X_b,bool),set(X_b),Ys))) -> (exists Xa ti(X_b,X_2) = hAPP(X_a,X_b,F,Xa)))))) # label(fact_939_ex__map__conv) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1015 (all X_a all P_2 all Xs_1 hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_2),hAPP(list(list(X_a)),list(X_a),concat(X_a),Xs_1)) = hAPP(list(list(X_a)),list(X_a),concat(X_a),hAPP(list(list(X_a)),list(list(X_a)),hAPP(fun(list(X_a),list(X_a)),fun(list(list(X_a)),list(list(X_a))),map(list(X_a),list(X_a)),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),filter(X_a),P_2)),Xs_1))) # label(fact_940_filter__concat) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1016 (all X_b all X_a all F all Xs_1 hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),hAPP(list(list(X_b)),list(X_b),concat(X_b),Xs_1)) = hAPP(list(list(X_a)),list(X_a),concat(X_a),hAPP(list(list(X_b)),list(list(X_a)),hAPP(fun(list(X_b),list(X_a)),fun(list(list(X_b)),list(list(X_a))),map(list(X_b),list(X_a)),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F)),Xs_1))) # label(fact_941_map__concat) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1017 (all X_a all Xs_1 hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(list(X_a)),list(X_a),concat(X_a),Xs_1)) = hAPP(list(list(X_a)),list(X_a),concat(X_a),hAPP(list(list(X_a)),list(list(X_a)),hAPP(fun(list(X_a),list(X_a)),fun(list(list(X_a)),list(list(X_a))),map(list(X_a),list(X_a)),rev(X_a)),hAPP(list(list(X_a)),list(list(X_a)),rev(list(X_a)),Xs_1)))) # label(fact_942_rev__concat) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1018 (all X_a all X_b all F all Xs_1 hAPP(list(list(X_a)),list(X_a),concat(X_a),hAPP(list(X_b),list(list(X_a)),hAPP(fun(X_b,list(X_a)),fun(list(X_b),list(list(X_a))),map(X_b,list(X_a)),F),Xs_1)) = hAPP(list(X_b),list(X_a),hAPP(fun(X_b,list(X_a)),fun(list(X_b),list(X_a)),maps(X_b,X_a),F),Xs_1)) # label(fact_943_concat__map__maps) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1019 (all X_b all X_a all F all Xs_1 hAPP(list(X_b),list(X_a),hAPP(fun(X_b,list(X_a)),fun(list(X_b),list(X_a)),maps(X_b,X_a),F),Xs_1) = hAPP(list(list(X_a)),list(X_a),concat(X_a),hAPP(list(X_b),list(list(X_a)),hAPP(fun(X_b,list(X_a)),fun(list(X_b),list(list(X_a))),map(X_b,list(X_a)),F),Xs_1))) # label(fact_944_maps__def) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1020 (all X_a all Xss hAPP(list(list(X_a)),list(X_a),concat(X_a),Xss) = hAPP(list(list(X_a)),list(X_a),hAPP(list(X_a),fun(list(list(X_a)),list(X_a)),hAPP(fun(list(X_a),fun(list(X_a),list(X_a))),fun(list(X_a),fun(list(list(X_a)),list(X_a))),foldl(list(X_a),list(X_a)),append(X_a)),nil(X_a)),Xss)) # label(fact_945_concat__conv__foldl) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1021 (all X_a all X all Xs hAPP(list(list(X_a)),list(X_a),concat(X_a),hAPP(list(list(X_a)),list(list(X_a)),hAPP(list(X_a),fun(list(list(X_a)),list(list(X_a))),cons(list(X_a)),X),Xs)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),X),hAPP(list(list(X_a)),list(X_a),concat(X_a),Xs))) # label(fact_946_concat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1022 (all X_a all Xss (nil(X_a) = hAPP(list(list(X_a)),list(X_a),concat(X_a),Xss) <-> (all X_2 (hBOOL(hAPP(fun(list(X_a),bool),bool,hAPP(list(X_a),fun(fun(list(X_a),bool),bool),member(list(X_a)),X_2),hAPP(list(list(X_a)),fun(list(X_a),bool),set(list(X_a)),Xss))) -> X_2 = nil(X_a))))) # label(fact_947_Nil__eq__concat__conv) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1023 (all X_a all Xss (hAPP(list(list(X_a)),list(X_a),concat(X_a),Xss) = nil(X_a) <-> (all X_2 (hBOOL(hAPP(fun(list(X_a),bool),bool,hAPP(list(X_a),fun(fun(list(X_a),bool),bool),member(list(X_a)),X_2),hAPP(list(list(X_a)),fun(list(X_a),bool),set(list(X_a)),Xss))) -> X_2 = nil(X_a))))) # label(fact_948_concat__eq__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1024 (all X_a hAPP(list(list(X_a)),list(X_a),concat(X_a),nil(list(X_a))) = nil(X_a)) # label(fact_949_concat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1025 (all X_a all I_1 hAPP(list(list(X_a)),list(X_a),concat(X_a),hAPP(list(X_a),list(list(X_a)),hAPP(nat,fun(list(X_a),list(list(X_a))),replicate(list(X_a)),I_1),nil(X_a))) = nil(X_a)) # label(fact_950_concat__replicate__trivial) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1026 (all X_a all Xs_1 all Xss hAPP(list(list(X_a)),list(X_a),hAPP(list(X_a),fun(list(list(X_a)),list(X_a)),hAPP(fun(list(X_a),fun(list(X_a),list(X_a))),fun(list(X_a),fun(list(list(X_a)),list(X_a))),foldl(list(X_a),list(X_a)),append(X_a)),Xs_1),Xss) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(list(X_a)),list(X_a),concat(X_a),Xss))) # label(fact_951_foldl__conv__concat) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1027 (all X_a all Xs all Ys_1 hAPP(list(list(X_a)),list(X_a),concat(X_a),hAPP(list(list(X_a)),list(list(X_a)),hAPP(list(list(X_a)),fun(list(list(X_a)),list(list(X_a))),append(list(X_a)),Xs),Ys_1)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(list(X_a)),list(X_a),concat(X_a),Xs)),hAPP(list(list(X_a)),list(X_a),concat(X_a),Ys_1))) # label(fact_952_concat__append) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1028 (all X_a all X_b all F all Xs_1 hAPP(list(list(X_a)),list(X_a),concat(X_a),hAPP(list(X_b),list(list(X_a)),hAPP(fun(X_b,list(X_a)),fun(list(X_b),list(list(X_a))),map(X_b,list(X_a)),hAPP(list(X_a),fun(X_b,list(X_a)),hAPP(fun(X_b,fun(list(X_a),list(X_a))),fun(list(X_a),fun(X_b,list(X_a))),combc(X_b,list(X_a),list(X_a)),hAPP(fun(X_b,X_a),fun(X_b,fun(list(X_a),list(X_a))),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(fun(X_b,X_a),fun(X_b,fun(list(X_a),list(X_a)))),combb(X_a,fun(list(X_a),list(X_a)),X_b),cons(X_a)),F)),nil(X_a))),Xs_1)) = hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1)) # label(fact_953_concat__map__singleton) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1029 (all X_a all X_1 all Xs_1 all Xss hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),hAPP(list(list(X_a)),list(list(X_a)),hAPP(list(X_a),fun(list(list(X_a)),list(list(X_a))),cons(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),Xss)) = hAPP(list(list(X_a)),list(list(X_a)),hAPP(list(X_a),fun(list(list(X_a)),list(list(X_a))),cons(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),hAPP(list(list(X_a)),list(X_a),concat(X_a),hAPP(list(list(X_a)),list(list(X_a)),hAPP(fun(list(X_a),list(X_a)),fun(list(list(X_a)),list(list(X_a))),map(list(X_a),list(X_a)),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),list(X_a)),hAPP(list(X_a),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),list(X_a))),list_case(list(X_a),X_a),nil(X_a)),hAPP(fun(X_a,list(X_a)),fun(X_a,fun(list(X_a),list(X_a))),hAPP(fun(list(X_a),fun(list(X_a),list(X_a))),fun(fun(X_a,list(X_a)),fun(X_a,fun(list(X_a),list(X_a)))),combb(list(X_a),fun(list(X_a),list(X_a)),X_a),combk(list(X_a),list(X_a))),hAPP(list(X_a),fun(X_a,list(X_a)),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),fun(X_a,list(X_a))),combc(X_a,list(X_a),list(X_a)),cons(X_a)),nil(X_a))))),Xss)))),hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),hAPP(list(list(X_a)),list(list(X_a)),hAPP(list(X_a),fun(list(list(X_a)),list(list(X_a))),cons(list(X_a)),Xs_1),hAPP(list(list(list(X_a))),list(list(X_a)),concat(list(X_a)),hAPP(list(list(X_a)),list(list(list(X_a))),hAPP(fun(list(X_a),list(list(X_a))),fun(list(list(X_a)),list(list(list(X_a)))),map(list(X_a),list(list(X_a))),hAPP(fun(X_a,fun(list(X_a),list(list(X_a)))),fun(list(X_a),list(list(X_a))),hAPP(list(list(X_a)),fun(fun(X_a,fun(list(X_a),list(list(X_a)))),fun(list(X_a),list(list(X_a)))),list_case(list(list(X_a)),X_a),nil(list(X_a))),hAPP(fun(list(X_a),list(list(X_a))),fun(X_a,fun(list(X_a),list(list(X_a)))),combk(fun(list(X_a),list(list(X_a))),X_a),hAPP(list(list(X_a)),fun(list(X_a),list(list(X_a))),hAPP(fun(list(X_a),fun(list(list(X_a)),list(list(X_a)))),fun(list(list(X_a)),fun(list(X_a),list(list(X_a)))),combc(list(X_a),list(list(X_a)),list(list(X_a))),cons(list(X_a))),nil(list(X_a)))))),Xss)))))) # label(fact_954_transpose_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1030 (all X_a all Xss hAPP(list(list(list(X_a))),list(list(X_a)),concat(list(X_a)),hAPP(list(list(X_a)),list(list(list(X_a))),hAPP(fun(list(X_a),list(list(X_a))),fun(list(list(X_a)),list(list(list(X_a)))),map(list(X_a),list(list(X_a))),hAPP(fun(X_a,fun(list(X_a),list(list(X_a)))),fun(list(X_a),list(list(X_a))),hAPP(list(list(X_a)),fun(fun(X_a,fun(list(X_a),list(list(X_a)))),fun(list(X_a),list(list(X_a)))),list_case(list(list(X_a)),X_a),nil(list(X_a))),hAPP(fun(list(X_a),list(list(X_a))),fun(X_a,fun(list(X_a),list(list(X_a)))),combk(fun(list(X_a),list(list(X_a))),X_a),hAPP(list(list(X_a)),fun(list(X_a),list(list(X_a))),hAPP(fun(list(X_a),fun(list(list(X_a)),list(list(X_a)))),fun(list(list(X_a)),fun(list(X_a),list(list(X_a)))),combc(list(X_a),list(list(X_a)),list(list(X_a))),cons(list(X_a))),nil(list(X_a)))))),Xss)) = hAPP(list(list(X_a)),list(list(X_a)),hAPP(fun(list(X_a),list(X_a)),fun(list(list(X_a)),list(list(X_a))),map(list(X_a),list(X_a)),tl(X_a)),hAPP(list(list(X_a)),list(list(X_a)),hAPP(fun(list(X_a),bool),fun(list(list(X_a)),list(list(X_a))),filter(list(X_a)),hAPP(fun(list(X_a),bool),fun(list(X_a),bool),hAPP(fun(bool,bool),fun(fun(list(X_a),bool),fun(list(X_a),bool)),combb(bool,bool,list(X_a)),fNot),hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(list(X_a),fun(list(X_a),bool)),fun(list(X_a),fun(list(X_a),bool)),combc(list(X_a),list(X_a),bool),fequal(list(X_a))),nil(X_a)))),Xss))) # label(fact_955_transpose__aux__filter__tail) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1031 (all X_a all X_1 all Xs_1 all Xss (hBOOL(hAPP(list(list(X_a)),bool,hAPP(fun(list(list(X_a)),fun(list(list(X_a)),bool)),fun(list(list(X_a)),bool),accp(list(list(X_a))),transpose_rel(X_a)),hAPP(list(list(X_a)),list(list(X_a)),hAPP(list(X_a),fun(list(list(X_a)),list(list(X_a))),cons(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),Xss))) -> hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),hAPP(list(list(X_a)),list(list(X_a)),hAPP(list(X_a),fun(list(list(X_a)),list(list(X_a))),cons(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),Xss)) = hAPP(list(list(X_a)),list(list(X_a)),hAPP(list(X_a),fun(list(list(X_a)),list(list(X_a))),cons(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),hAPP(list(list(X_a)),list(X_a),concat(X_a),hAPP(list(list(X_a)),list(list(X_a)),hAPP(fun(list(X_a),list(X_a)),fun(list(list(X_a)),list(list(X_a))),map(list(X_a),list(X_a)),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),list(X_a)),hAPP(list(X_a),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),list(X_a))),list_case(list(X_a),X_a),nil(X_a)),hAPP(fun(X_a,list(X_a)),fun(X_a,fun(list(X_a),list(X_a))),hAPP(fun(list(X_a),fun(list(X_a),list(X_a))),fun(fun(X_a,list(X_a)),fun(X_a,fun(list(X_a),list(X_a)))),combb(list(X_a),fun(list(X_a),list(X_a)),X_a),combk(list(X_a),list(X_a))),hAPP(list(X_a),fun(X_a,list(X_a)),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),fun(X_a,list(X_a))),combc(X_a,list(X_a),list(X_a)),cons(X_a)),nil(X_a))))),Xss)))),hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),hAPP(list(list(X_a)),list(list(X_a)),hAPP(list(X_a),fun(list(list(X_a)),list(list(X_a))),cons(list(X_a)),Xs_1),hAPP(list(list(list(X_a))),list(list(X_a)),concat(list(X_a)),hAPP(list(list(X_a)),list(list(list(X_a))),hAPP(fun(list(X_a),list(list(X_a))),fun(list(list(X_a)),list(list(list(X_a)))),map(list(X_a),list(list(X_a))),hAPP(fun(X_a,fun(list(X_a),list(list(X_a)))),fun(list(X_a),list(list(X_a))),hAPP(list(list(X_a)),fun(fun(X_a,fun(list(X_a),list(list(X_a)))),fun(list(X_a),list(list(X_a)))),list_case(list(list(X_a)),X_a),nil(list(X_a))),hAPP(fun(list(X_a),list(list(X_a))),fun(X_a,fun(list(X_a),list(list(X_a)))),combk(fun(list(X_a),list(list(X_a))),X_a),hAPP(list(list(X_a)),fun(list(X_a),list(list(X_a))),hAPP(fun(list(X_a),fun(list(list(X_a)),list(list(X_a)))),fun(list(list(X_a)),fun(list(X_a),list(list(X_a)))),combc(list(X_a),list(list(X_a)),list(list(X_a))),cons(list(X_a))),nil(list(X_a)))))),Xss))))))) # label(fact_956_transpose_Opsimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1032 (all X_b all X_a all F all G all Xs_1 all Ys (Xs_1 = Ys -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys))) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2))) -> hAPP(list(X_a),list(X_b),hAPP(fun(X_a,X_b),fun(list(X_a),list(X_b)),map(X_a,X_b),F),Xs_1) = hAPP(list(X_a),list(X_b),hAPP(fun(X_a,X_b),fun(list(X_a),list(X_b)),map(X_a,X_b),G),Ys)))) # label(fact_957_map__cong) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1033 (all X_a all Xss (hBOOL(hAPP(list(list(X_a)),bool,hAPP(fun(list(list(X_a)),fun(list(list(X_a)),bool)),fun(list(list(X_a)),bool),accp(list(list(X_a))),transpose_rel(X_a)),hAPP(list(list(X_a)),list(list(X_a)),hAPP(list(X_a),fun(list(list(X_a)),list(list(X_a))),cons(list(X_a)),nil(X_a)),Xss))) -> hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),hAPP(list(list(X_a)),list(list(X_a)),hAPP(list(X_a),fun(list(list(X_a)),list(list(X_a))),cons(list(X_a)),nil(X_a)),Xss)) = hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),Xss))) # label(fact_958_transpose_Opsimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1034 (all X_a all Aa all R_1 all Ba (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R_1),Ba)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,Aa),Ba)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R_1),Aa))))) # label(fact_959_accp__downward) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1035 (all X_a all R_1 all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R_1),Aa)) <-> (exists X_2 (ti(X_a,Aa) = ti(X_a,X_2) & (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,Xa),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R_1),Xa)))))))) # label(fact_960_accp_Osimps) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1036 (all X_a all R1 all R2 (hBOOL(hAPP(fun(X_a,fun(X_a,bool)),bool,hAPP(fun(X_a,fun(X_a,bool)),fun(fun(X_a,fun(X_a,bool)),bool),ord_less_eq(fun(X_a,fun(X_a,bool))),R1),R2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R2)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R1))))) # label(fact_961_accp__subset) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1037 (all X_a (hBOOL(hAPP(list(list(X_a)),bool,hAPP(fun(list(list(X_a)),fun(list(list(X_a)),bool)),fun(list(list(X_a)),bool),accp(list(list(X_a))),transpose_rel(X_a)),nil(list(X_a)))) -> hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),nil(list(X_a))) = nil(list(X_a)))) # label(fact_962_transpose_Opsimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1038 (all X_b all X_a all F all G all Xs_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2))) -> hAPP(list(X_a),list(X_b),hAPP(fun(X_a,X_b),fun(list(X_a),list(X_b)),map(X_a,X_b),F),Xs_1) = hAPP(list(X_a),list(X_b),hAPP(fun(X_a,X_b),fun(list(X_a),list(X_b)),map(X_a,X_b),G),Xs_1))) # label(fact_963_map__ext) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1039 (all X_a all F all Xs_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(X_a,X_a,F,X_2) = ti(X_a,X_2))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,X_a),fun(list(X_a),list(X_a)),map(X_a,X_a),F),Xs_1) = Xs_1)) # label(fact_964_map__idI) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1040 (all X_b all X_a all Q_1 all P_1 all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,X_1),Y_1)) -> (hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),P_1),Q_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_1),Y_1))))) # label(fact_965_rev__predicate2D) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1041 (all X_a all X_b all X_1 all Y_1 all P_1 all Q_1 (hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),P_1),Q_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,X_1),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_1),Y_1))))) # label(fact_966_predicate2D) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1042 (all X_b all X_a all Q_1 all P_1 ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_2),Y_2)))) -> hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),P_1),Q_1)))) # label(fact_967_predicate2I) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1043 (all X_a all X_b all X_1 all Xs_1 all F all Ys (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1) = hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Ys) <-> (exists Z exists Zs (Ys = hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Z),Zs) & ti(X_a,X_1) = hAPP(X_b,X_a,F,Z) & Xs_1 = hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Zs))))) # label(fact_968_Cons__eq__map__conv) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1044 (all X_b all X_a all F all Xs_1 all Y_1 all Ys (hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys) <-> (exists Z exists Zs (Xs_1 = hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Z),Zs) & hAPP(X_b,X_a,F,Z) = ti(X_a,Y_1) & hAPP(list(X_b),list(X_a),hAPP(fun(X_b,X_a),fun(list(X_b),list(X_a)),map(X_b,X_a),F),Zs) = Ys)))) # label(fact_969_map__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1045 (all X_a all N all Xs_1 ((Xs_1 = nil(list(X_a)) -> N = zero_zero(nat)) -> ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(list(X_a)),nat,size_size(list(list(X_a))),Xs_1))) -> hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(nat,list(X_a),hAPP(list(list(X_a)),fun(nat,list(X_a)),nth(list(X_a)),Xs_1),I_2)) = N)) -> hAPP(list(list(X_a)),list(list(X_a)),transpose(X_a),Xs_1) = hAPP(list(nat),list(list(X_a)),hAPP(fun(nat,list(X_a)),fun(list(nat),list(list(X_a))),map(nat,list(X_a)),hAPP(list(nat),fun(nat,list(X_a)),hAPP(fun(nat,fun(list(nat),list(X_a))),fun(list(nat),fun(nat,list(X_a))),combc(nat,list(nat),list(X_a)),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(list(nat),list(X_a))),hAPP(fun(fun(nat,X_a),fun(list(nat),list(X_a))),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(list(nat),list(X_a)))),combb(fun(nat,X_a),fun(list(nat),list(X_a)),nat),map(nat,X_a)),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a)),combc(nat,nat,X_a),hAPP(fun(nat,list(X_a)),fun(nat,fun(nat,X_a)),hAPP(fun(list(X_a),fun(nat,X_a)),fun(fun(nat,list(X_a)),fun(nat,fun(nat,X_a))),combb(list(X_a),fun(nat,X_a),nat),nth(X_a)),hAPP(list(list(X_a)),fun(nat,list(X_a)),nth(list(X_a)),Xs_1))))),hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,zero_zero(nat)),hAPP(list(list(X_a)),nat,size_size(list(list(X_a))),Xs_1)))),hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,zero_zero(nat)),N))))) # label(fact_970_transpose__rectangle) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1046 (all X_a all X_1 all I hAPP(list(nat),list(X_a),hAPP(fun(nat,X_a),fun(list(nat),list(X_a)),map(nat,X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),X_1)),hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,zero_zero(nat)),I)) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),I),X_1)) # label(fact_971_map__replicate__trivial) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1047 (all M all N hAPP(list(nat),list(nat),hAPP(fun(nat,nat),fun(list(nat),list(nat)),map(nat,nat),suc),hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,M),N)) = hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))) # label(fact_972_map__Suc__upt) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1048 (all I_1 all J hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I_1),J)))) # label(fact_973_sorted__upt) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1049 (all I_1 all K all J (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)),J)) -> hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),nth(nat),hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I_1),J)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K))) # label(fact_974_nth__upt) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1050 (all I_1 hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I_1),zero_zero(nat)) = nil(nat)) # label(fact_975_upt__0) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1051 (all I_1 all J ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J)) -> hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I_1),J) = hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),I_1),hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,hAPP(nat,nat,suc,I_1)),J))) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J)) -> hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I_1),J) = nil(nat)))) # label(fact_976_upt__rec) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1052 (all I_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J)) -> hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I_1),J) = hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),I_1),hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,hAPP(nat,nat,suc,I_1)),J)))) # label(fact_977_upt__conv__Cons) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1053 (all M_1 all I_1 all J hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),drop(nat),M_1),hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I_1),J)) = hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),M_1)),J)) # label(fact_978_drop__upt) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1054 (all I_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J)) -> hAPP(list(nat),nat,hd(nat),hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I_1),J)) = I_1)) # label(fact_979_hd__upt) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1055 (all I_1 all J hBOOL(hAPP(list(nat),bool,distinct(nat),hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I_1),J)))) # label(fact_980_distinct__upt) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1056 (all I_1 all J hAPP(list(nat),nat,size_size(list(nat)),hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I_1),J)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I_1)) # label(fact_981_length__upt) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1057 (all I_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),I_1),M_1)),N_1)) -> hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),take(nat),M_1),hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I_1),N_1)) = hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),M_1)))) # label(fact_982_take__upt) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1058 (all J all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),I_1)) -> hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I_1),J) = nil(nat))) # label(fact_983_upt__conv__Nil) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1059 (all I all J_1 (hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I),J_1) = nil(nat) <-> J_1 = zero_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),I)))) # label(fact_984_upt__eq__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1060 (all I_1 all J ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J)) -> hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I_1),hAPP(nat,nat,suc,J)) = hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I_1),J)),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),J),nil(nat)))) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J)) -> hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I_1),hAPP(nat,nat,suc,J)) = nil(nat)))) # label(fact_985_upt__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1061 (all I_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J)) -> hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I_1),hAPP(nat,nat,suc,J)) = hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I_1),J)),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),J),nil(nat))))) # label(fact_986_upt__Suc__append) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1062 (all K all I_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J)) -> hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K)) = hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,I_1),J)),hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,J),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))))) # label(fact_987_upt__add__eq__append) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1063 (all X_a all Xs_1 hAPP(list(nat),list(X_a),hAPP(fun(nat,X_a),fun(list(nat),list(X_a)),map(nat,X_a),hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1)),hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,zero_zero(nat)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) = Xs_1) # label(fact_988_map__nth) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1064 (all X_a all F all I all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M))) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(nat),list(X_a),hAPP(fun(nat,X_a),fun(list(nat),list(X_a)),map(nat,X_a),F),hAPP(nat,list(nat),hAPP(nat,fun(nat,list(nat)),upt,M),N))),I) = hAPP(nat,X_a,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),I)))) # label(fact_989_nth__map__upt) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1065 (all X_a all N all Xs_1 hAPP(list(X_a),list(list(X_a)),hAPP(nat,fun(list(X_a),list(list(X_a))),n_lists(X_a),hAPP(nat,nat,suc,N)),Xs_1) = hAPP(list(list(list(X_a))),list(list(X_a)),concat(list(X_a)),hAPP(list(list(X_a)),list(list(list(X_a))),hAPP(fun(list(X_a),list(list(X_a))),fun(list(list(X_a)),list(list(list(X_a)))),map(list(X_a),list(list(X_a))),hAPP(list(X_a),fun(list(X_a),list(list(X_a))),hAPP(fun(list(X_a),fun(list(X_a),list(list(X_a)))),fun(list(X_a),fun(list(X_a),list(list(X_a)))),combc(list(X_a),list(X_a),list(list(X_a))),hAPP(fun(list(X_a),fun(X_a,list(X_a))),fun(list(X_a),fun(list(X_a),list(list(X_a)))),hAPP(fun(fun(X_a,list(X_a)),fun(list(X_a),list(list(X_a)))),fun(fun(list(X_a),fun(X_a,list(X_a))),fun(list(X_a),fun(list(X_a),list(list(X_a))))),combb(fun(X_a,list(X_a)),fun(list(X_a),list(list(X_a))),list(X_a)),map(X_a,list(X_a))),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),fun(X_a,list(X_a))),combc(X_a,list(X_a),list(X_a)),cons(X_a)))),Xs_1)),hAPP(list(X_a),list(list(X_a)),hAPP(nat,fun(list(X_a),list(list(X_a))),n_lists(X_a),N),Xs_1)))) # label(fact_990_n__lists_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1066 (all X_a all X_1 all Xs_1 hAPP(list(X_a),list(list(X_a)),sublists(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)) = hAPP(list(list(X_a)),list(list(X_a)),hAPP(list(list(X_a)),fun(list(list(X_a)),list(list(X_a))),append(list(X_a)),hAPP(list(list(X_a)),list(list(X_a)),hAPP(fun(list(X_a),list(X_a)),fun(list(list(X_a)),list(list(X_a))),map(list(X_a),list(X_a)),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1)),hAPP(list(X_a),list(list(X_a)),sublists(X_a),Xs_1))),hAPP(list(X_a),list(list(X_a)),sublists(X_a),Xs_1))) # label(fact_991_sublists_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1067 (all X_a all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> hBOOL(hAPP(list(fun(X_a,bool)),bool,distinct(fun(X_a,bool)),hAPP(list(list(X_a)),list(fun(X_a,bool)),hAPP(fun(list(X_a),fun(X_a,bool)),fun(list(list(X_a)),list(fun(X_a,bool))),map(list(X_a),fun(X_a,bool)),set(X_a)),hAPP(list(X_a),list(list(X_a)),sublists(X_a),Xs_1)))))) # label(fact_992_distinct__set__sublists) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1068 (all X_a all N_1 all Xs (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs)) -> hBOOL(hAPP(list(list(X_a)),bool,distinct(list(X_a)),hAPP(list(X_a),list(list(X_a)),hAPP(nat,fun(list(X_a),list(list(X_a))),n_lists(X_a),N_1),Xs))))) # label(fact_993_distinct__n__lists) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1069 (all X_a all Ys all N all Xs_1 (hBOOL(hAPP(fun(list(X_a),bool),bool,hAPP(list(X_a),fun(fun(list(X_a),bool),bool),member(list(X_a)),Ys),hAPP(list(list(X_a)),fun(list(X_a),bool),set(list(X_a)),hAPP(list(X_a),list(list(X_a)),hAPP(nat,fun(list(X_a),list(list(X_a))),n_lists(X_a),N),Xs_1)))) -> hAPP(list(X_a),nat,size_size(list(X_a)),Ys) = N)) # label(fact_994_length__n__lists__elem) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1070 (all X_a hAPP(list(X_a),list(list(X_a)),sublists(X_a),nil(X_a)) = hAPP(list(list(X_a)),list(list(X_a)),hAPP(list(X_a),fun(list(list(X_a)),list(list(X_a))),cons(list(X_a)),nil(X_a)),nil(list(X_a)))) # label(fact_995_sublists_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1071 (all X_a all N all Xs_1 hAPP(list(list(X_a)),fun(list(X_a),bool),set(list(X_a)),hAPP(list(X_a),list(list(X_a)),hAPP(nat,fun(list(X_a),list(list(X_a))),n_lists(X_a),N),Xs_1)) = hAPP(fun(list(X_a),bool),fun(list(X_a),bool),collect(list(X_a)),hAPP(fun(list(X_a),bool),fun(list(X_a),bool),hAPP(fun(list(X_a),fun(bool,bool)),fun(fun(list(X_a),bool),fun(list(X_a),bool)),combs(list(X_a),bool,bool),hAPP(fun(list(X_a),bool),fun(list(X_a),fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(list(X_a),bool),fun(list(X_a),fun(bool,bool))),combb(bool,fun(bool,bool),list(X_a)),fconj),hAPP(nat,fun(list(X_a),bool),hAPP(fun(list(X_a),fun(nat,bool)),fun(nat,fun(list(X_a),bool)),combc(list(X_a),nat,bool),hAPP(fun(list(X_a),nat),fun(list(X_a),fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(list(X_a),nat),fun(list(X_a),fun(nat,bool))),combb(nat,fun(nat,bool),list(X_a)),fequal(nat)),size_size(list(X_a)))),N))),hAPP(fun(X_a,bool),fun(list(X_a),bool),hAPP(fun(list(X_a),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(list(X_a),bool)),combc(list(X_a),fun(X_a,bool),bool),hAPP(fun(list(X_a),fun(X_a,bool)),fun(list(X_a),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(list(X_a),fun(X_a,bool)),fun(list(X_a),fun(fun(X_a,bool),bool))),combb(fun(X_a,bool),fun(fun(X_a,bool),bool),list(X_a)),ord_less_eq(fun(X_a,bool))),set(X_a))),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_996_set__n__lists) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1072 (all X_a all Xs hAPP(list(X_a),list(list(X_a)),hAPP(nat,fun(list(X_a),list(list(X_a))),n_lists(X_a),zero_zero(nat)),Xs) = hAPP(list(list(X_a)),list(list(X_a)),hAPP(list(X_a),fun(list(list(X_a)),list(list(X_a))),cons(list(X_a)),nil(X_a)),nil(list(X_a)))) # label(fact_997_n__lists_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1073 (all T_2 all T_1 (enum(T_1) & enum(T_2) -> enum(fun(T_2,T_1)))) # label(arity_fun___Enum_Oenum) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1074 (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].
% 2.04/2.27 1075 (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].
% 2.04/2.27 1076 (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].
% 2.04/2.27 1077 (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].
% 2.04/2.27 1078 (all T_2 all T_1 (cl_HOL_Oequal(T_1) & enum(T_2) -> cl_HOL_Oequal(fun(T_2,T_1)))) # label(arity_fun___HOL_Oequal) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1079 (all T_1 cl_HOL_Oequal(list(T_1))) # label(arity_List_Olist___HOL_Oequal) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1080 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1081 (all X_a all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y) = ti(X_a,X)) # label(help_If_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1082 (all X_a all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X),Y) = ti(X_a,Y)) # label(help_If_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1083 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_If_3_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1084 (all X_a all P all X (-hBOOL(hAPP(X_a,bool,P,X)) | hBOOL(hAPP(fun(X_a,bool),bool,fEx(X_a),P)))) # label(help_fEx_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1085 (all P (-hBOOL(hAPP(bool,bool,fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1086 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1087 (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].
% 2.04/2.27 1088 (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].
% 2.04/2.27 1089 (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].
% 2.04/2.27 1090 (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].
% 2.04/2.27 1091 (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].
% 2.04/2.27 1092 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fTrue_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.04/2.27 1093 (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].
% 2.04/2.27 1094 (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].
% 2.13/2.40 1095 (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].
% 2.13/2.40 1096 (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].
% 2.13/2.40 1097 (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].
% 2.13/2.40 1098 (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].
% 2.13/2.40 1099 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.40 1100 (all X_a all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) | ti(X_a,X) = ti(X_a,Y))) # label(help_fequal_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.40 1101 (all X_a all X all Y (ti(X_a,X) != ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)))) # label(help_fequal_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.40 1102 -(exists C hBOOL(hAPP(list(arrow_2142409994le_alt),bool,distinct(arrow_2142409994le_alt),hAPP(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt)),cons(arrow_2142409994le_alt),a),hAPP(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt)),cons(arrow_2142409994le_alt),b),hAPP(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt)),cons(arrow_2142409994le_alt),C),nil(arrow_2142409994le_alt))))))) # label(conj_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.13/2.40
% 2.13/2.40 ============================== end of process non-clausal formulas ===
% 2.13/2.40
% 2.13/2.40 ============================== PROCESS INITIAL CLAUSES ===============
% 2.13/2.40
% 2.13/2.40 ============================== PREDICATE ELIMINATION =================
% 2.13/2.40 1103 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom). [assumption].
% 2.13/2.40 1104 -linorder(A) | ti(fun(fun(A,fun(A,A)),fun(fun(A,bool),A)),big_Sup_fin(A)) = big_Sup_fin(A) # label(tsy_c_Big__Operators_Olattice_OSup__fin_res) # label(axiom). [clausify(1)].
% 2.13/2.40 1105 -linorder(A) | big_linorder_Max(A) = ti(fun(fun(A,bool),A),big_linorder_Max(A)) # label(tsy_c_Big__Operators_Olinorder__class_OMax_res) # label(axiom). [clausify(2)].
% 2.13/2.40 1106 -linorder(A) | linord2118332866rt_key(B,A) = ti(fun(fun(B,A),fun(B,fun(list(B),list(B)))),linord2118332866rt_key(B,A)) # label(tsy_c_List_Olinorder__class_Oinsort__insert__key_res) # label(axiom). [clausify(29)].
% 2.13/2.40 1107 -linorder(A) | linorder_insort_key(B,A) = ti(fun(fun(B,A),fun(B,fun(list(B),list(B)))),linorder_insort_key(B,A)) # label(tsy_c_List_Olinorder__class_Oinsort__key_res) # label(axiom). [clausify(30)].
% 2.13/2.40 1108 -linorder(A) | linorder_sort_key(B,A) = ti(fun(fun(B,A),fun(list(B),list(B))),linorder_sort_key(B,A)) # label(tsy_c_List_Olinorder__class_Osort__key_res) # label(axiom). [clausify(31)].
% 2.13/2.40 1109 -linorder(A) | linorder_sorted(A) = ti(fun(list(A),bool),linorder_sorted(A)) # label(tsy_c_List_Olinorder__class_Osorted_res) # label(axiom). [clausify(32)].
% 2.13/2.40 1110 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),nil(A)))) # label(fact_29_sorted__single) # label(axiom). [clausify(108)].
% 2.13/2.40 1111 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),nil(A))) # label(fact_31_sorted_ONil) # label(axiom). [clausify(110)].
% 2.13/2.40 1112 -linorder(A) | nil(A) = B | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),butlast(A),B))) # label(fact_59_sorted__butlast) # label(axiom). [clausify(138)].
% 2.13/2.40 1113 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),tl(A),B))) # label(fact_94_sorted__tl) # label(axiom). [clausify(173)].
% 2.13/2.40 1114 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),dropWhile(A),C),B))) # label(fact_113_sorted__dropWhile) # label(axiom). [clausify(192)].
% 2.13/2.40 1115 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),takeWhile(A),C),B))) # label(fact_126_sorted__takeWhile) # label(axiom). [clausify(205)].
% 2.13/2.40 1116 -linorder(A) | hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),C),D),nil(B)) = hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),D),nil(B)) # label(fact_137_insort__key_Osimps_I1_J) # label(axiom). [clausify(216)].
% 2.13/2.40 1117 -linorder(A) | -hBOOL(hAPP(list(B),bool,distinct(B),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),C),D),E))) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),hAPP(list(B),fun(B,bool),set(B),E))) # label(fact_140_distinct__insort) # label(axiom). [clausify(219)].
% 2.13/2.40 1118 -linorder(A) | -hBOOL(hAPP(list(B),bool,distinct(B),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),C),D),E))) | hBOOL(hAPP(list(B),bool,distinct(B),E)) # label(fact_140_distinct__insort) # label(axiom). [clausify(219)].
% 2.13/2.40 1119 -linorder(A) | hBOOL(hAPP(list(B),bool,distinct(B),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),C),D),E))) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),hAPP(list(B),fun(B,bool),set(B),E))) | -hBOOL(hAPP(list(B),bool,distinct(B),E)) # label(fact_140_distinct__insort) # label(axiom). [clausify(219)].
% 2.13/2.40 1120 -linorder(A) | hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,A),fun(A,fun(list(A),list(A))),linorder_insort_key(A,A),combi(A)),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,A),fun(A,fun(list(A),list(A))),linorder_insort_key(A,A),combi(A)),C),D)) = hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,A),fun(A,fun(list(A),list(A))),linorder_insort_key(A,A),combi(A)),C),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,A),fun(A,fun(list(A),list(A))),linorder_insort_key(A,A),combi(A)),B),D)) # label(fact_141_insort__left__comm) # label(axiom). [clausify(220)].
% 2.13/2.40 1121 -linorder(A) | hAPP(B,A,C,D) = hAPP(B,A,C,E) | hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),C),D),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),C),E),F)) = hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),C),E),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),C),D),F)) # label(fact_143_insort__key__left__comm) # label(axiom). [clausify(222)].
% 2.13/2.40 1122 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,A),fun(A,fun(list(A),list(A))),linorder_insort_key(A,A),combi(A)),B),C))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) # label(fact_145_sorted__insort) # label(axiom). [clausify(224)].
% 2.13/2.40 1123 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,A),fun(A,fun(list(A),list(A))),linorder_insort_key(A,A),combi(A)),B),C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) # label(fact_145_sorted__insort) # label(axiom). [clausify(224)].
% 2.13/2.40 1124 -linorder(A) | hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),C),D),E) != nil(B) # label(fact_152_insort__not__Nil) # label(axiom). [clausify(231)].
% 2.13/2.40 1125 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | -hBOOL(hAPP(list(A),bool,distinct(A),B)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | -hBOOL(hAPP(list(A),bool,distinct(A),C)) | hAPP(list(A),fun(A,bool),set(A),C) != hAPP(list(A),fun(A,bool),set(A),B) | C = B # label(fact_170_sorted__distinct__set__unique) # label(axiom). [clausify(249)].
% 2.13/2.40 1126 -linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(list(A),fun(A,bool),set(A),C))) | hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,A),fun(A,fun(list(A),list(A))),linorder_insort_key(A,A),combi(A)),B),C) = hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,A),fun(A,fun(list(A),list(A))),linord2118332866rt_key(A,A),combi(A)),B),C) # label(fact_215_insort__insert__insort) # label(axiom). [clausify(294)].
% 2.13/2.40 1127 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(list(A),fun(A,bool),set(A),C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,A),fun(A,fun(list(A),list(A))),linorder_insort_key(A,A),combi(A)),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),remove1(A),B),C)) = C # label(fact_217_insort__remove1) # label(axiom). [clausify(296)].
% 2.13/2.40 1128 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(nat,fun(list(A),list(A)),take(A),C),B))) # label(fact_222_sorted__take) # label(axiom). [clausify(301)].
% 2.13/2.40 1129 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),remove1(A),C),B))) # label(fact_229_sorted__remove1) # label(axiom). [clausify(308)].
% 2.13/2.40 1130 -linorder(A) | hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),remove1(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,A),fun(A,fun(list(A),list(A))),linorder_insort_key(A,A),combi(A)),B),C)) = C # label(fact_238_remove1__insort) # label(axiom). [clausify(317)].
% 2.13/2.40 1131 -linorder(A) | -hBOOL(hAPP(list(B),bool,distinct(B),C)) | hBOOL(hAPP(list(B),bool,distinct(B),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linord2118332866rt_key(B,A),D),E),C))) # label(fact_241_distinct__insort__insert) # label(axiom). [clausify(320)].
% 2.13/2.40 1132 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(list(A),fun(A,bool),set(A),C))) | hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,A),fun(A,fun(list(A),list(A))),linord2118332866rt_key(A,A),combi(A)),B),C) = C # label(fact_243_insort__insert__triv) # label(axiom). [clausify(322)].
% 2.13/2.40 1133 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,A),fun(A,fun(list(A),list(A))),linord2118332866rt_key(A,A),combi(A)),C),B))) # label(fact_244_sorted__insort__insert) # label(axiom). [clausify(323)].
% 2.13/2.40 1134 -linorder(A) | hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),hAPP(fun(list(A),fun(A,list(A))),fun(list(A),fun(list(A),list(A))),foldl(list(A),A),hAPP(fun(A,fun(list(A),list(A))),fun(list(A),fun(A,list(A))),combc(A,list(A),list(A)),hAPP(fun(A,A),fun(A,fun(list(A),list(A))),linorder_insort_key(A,A),combi(A)))),nil(A)),B) = hAPP(list(A),list(A),hAPP(fun(A,A),fun(list(A),list(A)),linorder_sort_key(A,A),combi(A)),B) # label(fact_286_sort__foldl__insort) # label(axiom). [clausify(365)].
% 2.13/2.40 1135 -linorder(A) | hAPP(list(B),list(B),hAPP(fun(B,A),fun(list(B),list(B)),linorder_sort_key(B,A),C),nil(B)) = nil(B) # label(fact_290_sort__key__simps_I1_J) # label(axiom). [clausify(369)].
% 2.13/2.40 1136 -linorder(A) | hAPP(list(B),fun(B,bool),set(B),hAPP(list(B),list(B),hAPP(fun(B,A),fun(list(B),list(B)),linorder_sort_key(B,A),C),D)) = hAPP(list(B),fun(B,bool),set(B),D) # label(fact_291_set__sort) # label(axiom). [clausify(370)].
% 2.13/2.40 1137 -linorder(A) | -hBOOL(hAPP(list(B),bool,distinct(B),hAPP(list(B),list(B),hAPP(fun(B,A),fun(list(B),list(B)),linorder_sort_key(B,A),C),D))) | hBOOL(hAPP(list(B),bool,distinct(B),D)) # label(fact_292_distinct__sort) # label(axiom). [clausify(371)].
% 2.13/2.40 1138 -linorder(A) | hBOOL(hAPP(list(B),bool,distinct(B),hAPP(list(B),list(B),hAPP(fun(B,A),fun(list(B),list(B)),linorder_sort_key(B,A),C),D))) | -hBOOL(hAPP(list(B),bool,distinct(B),D)) # label(fact_292_distinct__sort) # label(axiom). [clausify(371)].
% 2.13/2.40 1139 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(fun(A,A),fun(list(A),list(A)),linorder_sort_key(A,A),combi(A)),B))) # label(fact_294_sorted__sort) # label(axiom). [clausify(373)].
% 2.13/2.40 1140 -linorder(A) | hAPP(list(B),list(B),hAPP(fun(B,A),fun(list(B),list(B)),linorder_sort_key(B,A),C),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),D),E)) = hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),C),D),hAPP(list(B),list(B),hAPP(fun(B,A),fun(list(B),list(B)),linorder_sort_key(B,A),C),E)) # label(fact_301_sort__key__simps_I2_J) # label(axiom). [clausify(380)].
% 2.13/2.40 1141 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),rev(A),B))) | nil(A) != B | hAPP(A,A,hAPP(list(A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(list(A),fun(A,A)),foldr(A,A),ord_max(A)),B),C) = ti(A,C) # label(fact_317_foldr__max__sorted) # label(axiom). [clausify(395)].
% 2.13/2.40 1142 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),rev(A),B))) | nil(A) = B | hAPP(A,A,hAPP(list(A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(list(A),fun(A,A)),foldr(A,A),ord_max(A)),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),zero_zero(nat))),C) # label(fact_317_foldr__max__sorted) # label(axiom). [clausify(395)].
% 2.13/2.40 1143 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D)))) # label(fact_369_sorted__many) # label(axiom). [clausify(445)].
% 2.13/2.40 1144 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_370_sorted__many__eq) # label(axiom). [clausify(446)].
% 2.13/2.40 1145 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D)))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D))) # label(fact_370_sorted__many__eq) # label(axiom). [clausify(446)].
% 2.13/2.40 1146 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D))) # label(fact_370_sorted__many__eq) # label(axiom). [clausify(446)].
% 2.13/2.40 1147 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,D)),hAPP(B,A,C,E))) | hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),C),D),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),E),F)) = hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),D),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),E),F)) # label(fact_371_insort__key_Osimps_I2_J) # label(axiom). [clausify(447)].
% 2.13/2.40 1148 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,D)),hAPP(B,A,C,E))) | hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),C),D),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),E),F)) = hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),E),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),C),D),F)) # label(fact_371_insort__key_Osimps_I2_J) # label(axiom). [clausify(447)].
% 2.13/2.40 1149 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) # label(fact_375_sorted__Cons) # label(axiom). [clausify(450)].
% 2.13/2.40 1150 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),hAPP(list(A),fun(A,bool),set(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_375_sorted__Cons) # label(axiom). [clausify(450)].
% 2.13/2.40 1151 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f111(A,B,C)),hAPP(list(A),fun(A,bool),set(A),C))) # label(fact_375_sorted__Cons) # label(axiom). [clausify(450)].
% 2.13/2.40 1152 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f111(A,B,C))) # label(fact_375_sorted__Cons) # label(axiom). [clausify(450)].
% 2.13/2.40 1153 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) # label(fact_376_sorted__append) # label(axiom). [clausify(451)].
% 2.13/2.40 1154 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) # label(fact_376_sorted__append) # label(axiom). [clausify(451)].
% 2.13/2.40 1155 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),hAPP(list(A),fun(A,bool),set(A),B))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),E),hAPP(list(A),fun(A,bool),set(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) # label(fact_376_sorted__append) # label(axiom). [clausify(451)].
% 2.13/2.40 1156 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f112(A,B,C)),hAPP(list(A),fun(A,bool),set(A),B))) # label(fact_376_sorted__append) # label(axiom). [clausify(451)].
% 2.13/2.40 1157 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f113(A,B,C)),hAPP(list(A),fun(A,bool),set(A),C))) # label(fact_376_sorted__append) # label(axiom). [clausify(451)].
% 2.13/2.40 1158 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f112(A,B,C)),f113(A,B,C))) # label(fact_376_sorted__append) # label(axiom). [clausify(451)].
% 2.13/2.40 1159 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | nil(A) = B | hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),f115(A,B)),f114(A,B)) = B # label(fact_377_sorted_Osimps) # label(axiom). [clausify(452)].
% 2.13/2.40 1160 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | nil(A) = B | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),hAPP(list(A),fun(A,bool),set(A),f114(A,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f115(A,B)),C)) # label(fact_377_sorted_Osimps) # label(axiom). [clausify(452)].
% 2.13/2.40 1161 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | nil(A) = B | hBOOL(hAPP(list(A),bool,linorder_sorted(A),f114(A,B))) # label(fact_377_sorted_Osimps) # label(axiom). [clausify(452)].
% 2.13/2.40 1162 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | nil(A) != B # label(fact_377_sorted_Osimps) # label(axiom). [clausify(452)].
% 2.13/2.40 1163 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D) != B | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f116(A,B,D,C)),hAPP(list(A),fun(A,bool),set(A),D))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),D)) # label(fact_377_sorted_Osimps) # label(axiom). [clausify(452)].
% 2.13/2.40 1164 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D) != B | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),f116(A,B,D,C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),D)) # label(fact_377_sorted_Osimps) # label(axiom). [clausify(452)].
% 2.13/2.40 1165 -linorder(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f117(B,A,C,D,E)),hAPP(list(B),fun(B,bool),set(B),E))) | hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),C),D),E) = hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),D),E) # label(fact_378_insort__is__Cons) # label(axiom). [clausify(453)].
% 2.13/2.40 1166 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,D)),hAPP(B,A,C,f117(B,A,C,D,E)))) | hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),C),D),E) = hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),D),E) # label(fact_378_insort__is__Cons) # label(axiom). [clausify(453)].
% 2.13/2.40 1167 -linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f118(A,B,C)),hAPP(list(A),fun(A,bool),set(A),C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C))) # label(fact_379_sorted_OCons) # label(axiom). [clausify(454)].
% 2.13/2.40 1168 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f118(A,B,C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C))) # label(fact_379_sorted_OCons) # label(axiom). [clausify(454)].
% 2.13/2.40 1169 -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_388_linorder__linear) # label(axiom). [clausify(463)].
% 2.13/2.40 1170 -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_402_linorder__le__cases) # label(axiom). [clausify(477)].
% 2.13/2.40 1171 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(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_404_le__max__iff__disj) # label(axiom). [clausify(479)].
% 2.13/2.40 1172 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_404_le__max__iff__disj) # label(axiom). [clausify(479)].
% 2.13/2.40 1173 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_404_le__max__iff__disj) # label(axiom). [clausify(479)].
% 2.13/2.40 1174 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_413_min__max_Ole__supE) # label(axiom). [clausify(488)].
% 2.13/2.40 1175 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_413_min__max_Ole__supE) # label(axiom). [clausify(488)].
% 2.13/2.40 1176 -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),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),E))) # label(fact_414_min__max_Osup__mono) # label(axiom). [clausify(489)].
% 2.13/2.40 1177 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),B) = ti(A,B) # label(fact_424_min__max_Osup_Oidem) # label(axiom). [clausify(499)].
% 2.13/2.40 1178 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) # label(fact_425_min__max_Osup_Ocommute) # label(axiom). [clausify(500)].
% 2.13/2.40 1179 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) # label(fact_426_min__max_Osup__commute) # label(axiom). [clausify(501)].
% 2.13/2.40 1180 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) # label(fact_427_min__max_Osup_Oleft__idem) # label(axiom). [clausify(502)].
% 2.13/2.40 1181 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) # label(fact_428_min__max_Osup__left__idem) # label(axiom). [clausify(503)].
% 2.13/2.40 1182 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) # label(fact_429_min__max_Osup_Oleft__commute) # label(axiom). [clausify(504)].
% 2.13/2.40 1183 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) # label(fact_430_min__max_Osup__left__commute) # label(axiom). [clausify(505)].
% 2.13/2.40 1184 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) # label(fact_431_min__max_Osup_Oassoc) # label(axiom). [clausify(506)].
% 2.13/2.40 1185 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) # label(fact_432_min__max_Osup__assoc) # label(axiom). [clausify(507)].
% 2.13/2.40 1186 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C))) # label(fact_433_le__maxI1) # label(axiom). [clausify(508)].
% 2.13/2.40 1187 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B))) # label(fact_434_le__maxI2) # label(axiom). [clausify(509)].
% 2.13/2.40 1188 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) = ti(A,C) # label(fact_435_min__max_Ole__iff__sup) # label(axiom). [clausify(510)].
% 2.13/2.40 1189 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) != ti(A,C) # label(fact_435_min__max_Ole__iff__sup) # label(axiom). [clausify(510)].
% 2.13/2.40 1190 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_436_min__max_Ole__sup__iff) # label(axiom). [clausify(511)].
% 2.13/2.40 1191 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_436_min__max_Ole__sup__iff) # label(axiom). [clausify(511)].
% 2.13/2.40 1192 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(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_436_min__max_Ole__sup__iff) # label(axiom). [clausify(511)].
% 2.13/2.40 1193 -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),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) # label(fact_437_min__max_Ole__supI1) # label(axiom). [clausify(512)].
% 2.13/2.40 1194 -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),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_438_min__max_Ole__supI2) # label(axiom). [clausify(513)].
% 2.13/2.40 1195 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) = ti(A,C) # label(fact_439_min__max_Osup__absorb2) # label(axiom). [clausify(514)].
% 2.13/2.40 1196 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) = ti(A,C) # label(fact_440_min__max_Osup__absorb1) # label(axiom). [clausify(515)].
% 2.13/2.40 1197 -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),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C)) # label(fact_441_min__max_Ole__supI) # label(axiom). [clausify(516)].
% 2.13/2.40 1198 -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),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C)) # label(fact_442_min__max_Osup__least) # label(axiom). [clausify(517)].
% 2.13/2.40 1199 -linorder(A) | hAPP(list(A),A,hAPP(A,fun(list(A),A),hAPP(fun(A,fun(A,A)),fun(A,fun(list(A),A)),foldl(A,A),ord_max(A)),B),C) = hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(list(A),fun(A,bool),set(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C))) # label(fact_445_Max__fin__set__fold) # label(axiom). [clausify(520)].
% 2.13/2.40 1200 -linorder(A) | hAPP(list(A),A,hAPP(A,fun(list(A),A),hAPP(fun(A,fun(A,A)),fun(A,fun(list(A),A)),foldl(A,A),ord_max(A)),B),C) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(list(A),fun(A,bool),set(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C))) # label(fact_451_min__max_OSup__fin__set__fold) # label(axiom). [clausify(526)].
% 2.13/2.40 1201 -linorder(A) | hAPP(fun(A,fun(A,bool)),fun(A,fun(A,A)),min(A),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),ord_less_eq(A))) = ord_max(A) # label(fact_462_dual__min) # label(axiom). [clausify(537)].
% 2.13/2.40 1202 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_466_min__max_Ole__infE) # label(axiom). [clausify(541)].
% 2.13/2.40 1203 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_466_min__max_Ole__infE) # label(axiom). [clausify(541)].
% 2.13/2.40 1204 -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),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),E))) # label(fact_467_min__max_Oinf__mono) # label(axiom). [clausify(542)].
% 2.13/2.40 1205 -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),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) # label(fact_468_min__max_Oinf__greatest) # label(axiom). [clausify(543)].
% 2.13/2.40 1206 -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),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) # label(fact_469_min__max_Ole__infI) # label(axiom). [clausify(544)].
% 2.13/2.40 1207 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),B) = ti(A,B) # label(fact_470_min__max_Oinf__absorb2) # label(axiom). [clausify(545)].
% 2.13/2.40 1208 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) = ti(A,B) # label(fact_471_min__max_Oinf__absorb1) # label(axiom). [clausify(546)].
% 2.13/2.40 1209 -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),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),B)),C)) # label(fact_472_min__max_Ole__infI2) # label(axiom). [clausify(547)].
% 2.13/2.40 1210 -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),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C)) # label(fact_473_min__max_Ole__infI1) # label(axiom). [clausify(548)].
% 2.13/2.40 1211 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_474_min__max_Ole__inf__iff) # label(axiom). [clausify(549)].
% 2.13/2.40 1212 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_474_min__max_Ole__inf__iff) # label(axiom). [clausify(549)].
% 2.13/2.40 1213 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(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_474_min__max_Ole__inf__iff) # label(axiom). [clausify(549)].
% 2.13/2.40 1214 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) = ti(A,B) # label(fact_475_min__max_Ole__iff__inf) # label(axiom). [clausify(550)].
% 2.13/2.40 1215 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) != ti(A,B) # label(fact_475_min__max_Ole__iff__inf) # label(axiom). [clausify(550)].
% 2.13/2.40 1216 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),C)) # label(fact_476_min__max_Oinf__le2) # label(axiom). [clausify(551)].
% 2.13/2.40 1217 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),B)) # label(fact_477_min__max_Oinf__le1) # label(axiom). [clausify(552)].
% 2.13/2.40 1218 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),B) = ti(A,B) # label(fact_478_min__max_Oinf_Oidem) # label(axiom). [clausify(553)].
% 2.13/2.40 1219 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),B) # label(fact_480_min__max_Oinf_Ocommute) # label(axiom). [clausify(555)].
% 2.13/2.40 1220 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),B) # label(fact_481_min__max_Oinf__commute) # label(axiom). [clausify(556)].
% 2.13/2.40 1221 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) # label(fact_482_min__max_Oinf_Oleft__idem) # label(axiom). [clausify(557)].
% 2.13/2.40 1222 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) # label(fact_483_min__max_Oinf__left__idem) # label(axiom). [clausify(558)].
% 2.13/2.40 1223 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_484_min__max_Oinf_Oleft__commute) # label(axiom). [clausify(559)].
% 2.13/2.40 1224 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_485_min__max_Oinf__left__commute) # label(axiom). [clausify(560)].
% 2.19/2.40 1225 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_486_min__max_Oinf_Oassoc) # label(axiom). [clausify(561)].
% 2.19/2.40 1226 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_487_min__max_Oinf__assoc) # label(axiom). [clausify(562)].
% 2.19/2.40 1227 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) = ti(A,B) # label(fact_489_min__max_Osup__inf__absorb) # label(axiom). [clausify(564)].
% 2.19/2.40 1228 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) = ti(A,B) # label(fact_490_min__max_Oinf__sup__absorb) # label(axiom). [clausify(565)].
% 2.19/2.40 1229 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_491_min__max_Osup__inf__distrib1) # label(axiom). [clausify(566)].
% 2.19/2.40 1230 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_492_min__max_Oinf__sup__distrib1) # label(axiom). [clausify(567)].
% 2.19/2.40 1231 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C) # label(fact_493_min__max_Osup__inf__distrib2) # label(axiom). [clausify(568)].
% 2.19/2.40 1232 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_494_min__max_Oinf__sup__distrib2) # label(axiom). [clausify(569)].
% 2.19/2.40 1233 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),B) = ti(A,B) # label(fact_521_Min_Oidem) # label(axiom). [clausify(596)].
% 2.19/2.40 1234 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(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_536_min__le__iff__disj) # label(axiom). [clausify(611)].
% 2.19/2.40 1235 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_536_min__le__iff__disj) # label(axiom). [clausify(611)].
% 2.19/2.40 1236 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_536_min__le__iff__disj) # label(axiom). [clausify(611)].
% 2.19/2.40 1237 -linorder(A) | hAPP(list(B),nat,size_size(list(B)),hAPP(list(B),list(B),hAPP(fun(B,A),fun(list(B),list(B)),linorder_sort_key(B,A),C),D)) = hAPP(list(B),nat,size_size(list(B)),D) # label(fact_539_length__sort) # label(axiom). [clausify(614)].
% 2.19/2.40 1238 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D))),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)))) # label(fact_541_min__max_Odistrib__inf__le) # label(axiom). [clausify(616)].
% 2.19/2.40 1239 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)))) # label(fact_542_min__max_Odistrib__sup__le) # label(axiom). [clausify(617)].
% 2.19/2.40 1240 -linorder(A) | hAPP(list(B),nat,size_size(list(B)),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),C),D),E)) = hAPP(nat,nat,suc,hAPP(list(B),nat,size_size(list(B)),E)) # label(fact_565_length__insort) # label(axiom). [clausify(640)].
% 2.19/2.40 1241 -linorder(A) | hAPP(fun(A,fun(A,bool)),fun(A,fun(A,A)),max(A),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),ord_less_eq(A))) = ord_min(A) # label(fact_569_dual__max) # label(axiom). [clausify(644)].
% 2.19/2.40 1242 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),B) = ti(A,B) # label(fact_575_Max_Oidem) # label(axiom). [clausify(650)].
% 2.19/2.40 1243 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f158(A,B,C,D)),f159(A,B,C,D))),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f158(A,B,C,D)),f160(A,B,C,D))) != hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f158(A,B,C,D)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f159(A,B,C,D)),f160(A,B,C,D))) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_581_min__max_Odistrib__imp2) # label(axiom). [clausify(656)].
% 2.19/2.40 1244 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f161(A,B,C,D)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f162(A,B,C,D)),f163(A,B,C,D))) != hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f161(A,B,C,D)),f162(A,B,C,D))),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f161(A,B,C,D)),f163(A,B,C,D))) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_585_min__max_Odistrib__imp1) # label(axiom). [clausify(660)].
% 2.19/2.40 1245 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),rev(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),D),hAPP(list(A),nat,size_size(list(A)),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),D)),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),C))) # label(fact_597_sorted__rev__nth__mono) # label(axiom). [clausify(672)].
% 2.19/2.40 1246 -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_612_linorder__antisym__conv2) # label(axiom). [clausify(687)].
% 2.19/2.40 1247 -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_612_linorder__antisym__conv2) # label(axiom). [clausify(687)].
% 2.19/2.40 1248 -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_615_leD) # label(axiom). [clausify(690)].
% 2.19/2.40 1249 -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_618_linorder__antisym__conv1) # label(axiom). [clausify(693)].
% 2.19/2.40 1250 -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_618_linorder__antisym__conv1) # label(axiom). [clausify(693)].
% 2.19/2.40 1251 -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_619_not__leE) # label(axiom). [clausify(694)].
% 2.19/2.40 1252 -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_620_leI) # label(axiom). [clausify(695)].
% 2.19/2.40 1253 -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_624_linorder__le__less__linear) # label(axiom). [clausify(699)].
% 2.19/2.40 1254 -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_625_linorder__not__le) # label(axiom). [clausify(700)].
% 2.19/2.40 1255 -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_625_linorder__not__le) # label(axiom). [clausify(700)].
% 2.19/2.40 1256 -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_626_linorder__not__less) # label(axiom). [clausify(701)].
% 2.19/2.40 1257 -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_626_linorder__not__less) # label(axiom). [clausify(701)].
% 2.19/2.40 1258 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) | 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),D)) # label(fact_654_less__max__iff__disj) # label(axiom). [clausify(729)].
% 2.19/2.40 1259 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_654_less__max__iff__disj) # label(axiom). [clausify(729)].
% 2.19/2.40 1260 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_654_less__max__iff__disj) # label(axiom). [clausify(729)].
% 2.19/2.40 1261 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_655_max__less__iff__conj) # label(axiom). [clausify(730)].
% 2.19/2.40 1262 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_655_max__less__iff__conj) # label(axiom). [clausify(730)].
% 2.19/2.40 1263 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_655_max__less__iff__conj) # label(axiom). [clausify(730)].
% 2.19/2.40 1264 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_675_linorder__cases) # label(axiom). [clausify(750)].
% 2.19/2.40 1265 -linorder(A) | ti(A,B) = ti(A,C) | 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_691_linorder__neqE) # label(axiom). [clausify(766)].
% 2.19/2.40 1266 -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_692_linorder__antisym__conv3) # label(axiom). [clausify(767)].
% 2.19/2.40 1267 -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_692_linorder__antisym__conv3) # label(axiom). [clausify(767)].
% 2.19/2.40 1268 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_693_linorder__less__linear) # label(axiom). [clausify(768)].
% 2.19/2.40 1269 -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_694_not__less__iff__gr__or__eq) # label(axiom). [clausify(769)].
% 2.19/2.40 1270 -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_694_not__less__iff__gr__or__eq) # label(axiom). [clausify(769)].
% 2.19/2.40 1271 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_694_not__less__iff__gr__or__eq) # label(axiom). [clausify(769)].
% 2.19/2.40 1272 -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_695_linorder__neq__iff) # label(axiom). [clausify(770)].
% 2.19/2.40 1273 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_695_linorder__neq__iff) # label(axiom). [clausify(770)].
% 2.19/2.40 1274 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_695_linorder__neq__iff) # label(axiom). [clausify(770)].
% 2.19/2.40 1275 -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),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_697_min__max_Oless__supI2) # label(axiom). [clausify(772)].
% 2.19/2.40 1276 -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),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) # label(fact_698_min__max_Oless__supI1) # label(axiom). [clausify(773)].
% 2.19/2.40 1277 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_699_min__less__iff__disj) # label(axiom). [clausify(774)].
% 2.19/2.40 1278 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_699_min__less__iff__disj) # label(axiom). [clausify(774)].
% 2.19/2.40 1279 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_699_min__less__iff__disj) # label(axiom). [clausify(774)].
% 2.19/2.40 1280 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_700_min__less__iff__conj) # label(axiom). [clausify(775)].
% 2.19/2.40 1281 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_700_min__less__iff__conj) # label(axiom). [clausify(775)].
% 2.19/2.40 1282 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | -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),D)) # label(fact_700_min__less__iff__conj) # label(axiom). [clausify(775)].
% 2.19/2.40 1283 -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),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),B)),C)) # label(fact_701_min__max_Oless__infI2) # label(axiom). [clausify(776)].
% 2.19/2.40 1284 -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),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C)) # label(fact_702_min__max_Oless__infI1) # label(axiom). [clausify(777)].
% 2.19/2.40 1285 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(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),D),hAPP(list(A),nat,size_size(list(A)),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),C)),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),D))) # label(fact_759_sorted__nth__mono) # label(axiom). [clausify(834)].
% 2.19/2.40 1286 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),hAPP(list(A),nat,size_size(list(A)),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),D)),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),C))) # label(fact_760_sorted__equals__nth__mono) # label(axiom). [clausify(835)].
% 2.19/2.40 1287 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f179(A,B)),hAPP(list(A),nat,size_size(list(A)),B))) # label(fact_760_sorted__equals__nth__mono) # label(axiom). [clausify(835)].
% 2.19/2.40 1288 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f180(A,B)),f179(A,B))) # label(fact_760_sorted__equals__nth__mono) # label(axiom). [clausify(835)].
% 2.19/2.40 1289 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),f180(A,B))),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),f179(A,B)))) # label(fact_760_sorted__equals__nth__mono) # label(axiom). [clausify(835)].
% 2.19/2.40 1290 -linorder(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f181(A,B)),f182(A,B))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) # label(fact_763_sorted__nth__monoI) # label(axiom). [clausify(838)].
% 2.19/2.40 1291 -linorder(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f182(A,B)),hAPP(list(A),nat,size_size(list(A)),B))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) # label(fact_763_sorted__nth__monoI) # label(axiom). [clausify(838)].
% 2.19/2.40 1292 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),f181(A,B))),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),f182(A,B)))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) # label(fact_763_sorted__nth__monoI) # label(axiom). [clausify(838)].
% 2.19/2.40 1293 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(nat,fun(list(A),list(A)),drop(A),C),B))) # label(fact_805_sorted__drop) # label(axiom). [clausify(880)].
% 2.19/2.40 1294 -linorder(A) | hBOOL(hAPP(B,bool,C,D)) | hAPP(list(B),list(B),hAPP(fun(B,bool),fun(list(B),list(B)),filter(B),C),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),E),D),F)) = hAPP(list(B),list(B),hAPP(fun(B,bool),fun(list(B),list(B)),filter(B),C),F) # label(fact_871_filter__insort__triv) # label(axiom). [clausify(946)].
% 2.19/2.40 1295 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),filter(A),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),hAPP(list(A),A,B,C))),C))) # label(fact_880_sorted__same) # label(axiom). [clausify(955)].
% 2.19/2.40 1296 -linorder(A) | hAPP(list(B),list(B),hAPP(fun(B,A),fun(list(B),list(B)),linorder_sort_key(B,A),C),hAPP(list(B),list(B),hAPP(fun(B,bool),fun(list(B),list(B)),filter(B),D),E)) = hAPP(list(B),list(B),hAPP(fun(B,bool),fun(list(B),list(B)),filter(B),D),hAPP(list(B),list(B),hAPP(fun(B,A),fun(list(B),list(B)),linorder_sort_key(B,A),C),E)) # label(fact_881_filter__sort) # label(axiom). [clausify(956)].
% 2.19/2.40 1297 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(B),list(A),hAPP(fun(B,A),fun(list(B),list(A)),map(B,A),C),D))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(B),list(A),hAPP(fun(B,A),fun(list(B),list(A)),map(B,A),C),hAPP(list(B),list(B),hAPP(fun(B,bool),fun(list(B),list(B)),filter(B),E),D)))) # label(fact_908_sorted__filter) # label(axiom). [clausify(983)].
% 2.19/2.40 1298 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(B),list(A),hAPP(fun(B,A),fun(list(B),list(A)),map(B,A),C),hAPP(list(B),list(B),hAPP(fun(B,bool),fun(list(B),list(B)),filter(B),hAPP(A,fun(B,bool),hAPP(fun(B,fun(A,bool)),fun(A,fun(B,bool)),combc(B,A,bool),hAPP(fun(B,A),fun(B,fun(A,bool)),hAPP(fun(A,fun(A,bool)),fun(fun(B,A),fun(B,fun(A,bool))),combb(A,fun(A,bool),B),fequal(A)),C)),hAPP(list(B),A,D,E))),E)))) # label(fact_909_sorted__map__same) # label(axiom). [clausify(984)].
% 2.19/2.40 1299 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(B),list(A),hAPP(fun(B,A),fun(list(B),list(A)),map(B,A),C),D))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(B),list(A),hAPP(fun(B,A),fun(list(B),list(A)),map(B,A),C),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),remove1(B),E),D)))) # label(fact_911_sorted__map__remove1) # label(axiom). [clausify(986)].
% 2.19/2.40 1300 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(B),list(A),hAPP(fun(B,A),fun(list(B),list(A)),map(B,A),C),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),C),D),E)))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(B),list(A),hAPP(fun(B,A),fun(list(B),list(A)),map(B,A),C),E))) # label(fact_912_sorted__insort__key) # label(axiom). [clausify(987)].
% 2.19/2.40 1301 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(B),list(A),hAPP(fun(B,A),fun(list(B),list(A)),map(B,A),C),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),C),D),E)))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(B),list(A),hAPP(fun(B,A),fun(list(B),list(A)),map(B,A),C),E))) # label(fact_912_sorted__insort__key) # label(axiom). [clausify(987)].
% 2.19/2.40 1302 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(B),list(A),hAPP(fun(B,A),fun(list(B),list(A)),map(B,A),C),hAPP(list(B),list(B),hAPP(fun(B,A),fun(list(B),list(B)),linorder_sort_key(B,A),C),D)))) # label(fact_913_sorted__sort__key) # label(axiom). [clausify(988)].
% 2.19/2.40 1303 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(B),list(A),hAPP(fun(B,A),fun(list(B),list(A)),map(B,A),C),D))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(B),list(A),hAPP(fun(B,A),fun(list(B),list(A)),map(B,A),C),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linord2118332866rt_key(B,A),C),E),D)))) # label(fact_914_sorted__insort__insert__key) # label(axiom). [clausify(989)].
% 2.19/2.40 1304 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(B),list(A),hAPP(fun(B,A),fun(list(B),list(A)),map(B,A),C),D))) | -hBOOL(hAPP(B,bool,E,F)) | hAPP(list(B),list(B),hAPP(fun(B,bool),fun(list(B),list(B)),filter(B),E),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),C),F),D)) = hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),C),F),hAPP(list(B),list(B),hAPP(fun(B,bool),fun(list(B),list(B)),filter(B),E),D)) # label(fact_931_filter__insort) # label(axiom). [clausify(1006)].
% 2.19/2.40 1305 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),rev(A),hAPP(list(B),list(A),hAPP(fun(B,A),fun(list(B),list(A)),map(B,A),C),D)))) | hAPP(list(B),list(B),hAPP(fun(B,bool),fun(list(B),list(B)),takeWhile(B),hAPP(fun(B,A),fun(B,bool),hAPP(fun(A,bool),fun(fun(B,A),fun(B,bool)),combb(A,bool,B),hAPP(A,fun(A,bool),ord_less(A),E)),C)),D) = hAPP(list(B),list(B),hAPP(fun(B,bool),fun(list(B),list(B)),filter(B),hAPP(fun(B,A),fun(B,bool),hAPP(fun(A,bool),fun(fun(B,A),fun(B,bool)),combb(A,bool,B),hAPP(A,fun(A,bool),ord_less(A),E)),C)),D) # label(fact_935_filter__equals__takeWhile__sorted__rev) # label(axiom). [clausify(1010)].
% 2.19/2.40 1306 -linorder(A) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),C),hAPP(list(B),fun(B,bool),set(B),D))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(B),list(A),hAPP(fun(B,A),fun(list(B),list(A)),map(B,A),E),D))) | hAPP(list(B),B,hd(B),hAPP(list(B),list(B),hAPP(fun(B,bool),fun(list(B),list(B)),filter(B),hAPP(fun(B,A),fun(B,bool),hAPP(fun(A,bool),fun(fun(B,A),fun(B,bool)),combb(A,bool,B),hAPP(A,fun(A,bool),fequal(A),hAPP(B,A,E,C))),E)),D)) != ti(B,C) | hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),hAPP(fun(B,A),fun(B,fun(list(B),list(B))),linorder_insort_key(B,A),E),C),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),remove1(B),C),D)) = D # label(fact_937_insort__key__remove1) # label(axiom). [clausify(1012)].
% 2.19/2.40 Derived: ti(fun(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat)),big_Sup_fin(nat)) = big_Sup_fin(nat). [resolve(1103,a,1104,a)].
% 2.19/2.40 Derived: big_linorder_Max(nat) = ti(fun(fun(nat,bool),nat),big_linorder_Max(nat)). [resolve(1103,a,1105,a)].
% 2.19/2.40 Derived: linord2118332866rt_key(A,nat) = ti(fun(fun(A,nat),fun(A,fun(list(A),list(A)))),linord2118332866rt_key(A,nat)). [resolve(1103,a,1106,a)].
% 2.19/2.40 Derived: linorder_insort_key(A,nat) = ti(fun(fun(A,nat),fun(A,fun(list(A),list(A)))),linorder_insort_key(A,nat)). [resolve(1103,a,1107,a)].
% 2.19/2.40 Derived: linorder_sort_key(A,nat) = ti(fun(fun(A,nat),fun(list(A),list(A))),linorder_sort_key(A,nat)). [resolve(1103,a,1108,a)].
% 2.19/2.40 Derived: linorder_sorted(nat) = ti(fun(list(nat),bool),linorder_sorted(nat)). [resolve(1103,a,1109,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),nil(nat)))). [resolve(1103,a,1110,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),nil(nat))). [resolve(1103,a,1111,a)].
% 2.19/2.40 Derived: nil(nat) = A | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),butlast(nat),A))). [resolve(1103,a,1112,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),tl(nat),A))). [resolve(1103,a,1113,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(fun(nat,bool),fun(list(nat),list(nat)),dropWhile(nat),B),A))). [resolve(1103,a,1114,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(fun(nat,bool),fun(list(nat),list(nat)),takeWhile(nat),B),A))). [resolve(1103,a,1115,a)].
% 2.19/2.40 Derived: hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),B),C),nil(A)) = hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),nil(A)). [resolve(1103,a,1116,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(A),bool,distinct(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),B),C),D))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),hAPP(list(A),fun(A,bool),set(A),D))). [resolve(1103,a,1117,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(A),bool,distinct(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),B),C),D))) | hBOOL(hAPP(list(A),bool,distinct(A),D)). [resolve(1103,a,1118,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(list(A),bool,distinct(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),B),C),D))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),hAPP(list(A),fun(A,bool),set(A),D))) | -hBOOL(hAPP(list(A),bool,distinct(A),D)). [resolve(1103,a,1119,a)].
% 2.19/2.40 Derived: hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),hAPP(fun(nat,nat),fun(nat,fun(list(nat),list(nat))),linorder_insort_key(nat,nat),combi(nat)),A),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),hAPP(fun(nat,nat),fun(nat,fun(list(nat),list(nat))),linorder_insort_key(nat,nat),combi(nat)),B),C)) = hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),hAPP(fun(nat,nat),fun(nat,fun(list(nat),list(nat))),linorder_insort_key(nat,nat),combi(nat)),B),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),hAPP(fun(nat,nat),fun(nat,fun(list(nat),list(nat))),linorder_insort_key(nat,nat),combi(nat)),A),C)). [resolve(1103,a,1120,a)].
% 2.19/2.40 Derived: hAPP(A,nat,B,C) = hAPP(A,nat,B,D) | hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),B),C),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),B),D),E)) = hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),B),D),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),B),C),E)). [resolve(1103,a,1121,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),hAPP(fun(nat,nat),fun(nat,fun(list(nat),list(nat))),linorder_insort_key(nat,nat),combi(nat)),A),B))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)). [resolve(1103,a,1122,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),hAPP(fun(nat,nat),fun(nat,fun(list(nat),list(nat))),linorder_insort_key(nat,nat),combi(nat)),A),B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)). [resolve(1103,a,1123,a)].
% 2.19/2.40 Derived: hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),B),C),D) != nil(A). [resolve(1103,a,1124,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | -hBOOL(hAPP(list(nat),bool,distinct(nat),A)) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | -hBOOL(hAPP(list(nat),bool,distinct(nat),B)) | hAPP(list(nat),fun(nat,bool),set(nat),B) != hAPP(list(nat),fun(nat,bool),set(nat),A) | B = A. [resolve(1103,a,1125,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),A),hAPP(list(nat),fun(nat,bool),set(nat),B))) | hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),hAPP(fun(nat,nat),fun(nat,fun(list(nat),list(nat))),linorder_insort_key(nat,nat),combi(nat)),A),B) = hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),hAPP(fun(nat,nat),fun(nat,fun(list(nat),list(nat))),linord2118332866rt_key(nat,nat),combi(nat)),A),B). [resolve(1103,a,1126,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),A),hAPP(list(nat),fun(nat,bool),set(nat),B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),hAPP(fun(nat,nat),fun(nat,fun(list(nat),list(nat))),linorder_insort_key(nat,nat),combi(nat)),A),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),remove1(nat),A),B)) = B. [resolve(1103,a,1127,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),take(nat),B),A))). [resolve(1103,a,1128,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),remove1(nat),B),A))). [resolve(1103,a,1129,a)].
% 2.19/2.40 Derived: hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),remove1(nat),A),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),hAPP(fun(nat,nat),fun(nat,fun(list(nat),list(nat))),linorder_insort_key(nat,nat),combi(nat)),A),B)) = B. [resolve(1103,a,1130,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(A),bool,distinct(A),B)) | hBOOL(hAPP(list(A),bool,distinct(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linord2118332866rt_key(A,nat),C),D),B))). [resolve(1103,a,1131,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),A),hAPP(list(nat),fun(nat,bool),set(nat),B))) | hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),hAPP(fun(nat,nat),fun(nat,fun(list(nat),list(nat))),linord2118332866rt_key(nat,nat),combi(nat)),A),B) = B. [resolve(1103,a,1132,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),hAPP(fun(nat,nat),fun(nat,fun(list(nat),list(nat))),linord2118332866rt_key(nat,nat),combi(nat)),B),A))). [resolve(1103,a,1133,a)].
% 2.19/2.40 Derived: hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),hAPP(fun(list(nat),fun(nat,list(nat))),fun(list(nat),fun(list(nat),list(nat))),foldl(list(nat),nat),hAPP(fun(nat,fun(list(nat),list(nat))),fun(list(nat),fun(nat,list(nat))),combc(nat,list(nat),list(nat)),hAPP(fun(nat,nat),fun(nat,fun(list(nat),list(nat))),linorder_insort_key(nat,nat),combi(nat)))),nil(nat)),A) = hAPP(list(nat),list(nat),hAPP(fun(nat,nat),fun(list(nat),list(nat)),linorder_sort_key(nat,nat),combi(nat)),A). [resolve(1103,a,1134,a)].
% 2.19/2.40 Derived: hAPP(list(A),list(A),hAPP(fun(A,nat),fun(list(A),list(A)),linorder_sort_key(A,nat),B),nil(A)) = nil(A). [resolve(1103,a,1135,a)].
% 2.19/2.40 Derived: hAPP(list(A),fun(A,bool),set(A),hAPP(list(A),list(A),hAPP(fun(A,nat),fun(list(A),list(A)),linorder_sort_key(A,nat),B),C)) = hAPP(list(A),fun(A,bool),set(A),C). [resolve(1103,a,1136,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(A),bool,distinct(A),hAPP(list(A),list(A),hAPP(fun(A,nat),fun(list(A),list(A)),linorder_sort_key(A,nat),B),C))) | hBOOL(hAPP(list(A),bool,distinct(A),C)). [resolve(1103,a,1137,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(list(A),bool,distinct(A),hAPP(list(A),list(A),hAPP(fun(A,nat),fun(list(A),list(A)),linorder_sort_key(A,nat),B),C))) | -hBOOL(hAPP(list(A),bool,distinct(A),C)). [resolve(1103,a,1138,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(fun(nat,nat),fun(list(nat),list(nat)),linorder_sort_key(nat,nat),combi(nat)),A))). [resolve(1103,a,1139,a)].
% 2.19/2.40 Derived: hAPP(list(A),list(A),hAPP(fun(A,nat),fun(list(A),list(A)),linorder_sort_key(A,nat),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D)) = hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),B),C),hAPP(list(A),list(A),hAPP(fun(A,nat),fun(list(A),list(A)),linorder_sort_key(A,nat),B),D)). [resolve(1103,a,1140,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),rev(nat),A))) | nil(nat) != A | hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(list(nat),fun(nat,nat)),foldr(nat,nat),ord_max(nat)),A),B) = ti(nat,B). [resolve(1103,a,1141,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),rev(nat),A))) | nil(nat) = A | hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(list(nat),fun(nat,nat)),foldr(nat,nat),ord_max(nat)),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),nth(nat),A),zero_zero(nat))),B). [resolve(1103,a,1142,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),B),C))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),B),C)))). [resolve(1103,a,1143,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),B),C)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1103,a,1144,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),B),C)))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),B),C))). [resolve(1103,a,1145,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,C)),hAPP(A,nat,B,D))) | hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),B),C),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E)) = hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E)). [resolve(1103,a,1147,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,C)),hAPP(A,nat,B,D))) | hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),B),C),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E)) = hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),B),C),E)). [resolve(1103,a,1148,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),B))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)). [resolve(1103,a,1149,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),B))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),C),hAPP(list(nat),fun(nat,bool),set(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1103,a,1150,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f111(nat,A,B)),hAPP(list(nat),fun(nat,bool),set(nat),B))). [resolve(1103,a,1151,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f111(nat,A,B))). [resolve(1103,a,1152,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),A),B))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)). [resolve(1103,a,1153,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),A),B))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)). [resolve(1103,a,1154,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),A),B))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),C),hAPP(list(nat),fun(nat,bool),set(nat),A))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),D),hAPP(list(nat),fun(nat,bool),set(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)). [resolve(1103,a,1155,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),A),B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f112(nat,A,B)),hAPP(list(nat),fun(nat,bool),set(nat),A))). [resolve(1103,a,1156,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),A),B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f113(nat,A,B)),hAPP(list(nat),fun(nat,bool),set(nat),B))). [resolve(1103,a,1157,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),A),B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f112(nat,A,B)),f113(nat,A,B))). [resolve(1103,a,1158,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | nil(nat) = A | hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),f115(nat,A)),f114(nat,A)) = A. [resolve(1103,a,1159,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | nil(nat) = A | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),hAPP(list(nat),fun(nat,bool),set(nat),f114(nat,A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f115(nat,A)),B)). [resolve(1103,a,1160,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | nil(nat) = A | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),f114(nat,A))). [resolve(1103,a,1161,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | nil(nat) != A. [resolve(1103,a,1162,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),B),C) != A | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f116(nat,A,C,B)),hAPP(list(nat),fun(nat,bool),set(nat),C))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),C)). [resolve(1103,a,1163,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),B),C) != A | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f116(nat,A,C,B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),C)). [resolve(1103,a,1164,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f117(A,nat,B,C,D)),hAPP(list(A),fun(A,bool),set(A),D))) | hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),B),C),D) = hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D). [resolve(1103,a,1165,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,C)),hAPP(A,nat,B,f117(A,nat,B,C,D)))) | hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),B),C),D) = hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D). [resolve(1103,a,1166,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f118(nat,A,B)),hAPP(list(nat),fun(nat,bool),set(nat),B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),B))). [resolve(1103,a,1167,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f118(nat,A,B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),B))). [resolve(1103,a,1168,a)].
% 2.19/2.40 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(1103,a,1169,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(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(1103,a,1171,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1103,a,1172,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1103,a,1173,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1103,a,1174,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1103,a,1175,a)].
% 2.19/2.40 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),ord_max(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),D))). [resolve(1103,a,1176,a)].
% 2.19/2.40 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),A) = ti(nat,A). [resolve(1103,a,1177,a)].
% 2.19/2.40 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A). [resolve(1103,a,1178,a)].
% 2.19/2.40 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B). [resolve(1103,a,1180,a)].
% 2.19/2.40 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)). [resolve(1103,a,1182,a)].
% 2.19/2.40 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)). [resolve(1103,a,1184,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B))). [resolve(1103,a,1186,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A))). [resolve(1103,a,1187,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B) = ti(nat,B). [resolve(1103,a,1188,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B) != ti(nat,B). [resolve(1103,a,1189,a)].
% 2.19/2.40 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(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(1103,a,1192,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A) = ti(nat,B). [resolve(1103,a,1196,a)].
% 2.19/2.40 Derived: hAPP(list(nat),nat,hAPP(nat,fun(list(nat),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(list(nat),nat)),foldl(nat,nat),ord_max(nat)),A),B) = hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(list(nat),fun(nat,bool),set(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),B))). [resolve(1103,a,1199,a)].
% 2.19/2.40 Derived: hAPP(list(nat),nat,hAPP(nat,fun(list(nat),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(list(nat),nat)),foldl(nat,nat),ord_max(nat)),A),B) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(list(nat),fun(nat,bool),set(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),B))). [resolve(1103,a,1200,a)].
% 2.19/2.40 Derived: hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,nat)),min(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat))) = ord_max(nat). [resolve(1103,a,1201,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1103,a,1202,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1103,a,1203,a)].
% 2.19/2.40 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),ord_min(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),D))). [resolve(1103,a,1204,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))). [resolve(1103,a,1205,a)].
% 2.19/2.40 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),A) = ti(nat,A). [resolve(1103,a,1207,a)].
% 2.19/2.41 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B) = ti(nat,A). [resolve(1103,a,1208,a)].
% 2.19/2.41 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),ord_min(nat),C),A)),B)). [resolve(1103,a,1209,a)].
% 2.19/2.41 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),ord_min(nat),A),C)),B)). [resolve(1103,a,1210,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B) != ti(nat,A). [resolve(1103,a,1215,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),B)). [resolve(1103,a,1216,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),A)). [resolve(1103,a,1217,a)].
% 2.19/2.41 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),A) = ti(nat,A). [resolve(1103,a,1218,a)].
% 2.19/2.41 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),A). [resolve(1103,a,1219,a)].
% 2.19/2.41 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B). [resolve(1103,a,1221,a)].
% 2.19/2.41 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)). [resolve(1103,a,1223,a)].
% 2.19/2.41 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)). [resolve(1103,a,1225,a)].
% 2.19/2.41 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)) = ti(nat,A). [resolve(1103,a,1227,a)].
% 2.19/2.41 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)) = ti(nat,A). [resolve(1103,a,1228,a)].
% 2.19/2.41 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)). [resolve(1103,a,1229,a)].
% 2.19/2.41 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)). [resolve(1103,a,1230,a)].
% 2.19/2.41 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),B). [resolve(1103,a,1231,a)].
% 2.19/2.41 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)). [resolve(1103,a,1232,a)].
% 2.19/2.41 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(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(1103,a,1234,a)].
% 2.19/2.41 Derived: hAPP(list(A),nat,size_size(list(A)),hAPP(list(A),list(A),hAPP(fun(A,nat),fun(list(A),list(A)),linorder_sort_key(A,nat),B),C)) = hAPP(list(A),nat,size_size(list(A)),C). [resolve(1103,a,1237,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)))). [resolve(1103,a,1238,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)))). [resolve(1103,a,1239,a)].
% 2.19/2.41 Derived: hAPP(list(A),nat,size_size(list(A)),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),B),C),D)) = hAPP(nat,nat,suc,hAPP(list(A),nat,size_size(list(A)),D)). [resolve(1103,a,1240,a)].
% 2.19/2.41 Derived: hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,nat)),max(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat))) = ord_min(nat). [resolve(1103,a,1241,a)].
% 2.19/2.41 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),rev(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),C),hAPP(list(nat),nat,size_size(list(nat)),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),nth(nat),A),C)),hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),nth(nat),A),B))). [resolve(1103,a,1245,a)].
% 2.19/2.41 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(1103,a,1246,a)].
% 2.19/2.41 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(1103,a,1247,a)].
% 2.19/2.41 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(1103,a,1248,a)].
% 2.19/2.41 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(1103,a,1250,a)].
% 2.19/2.41 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(1103,a,1251,a)].
% 2.19/2.41 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))) | 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),C)). [resolve(1103,a,1258,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1103,a,1259,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1103,a,1260,a)].
% 2.19/2.41 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1103,a,1261,a)].
% 2.19/2.41 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(1103,a,1262,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(1103,a,1263,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,A) = ti(nat,B) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(1103,a,1264,a)].
% 2.19/2.41 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)) | ti(nat,A) != ti(nat,B). [resolve(1103,a,1267,a)].
% 2.19/2.41 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(1103,a,1270,a)].
% 2.19/2.41 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) != ti(nat,A). [resolve(1103,a,1271,a)].
% 2.19/2.41 Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1103,a,1274,a)].
% 2.19/2.41 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(1103,a,1277,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1103,a,1278,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(1103,a,1279,a)].
% 2.19/2.41 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1103,a,1280,a)].
% 2.19/2.41 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1103,a,1281,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | -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),C)). [resolve(1103,a,1282,a)].
% 2.19/2.41 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(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),C),hAPP(list(nat),nat,size_size(list(nat)),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),nth(nat),A),B)),hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),nth(nat),A),C))). [resolve(1103,a,1285,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f179(nat,A)),hAPP(list(nat),nat,size_size(list(nat)),A))). [resolve(1103,a,1287,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f180(nat,A)),f179(nat,A))). [resolve(1103,a,1288,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),nth(nat),A),f180(nat,A))),hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),nth(nat),A),f179(nat,A)))). [resolve(1103,a,1289,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f181(nat,A)),f182(nat,A))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)). [resolve(1103,a,1290,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f182(nat,A)),hAPP(list(nat),nat,size_size(list(nat)),A))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)). [resolve(1103,a,1291,a)].
% 2.19/2.41 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),nth(nat),A),f181(nat,A))),hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),nth(nat),A),f182(nat,A)))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)). [resolve(1103,a,1292,a)].
% 2.19/2.41 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),drop(nat),B),A))). [resolve(1103,a,1293,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(A,bool,B,C)) | hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),filter(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),D),C),E)) = hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),filter(A),B),E). [resolve(1103,a,1294,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(fun(nat,bool),fun(list(nat),list(nat)),filter(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),fequal(nat)),hAPP(list(nat),nat,A,B))),B))). [resolve(1103,a,1295,a)].
% 2.19/2.41 Derived: hAPP(list(A),list(A),hAPP(fun(A,nat),fun(list(A),list(A)),linorder_sort_key(A,nat),B),hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),filter(A),C),D)) = hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),filter(A),C),hAPP(list(A),list(A),hAPP(fun(A,nat),fun(list(A),list(A)),linorder_sort_key(A,nat),B),D)). [resolve(1103,a,1296,a)].
% 2.19/2.41 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(A),list(nat),hAPP(fun(A,nat),fun(list(A),list(nat)),map(A,nat),B),C))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(A),list(nat),hAPP(fun(A,nat),fun(list(A),list(nat)),map(A,nat),B),hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),filter(A),D),C)))). [resolve(1103,a,1297,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(A),list(nat),hAPP(fun(A,nat),fun(list(A),list(nat)),map(A,nat),B),hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),filter(A),hAPP(nat,fun(A,bool),hAPP(fun(A,fun(nat,bool)),fun(nat,fun(A,bool)),combc(A,nat,bool),hAPP(fun(A,nat),fun(A,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(A,nat),fun(A,fun(nat,bool))),combb(nat,fun(nat,bool),A),fequal(nat)),B)),hAPP(list(A),nat,C,D))),D)))). [resolve(1103,a,1298,a)].
% 2.19/2.41 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(A),list(nat),hAPP(fun(A,nat),fun(list(A),list(nat)),map(A,nat),B),C))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(A),list(nat),hAPP(fun(A,nat),fun(list(A),list(nat)),map(A,nat),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),remove1(A),D),C)))). [resolve(1103,a,1299,a)].
% 2.19/2.41 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(A),list(nat),hAPP(fun(A,nat),fun(list(A),list(nat)),map(A,nat),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),B),C),D)))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(A),list(nat),hAPP(fun(A,nat),fun(list(A),list(nat)),map(A,nat),B),D))). [resolve(1103,a,1300,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(A),list(nat),hAPP(fun(A,nat),fun(list(A),list(nat)),map(A,nat),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),B),C),D)))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(A),list(nat),hAPP(fun(A,nat),fun(list(A),list(nat)),map(A,nat),B),D))). [resolve(1103,a,1301,a)].
% 2.19/2.41 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(A),list(nat),hAPP(fun(A,nat),fun(list(A),list(nat)),map(A,nat),B),hAPP(list(A),list(A),hAPP(fun(A,nat),fun(list(A),list(A)),linorder_sort_key(A,nat),B),C)))). [resolve(1103,a,1302,a)].
% 2.19/2.41 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(A),list(nat),hAPP(fun(A,nat),fun(list(A),list(nat)),map(A,nat),B),C))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(A),list(nat),hAPP(fun(A,nat),fun(list(A),list(nat)),map(A,nat),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linord2118332866rt_key(A,nat),B),D),C)))). [resolve(1103,a,1303,a)].
% 2.19/2.41 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(A),list(nat),hAPP(fun(A,nat),fun(list(A),list(nat)),map(A,nat),B),C))) | -hBOOL(hAPP(A,bool,D,E)) | hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),filter(A),D),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),B),E),C)) = hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),B),E),hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),filter(A),D),C)). [resolve(1103,a,1304,a)].
% 2.43/2.70 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),rev(nat),hAPP(list(A),list(nat),hAPP(fun(A,nat),fun(list(A),list(nat)),map(A,nat),B),C)))) | hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),takeWhile(A),hAPP(fun(A,nat),fun(A,bool),hAPP(fun(nat,bool),fun(fun(A,nat),fun(A,bool)),combb(nat,bool,A),hAPP(nat,fun(nat,bool),ord_less(nat),D)),B)),C) = hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),filter(A),hAPP(fun(A,nat),fun(A,bool),hAPP(fun(nat,bool),fun(fun(A,nat),fun(A,bool)),combb(nat,bool,A),hAPP(nat,fun(nat,bool),ord_less(nat),D)),B)),C). [resolve(1103,a,1305,a)].
% 2.43/2.70 Derived: -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(list(A),fun(A,bool),set(A),C))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(A),list(nat),hAPP(fun(A,nat),fun(list(A),list(nat)),map(A,nat),D),C))) | hAPP(list(A),A,hd(A),hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),filter(A),hAPP(fun(A,nat),fun(A,bool),hAPP(fun(nat,bool),fun(fun(A,nat),fun(A,bool)),combb(nat,bool,A),hAPP(nat,fun(nat,bool),fequal(nat),hAPP(A,nat,D,B))),D)),C)) != ti(A,B) | hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),hAPP(fun(A,nat),fun(A,fun(list(A),list(A))),linorder_insort_key(A,nat),D),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),remove1(A),B),C)) = C. [resolve(1103,a,1306,a)].
% 2.43/2.70 1307 semigroup_add(nat) # label(arity_Nat_Onat___Groups_Osemigroup__add) # label(axiom). [assumption].
% 2.43/2.70 1308 -semigroup_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_res) # label(axiom). [clausify(11)].
% 2.43/2.70 1309 -semigroup_add(A) | hAPP(list(A),A,hAPP(A,fun(list(A),A),hAPP(fun(A,fun(A,A)),fun(A,fun(list(A),A)),foldl(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(list(A),A,hAPP(A,fun(list(A),A),hAPP(fun(A,fun(A,A)),fun(A,fun(list(A),A)),foldl(A,A),plus_plus(A)),C),D)) # label(fact_259_foldl__assoc) # label(axiom). [clausify(338)].
% 2.43/2.70 Derived: plus_plus(nat) = ti(fun(nat,fun(nat,nat)),plus_plus(nat)). [resolve(1307,a,1308,a)].
% 2.43/2.70 Derived: hAPP(list(nat),nat,hAPP(nat,fun(list(nat),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(list(nat),nat)),foldl(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(list(nat),nat,hAPP(nat,fun(list(nat),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(list(nat),nat)),foldl(nat,nat),plus_plus(nat)),B),C)). [resolve(1307,a,1309,a)].
% 2.43/2.70 1310 zero(nat) # label(arity_Nat_Onat___Groups_Ozero) # label(axiom). [assumption].
% 2.43/2.70 1311 -zero(A) | zero_zero(A) = ti(A,zero_zero(A)) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom). [clausify(12)].
% 2.43/2.70 Derived: zero_zero(nat) = ti(nat,zero_zero(nat)). [resolve(1310,a,1311,a)].
% 2.43/2.70 1312 monoid_add(nat) # label(arity_Nat_Onat___Groups_Omonoid__add) # label(axiom). [assumption].
% 2.43/2.70 1313 -monoid_add(A) | hAPP(list(A),A,hAPP(A,fun(list(A),A),hAPP(fun(A,fun(A,A)),fun(A,fun(list(A),A)),foldl(A,A),plus_plus(A)),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(list(A),A,hAPP(A,fun(list(A),A),hAPP(fun(A,fun(A,A)),fun(A,fun(list(A),A)),foldl(A,A),plus_plus(A)),zero_zero(A)),C)) # label(fact_252_foldl__absorb0) # label(axiom). [clausify(331)].
% 2.43/2.70 1314 -monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_266_add__0__right) # label(axiom). [clausify(345)].
% 2.43/2.70 1315 -monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_269_add__0__left) # label(axiom). [clausify(348)].
% 2.43/2.70 1316 -monoid_add(A) | hAPP(list(A),A,hAPP(A,fun(list(A),A),hAPP(fun(A,fun(A,A)),fun(A,fun(list(A),A)),foldl(A,A),plus_plus(A)),zero_zero(A)),B) = hAPP(A,A,hAPP(list(A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(list(A),fun(A,A)),foldr(A,A),plus_plus(A)),B),zero_zero(A)) # label(fact_305_foldl__foldr1) # label(axiom). [clausify(384)].
% 2.65/2.87 1317 -monoid_add(A) | hAPP(list(A),A,hAPP(A,fun(list(A),A),hAPP(fun(A,fun(A,A)),fun(A,fun(list(A),A)),foldl(A,A),plus_plus(A)),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(list(A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(list(A),fun(A,A)),foldr(A,A),plus_plus(A)),C),zero_zero(A))) # label(fact_306_foldl__foldr1__lemma) # label(axiom). [clausify(385)].
% 2.65/2.87 Derived: hAPP(list(nat),nat,hAPP(nat,fun(list(nat),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(list(nat),nat)),foldl(nat,nat),plus_plus(nat)),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(list(nat),nat,hAPP(nat,fun(list(nat),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(list(nat),nat)),foldl(nat,nat),plus_plus(nat)),zero_zero(nat)),B)). [resolve(1312,a,1313,a)].
% 2.65/2.87 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),zero_zero(nat)) = ti(nat,A). [resolve(1312,a,1314,a)].
% 2.65/2.87 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),A) = ti(nat,A). [resolve(1312,a,1315,a)].
% 2.65/2.87 Derived: hAPP(list(nat),nat,hAPP(nat,fun(list(nat),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(list(nat),nat)),foldl(nat,nat),plus_plus(nat)),zero_zero(nat)),A) = hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(list(nat),fun(nat,nat)),foldr(nat,nat),plus_plus(nat)),A),zero_zero(nat)). [resolve(1312,a,1316,a)].
% 2.65/2.87 Derived: hAPP(list(nat),nat,hAPP(nat,fun(list(nat),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(list(nat),nat)),foldl(nat,nat),plus_plus(nat)),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(list(nat),fun(nat,nat)),foldr(nat,nat),plus_plus(nat)),B),zero_zero(nat))). [resolve(1312,a,1317,a)].
% 2.65/2.87 1318 cancel_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.65/2.87 1319 -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_253_add__right__imp__eq) # label(axiom). [clausify(332)].
% 2.65/2.87 1320 -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_255_add__left__imp__eq) # label(axiom). [clausify(334)].
% 2.65/2.87 1321 -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_256_add__right__cancel) # label(axiom). [clausify(335)].
% 2.65/2.87 1322 -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_256_add__right__cancel) # label(axiom). [clausify(335)].
% 2.65/2.87 1323 -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_257_add__left__cancel) # label(axiom). [clausify(336)].
% 2.65/2.87 1324 -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_257_add__left__cancel) # label(axiom). [clausify(336)].
% 2.65/2.87 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(1318,a,1319,a)].
% 2.65/2.87 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(1318,a,1320,a)].
% 2.65/2.87 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(1318,a,1322,a)].
% 2.65/2.87 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(1318,a,1324,a)].
% 2.65/2.87 1325 cancel146912293up_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.98/3.22 1326 -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_254_add__imp__eq) # label(axiom). [clausify(333)].
% 2.98/3.22 1327 ab_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 2.98/3.22 1328 -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_258_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom). [clausify(337)].
% 2.98/3.22 1329 -ab_semigroup_add(A) | hAPP(list(A),A,hAPP(A,fun(list(A),A),hAPP(fun(A,fun(A,A)),fun(A,fun(list(A),A)),foldl(A,A),plus_plus(A)),B),C) = hAPP(A,A,hAPP(list(A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(list(A),fun(A,A)),foldr(A,A),plus_plus(A)),C),B) # label(fact_312_foldr__conv__foldl) # label(axiom). [clausify(390)].
% 2.98/3.22 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(1327,a,1328,a)].
% 2.98/3.22 Derived: hAPP(list(nat),nat,hAPP(nat,fun(list(nat),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(list(nat),nat)),foldl(nat,nat),plus_plus(nat)),A),B) = hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(list(nat),fun(nat,nat)),foldr(nat,nat),plus_plus(nat)),B),A). [resolve(1327,a,1329,a)].
% 2.98/3.22 1330 comm_monoid_add(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 2.98/3.22 1331 -comm_monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_265_add_Ocomm__neutral) # label(axiom). [clausify(344)].
% 2.98/3.22 1332 -comm_monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_268_add__0) # label(axiom). [clausify(347)].
% 2.98/3.22 1333 comm_semiring_1(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 2.98/3.22 1334 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_287_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom). [clausify(366)].
% 2.98/3.22 1335 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_288_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom). [clausify(367)].
% 2.98/3.22 1336 -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_295_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom). [clausify(374)].
% 2.98/3.22 1337 -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_296_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom). [clausify(375)].
% 2.98/3.22 1338 -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_297_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom). [clausify(376)].
% 2.98/3.22 1339 -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_298_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom). [clausify(377)].
% 2.98/3.22 1340 -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_299_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom). [clausify(378)].
% 3.18/3.38 1341 -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_300_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom). [clausify(379)].
% 3.18/3.38 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(1333,a,1336,a)].
% 3.18/3.38 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(1333,a,1337,a)].
% 3.18/3.38 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(1333,a,1340,a)].
% 3.18/3.38 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(1333,a,1341,a)].
% 3.18/3.38 1342 semiri456707255roduct(nat) # label(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption].
% 3.18/3.38 1343 -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_289_add__0__iff) # label(axiom). [clausify(368)].
% 3.18/3.38 1344 -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_289_add__0__iff) # label(axiom). [clausify(368)].
% 3.18/3.38 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != ti(nat,A) | zero_zero(nat) = ti(nat,B). [resolve(1342,a,1343,a)].
% 3.18/3.38 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = ti(nat,A) | zero_zero(nat) != ti(nat,B). [resolve(1342,a,1344,a)].
% 3.18/3.38 1345 ordere236663937imp_le(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 3.18/3.38 1346 -ordere236663937imp_le(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(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)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C) # label(fact_328_max__add__distrib__left) # label(axiom). [clausify(404)].
% 3.18/3.38 1347 -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_332_add__le__cancel__right) # label(axiom). [clausify(408)].
% 3.18/3.38 1348 -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_332_add__le__cancel__right) # label(axiom). [clausify(408)].
% 3.18/3.38 1349 -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_333_add__le__cancel__left) # label(axiom). [clausify(409)].
% 3.18/3.38 1350 -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_333_add__le__cancel__left) # label(axiom). [clausify(409)].
% 3.18/3.38 1351 -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_337_add__le__imp__le__right) # label(axiom). [clausify(413)].
% 3.18/3.38 1352 -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_338_add__le__imp__le__left) # label(axiom). [clausify(414)].
% 3.18/3.38 1353 -ordere236663937imp_le(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(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)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C) # label(fact_503_min__add__distrib__left) # label(axiom). [clausify(578)].
% 3.18/3.38 1354 -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_668_add__less__cancel__right) # label(axiom). [clausify(743)].
% 3.18/3.38 1355 -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_668_add__less__cancel__right) # label(axiom). [clausify(743)].
% 3.18/3.38 1356 -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_669_add__less__cancel__left) # label(axiom). [clausify(744)].
% 3.18/3.38 1357 -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_669_add__less__cancel__left) # label(axiom). [clausify(744)].
% 3.18/3.38 1358 -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_673_add__less__imp__less__right) # label(axiom). [clausify(748)].
% 3.18/3.38 1359 -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_674_add__less__imp__less__left) # label(axiom). [clausify(749)].
% 3.18/3.38 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(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)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)),B). [resolve(1345,a,1346,a)].
% 3.18/3.38 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(1345,a,1347,a)].
% 3.18/3.38 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(1345,a,1348,a)].
% 3.18/3.38 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(1345,a,1349,a)].
% 3.18/3.38 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(1345,a,1350,a)].
% 3.18/3.38 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(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)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),B). [resolve(1345,a,1353,a)].
% 3.32/3.55 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(1345,a,1354,a)].
% 3.32/3.55 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(1345,a,1355,a)].
% 3.32/3.55 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(1345,a,1356,a)].
% 3.32/3.55 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(1345,a,1357,a)].
% 3.32/3.55 1360 ordere779506340up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 3.32/3.55 1361 -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_334_add__right__mono) # label(axiom). [clausify(410)].
% 3.32/3.55 1362 -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_335_add__left__mono) # label(axiom). [clausify(411)].
% 3.32/3.55 1363 -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_336_add__mono) # label(axiom). [clausify(412)].
% 3.32/3.55 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(1360,a,1363,a)].
% 3.32/3.55 1364 ordere216010020id_add(nat) # label(arity_Nat_Onat___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 3.32/3.55 1365 -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_362_add__nonpos__nonpos) # label(axiom). [clausify(438)].
% 3.32/3.55 1366 -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_363_add__increasing2) # label(axiom). [clausify(439)].
% 3.32/3.55 1367 -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_364_add__increasing) # label(axiom). [clausify(440)].
% 3.32/3.55 1368 -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_365_add__nonneg__eq__0__iff) # label(axiom). [clausify(441)].
% 3.32/3.55 1369 -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_365_add__nonneg__eq__0__iff) # label(axiom). [clausify(441)].
% 3.32/3.55 1370 -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_365_add__nonneg__eq__0__iff) # label(axiom). [clausify(441)].
% 3.32/3.55 1371 -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_366_add__nonneg__nonneg) # label(axiom). [clausify(442)].
% 3.32/3.55 1372 -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_708_add__pos__pos) # label(axiom). [clausify(783)].
% 3.32/3.55 1373 -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_709_add__neg__neg) # label(axiom). [clausify(784)].
% 3.32/3.55 1374 -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_737_add__nonpos__neg) # label(axiom). [clausify(812)].
% 3.32/3.55 1375 -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_738_add__neg__nonpos) # label(axiom). [clausify(813)].
% 3.32/3.55 1376 -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_739_add__strict__increasing2) # label(axiom). [clausify(814)].
% 3.32/3.55 1377 -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_740_add__strict__increasing) # label(axiom). [clausify(815)].
% 3.32/3.55 1378 -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),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_741_add__nonneg__pos) # label(axiom). [clausify(816)].
% 3.32/3.55 1379 -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),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_742_add__pos__nonneg) # label(axiom). [clausify(817)].
% 3.32/3.55 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(1364,a,1365,a)].
% 3.64/3.87 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(1364,a,1366,a)].
% 3.64/3.87 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(1364,a,1367,a)].
% 3.64/3.87 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(1364,a,1368,a)].
% 3.64/3.87 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(1364,a,1369,a)].
% 3.64/3.87 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(1364,a,1370,a)].
% 3.64/3.87 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(1364,a,1372,a)].
% 3.64/3.87 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(1364,a,1373,a)].
% 3.64/3.87 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(1364,a,1374,a)].
% 3.64/3.87 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(1364,a,1375,a)].
% 3.64/3.87 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(1364,a,1376,a)].
% 3.64/3.87 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(1364,a,1377,a)].
% 3.64/3.87 1380 ordere223160158up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.64/3.87 1381 -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_670_add__strict__right__mono) # label(axiom). [clausify(745)].
% 4.47/4.71 1382 -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_671_add__strict__left__mono) # label(axiom). [clausify(746)].
% 4.47/4.71 1383 -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_672_add__strict__mono) # label(axiom). [clausify(747)].
% 4.47/4.71 1384 -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_703_add__le__less__mono) # label(axiom). [clausify(778)].
% 4.47/4.71 1385 -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_704_add__less__le__mono) # label(axiom). [clausify(779)].
% 4.47/4.71 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(1380,a,1383,a)].
% 4.47/4.71 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(1380,a,1384,a)].
% 4.47/4.71 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(1380,a,1385,a)].
% 4.47/4.71 1386 linordered_semidom(nat) # label(arity_Nat_Onat___Rings_Olinordered__semidom) # label(axiom). [assumption].
% 4.47/4.71 1387 -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_788_pos__add__strict) # label(axiom). [clausify(863)].
% 4.47/4.71 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(1386,a,1387,a)].
% 4.47/4.71
% 4.47/4.71 ============================== end predicate elimination =============
% 4.47/4.71
% 4.47/4.71 Auto_denials: (non-Horn, no changes).
% 4.47/4.71
% 4.47/4.71 Term ordering decisions:
% 4.47/4.71 Function symbol KB weights: nat=1. bool=1. suc=1. upt=1. arrow_2142409994le_alt=1. fNot=1. fconj=1. fFalse=1. fTrue=1. fdisj=1. nat_size=1. bool_size=1. a=1. b=1. c1=1. c2=1. c3=1. fun=1. ti=1. map=1. foldl=1. linorder_insort_key=1. foldr=1. linorder_sort_key=1. combk=1. list_case=1. linord2118332866rt_key=1. maps=1. map_filter=1. list_rec=1. option_case=1. f1=1. f2=1. f3=1. f4=1. f13=1. f14=1. f15=1. f16=1. f17=1. f18=1. f79=1. f80=1. f101=1. f110=1. f114=1. f115=1. f120=1. f149=1. f168=1. f169=1. f176=1. f177=1. f179=1. f180=1. f181=1. f182=1. f197=1. f198=1. f199=1. f206=1. f207=1. f238=1. f248=1. f249=1. list=1. ord_less_eq=1. ord_less=1. cons=1. nil=1. append=1. plus_plus=1. size_size=1. zero_zero=1. member=1. set=1. minus_minus=1. nth=1. linorder_sorted=1. filter=1. ord_max=1. take=1. ord_min=1. rev=1. distinct=1. drop=1. replicate=1. takeWhile=1. list_all=1. list_update=1. dropWhile=1. transpose=1. concat=1. butlast=1. last=1. fequal=1. remove1=1. hd=1. tl=1. combi=1. listMem=1. listrelp=1. sublist=1. list_ex1=1. accp=1. collect=1. nat_case=1. member_1=1. rotate1=1. equal_equal=1. list_size=1. option=1. null=1. insert=1. n_lists=1. splice=1. fEx=1. sublists=1. if=1. transpose_rel=1. max=1. min=1. big_Sup_fin=1. big_linorder_Max=1. set_Cons=1. undefined=1. f78=1. f81=1. f126=1. f127=1. f167=1. f200=1. combb=1. combc=1. combs=1. f5=1. f6=1. f7=1. f11=1. f12=1. f20=1. f21=1. f22=1. f23=1. f24=1. f37=1. f38=1. f42=1. f45=1. f46=1. f47=1. f48=1. f49=1. f50=1. f51=1. f52=1. f53=1. f56=1. f57=1. f58=1. f59=1. f60=1. f61=1. f62=1. f63=1. f64=1. f65=1. f66=1. f67=1. f68=1. f69=1. f70=1. f71=1. f73=1. f74=1. f75=1. f76=1. f82=1. f84=1. f85=1. f86=1. f87=1. f88=1. f89=1. f90=1. f91=1. f92=1. f93=1. f111=1. f112=1. f113=1. f118=1. f122=1. f123=1. f125=1. f128=1. f129=1. f154=1. f155=1. f156=1. f157=1. f164=1. f165=1. f166=1. f170=1. f171=1. f172=1. f173=1. f174=1. f175=1. f178=1. f189=1. f190=1. f191=1. f194=1. f195=1. f196=1. f203=1. f204=1. f205=1. f227=1. f228=1. f229=1. f236=1. f237=1. f251=1. f254=1. f261=1. hAPP=1. f19=1. f33=1. f34=1. f35=1. f36=1. f39=1. f40=1. f41=1. f43=1. f44=1. f116=1. f119=1. f121=1. f124=1. f183=1. f184=1. f185=1. f186=1. f187=1. f188=1. f192=1. f193=1. f201=1. f202=1. f246=1. f247=1. f252=1. f255=1. f256=1. f8=1. f9=1. f10=1. f25=1. f26=1. f27=1. f28=1. f29=1. f30=1. f31=1. f32=1. f54=1. f55=1. f72=1. f83=1. f94=1. f95=1. f96=1. f117=1. f132=1. f133=1. f136=1. f137=1. f150=1. f151=1. f152=1. f153=1. f230=1. f231=1. f233=1. f234=1. f239=1. f240=1. f241=1. f242=1. f243=1. f244=1. f245=1. f253=1. f77=1. f99=1. f100=1. f102=1. f103=1. f104=1. f130=1. f131=1. f134=1. f135=1. f138=1. f139=1. f140=1. f141=1. f142=1. f143=1. f144=1. f145=1. f210=1. f211=1. f212=1. f213=1. f214=1. f215=1. f216=1. f217=1. f218=1. f219=1. f220=1. f221=1. f222=1. f223=1. f224=1. f225=1. f250=1. f257=1. f258=1. f259=1. f260=1. f105=1. f106=1. f107=1. f146=1. f147=1. f148=1. f232=1. f235=1. f97=1. f98=1. f108=1. f109=1.
% 6.73/6.96
% 6.73/6.96 ============================== end of process initial clauses ========
% 6.73/6.96
% 6.73/6.96 ============================== CLAUSES FOR SEARCH ====================
% 6.73/6.96
% 6.73/6.96 ============================== end of clauses for search =============
% 6.73/6.96
% 6.73/6.96 ============================== SEARCH ================================
% 6.73/6.96
% 6.73/6.96 % Starting search at 2.71 seconds.
% 6.73/6.96
% 6.73/6.96 Low Water (keep): wt=182.000, iters=3583
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% 6.73/6.96 Low Water (keep): wt=170.000, iters=3474
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% 6.73/6.96 Low Water (keep): wt=160.000, iters=3387
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% 6.73/6.96 Low Water (keep): wt=157.000, iters=3380
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% 6.73/6.96 Low Water (keep): wt=151.000, iters=3348
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% 6.73/6.96 Low Water (keep): wt=148.000, iters=3340
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% 6.73/6.96 Low Water (keep): wt=139.000, iters=3366
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% 6.73/6.96 Low Water (keep): wt=112.000, iters=3349
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% 6.73/6.96 Low Water (keep): wt=111.000, iters=3396
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% 6.73/6.96 Low Water (keep): wt=108.000, iters=3435
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% 6.73/6.96 Low Water (keep): wt=92.000, iters=3380
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% 6.73/6.96 Low Water (keep): wt=91.000, iters=3353
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% 6.73/6.96 Low Water (keep): wt=88.000, iters=3392
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% 6.73/6.96 Low Water (keep): wt=86.000, iters=3343
% 6.73/6.96
% 6.73/6.96 Low Water (keep): wt=85.000, iters=3337
% 6.73/6.96
% 6.73/6.96 Low Water (keep): wt=83.000, iters=3341
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=80.000, iters=3350
% 227.56/227.87
% 227.56/227.87 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 100 (0.00 of 5.10 sec).
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=79.000, iters=3361
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=78.000, iters=3377
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% 227.56/227.87 Low Water (keep): wt=77.000, iters=3353
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% 227.56/227.87 Low Water (keep): wt=76.000, iters=3354
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=75.000, iters=3466
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=74.000, iters=3506
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=72.000, iters=3401
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% 227.56/227.87 Low Water (keep): wt=71.000, iters=3363
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=70.000, iters=3407
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=69.000, iters=3362
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% 227.56/227.87 Low Water (keep): wt=68.000, iters=3349
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=67.000, iters=3336
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=66.000, iters=3388
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=65.000, iters=3344
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=64.000, iters=3356
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=63.000, iters=3342
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=62.000, iters=3334
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=61.000, iters=3336
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=60.000, iters=3354
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% 227.56/227.87 Low Water (keep): wt=59.000, iters=3351
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% 227.56/227.87 Low Water (keep): wt=58.000, iters=3339
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=57.000, iters=3357
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=56.000, iters=3362
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=55.000, iters=3352
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=54.000, iters=3378
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=53.000, iters=3350
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=52.000, iters=3380
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=51.000, iters=3374
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=50.000, iters=3368
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=49.000, iters=3356
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=48.000, iters=3367
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=47.000, iters=3394
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=46.000, iters=3335
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=45.000, iters=3342
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=4165, wt=199.000
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=4769, wt=197.000
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=13620, wt=40.000
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=13621, wt=39.000
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=13625, wt=32.000
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=14275, wt=31.000
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=14371, wt=29.000
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=44.000, iters=3406
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=14653, wt=28.000
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=14692, wt=27.000
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=14956, wt=26.000
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=15217, wt=25.000
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=15574, wt=23.000
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=15576, wt=22.000
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=15929, wt=21.000
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=17174, wt=20.000
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=18275, wt=19.000
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=18856, wt=17.000
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=19090, wt=16.000
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=19402, wt=14.000
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=42.000, iters=3721
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=41.000, iters=3496
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=21076, wt=12.000
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=40.000, iters=3333
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=39.000, iters=3333
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=40548, wt=11.000
% 227.56/227.87
% 227.56/227.87 Low Water (displace): id=52063, wt=10.000
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=38.000, iters=3586
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=37.000, iters=3336
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=36.000, iters=3343
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=35.000, iters=3343
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=34.000, iters=3360
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=33.000, iters=3354
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=32.000, iters=3337
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=31.000, iters=3436
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=30.000, iters=3390
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=29.000, iters=3333
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=28.000, iters=3413
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=27.000, iters=3334
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=26.000, iters=3333
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=25.000, iters=3346
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=24.000, iters=3334
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=23.000, iters=3391
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=22.000, iters=3335
% 227.56/227.87
% 227.56/227.87 Low Water (keep): wt=21.000, iters=3333
% 227.56/227.87
% 227.56/227.87 ============================== STATISTICS ============================
% 227.56/227.87
% 227.56/227.87 Given=10856. Generated=3618065. Kept=227204. proofs=0.
% 227.56/227.87 Usable=10576. Sos=9999. Demods=817. Limbo=11, Disabled=208477. Hints=0.
% 227.56/227.87 Kept_by_rule=0, Deleted_by_rule=91780.
% 227.56/227.87 Forward_subsumed=464536. Back_subsumed=70.
% 227.56/227.87 Sos_limit_deleted=2834544. Sos_displaced=205648. Sos_removed=0.
% 227.56/227.87 New_demodulators=1598 (0 lex), Back_demodulated=898. Back_unit_deleted=2.
% 227.56/227.87 Demod_attempts=205501026. Demod_rewrites=615419.
% 227.56/227.87 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
% 227.56/227.87 Nonunit_fsub_feature_tests=4706716. Nonunit_bsub_feature_tests=12902.
% 227.56/227.87 Megabytes=419.43.
% 227.56/227.87 User_CPU=223.63, System_CPU=2.18, Wall_clock=226.
% 227.56/227.87
% 227.56/227.87 Megs malloced by palloc(): 400.
% 227.56/227.87 type (bytes each) gets frees in use bytes
% 227.56/227.87 chunk ( 104) 86112 86112 0 0.0 K
% 227.56/227.87 string_buf ( 8) 77288 77288 0 0.0 K
% 227.56/227.87 token ( 20) 198213 198213 0 0.0 K
% 227.56/227.87 pterm ( 16) 136127 136127 0 0.0 K
% 227.56/227.87 hashtab ( 8) 1102 1102 0 0.0 K
% 227.56/227.87 hashnode ( 8) 4308 4308 0 0.0 K
% 227.56/227.87 term ( 20) 332250951 325253435 6997516 136670.2 K
% 227.56/227.87 term arg arrays: 29918.1 K
% 227.56/227.87 attribute ( 12) 8912 286 8626 101.1 K
% 227.56/227.87 ilist ( 8) 1635458910 1634211590 1247320 9744.7 K
% 227.56/227.87 plist ( 8) 7642856 7377149 265707 2075.8 K
% 227.56/227.87 i2list ( 12) 30594936 30594936 0 0.0 K
% 227.56/227.87 just ( 12) 4586920 4300459 286461 3357.0 K
% 227.56/227.87 parajust ( 16) 3033497 2862436 171061 2672.8 K
% 227.56/227.87 instancejust ( 8) 0 0 0 0.0 K
% 227.56/227.87 ivyjust ( 24) 0 0 0 0.0 K
% 227.56/227.87 formula ( 28) 45835 29787 16048 438.8 K
% 227.56/227.87 formula arg arrays: 54.1 K
% 227.56/227.87 topform ( 52) 3621092 3390860 230232 11691.5 K
% 227.56/227.87 clist_pos ( 20) 678515 448635 229880 4489.8 K
% 227.56/227.87 clist ( 16) 8 1 7 0.1 K
% 227.56/227.87 context ( 808) 26596382 26596380 2 1.6 K
% 227.56/227.87 trail ( 12) 19011021 19011020 1 0.0 K
% 227.56/227.87 ac_match_pos (70044) 0 0 0 0.0 K
% 227.56/227.87 ac_match_free_vars_pos (20020)
% 227.56/227.87 0 0 0 0.0 K
% 227.56/227.87 btm_state ( 60) 0 0 0 0.0 K
% 227.56/227.87 btu_state ( 60) 0 0 0 0.0 K
% 227.56/227.87 ac_position (285432) 0 0 0 0.0 K
% 227.56/227.87 fpa_trie ( 20) 1112343 843097 269246 5258.7 K
% 227.56/227.87 fpa_state ( 28) 10566130 10566130 0 0.0 K
% 227.56/227.87 fpa_index ( 12) 10 0 10 0.1 K
% 227.56/227.87 fpa_chunk ( 20) 1676595 1567206 109389 2136.5 K
% 227.56/227.87 fpa_list ( 16) 901792 0 901792 14090.5 K
% 227.56/227.87 fpa_list chunks: 9943.6 K
% 227.56/227.87 discrim ( 12) 1665375 1584874 80501 943.4 K
% 227.56/227.87 discrim_pos ( 16) 695263 695263 0 0.0 K
% 227.56/227.87 flat2 ( 32) 142239039 142239039 0 0.0 K
% 227.56/227.87 flat ( 48) 0 0 0 0.0 K
% 227.56/227.87 flatterm ( 32) 268220200 268220200 0 0.0 K
% 227.56/227.87 mindex ( 28) 13 0 13 0.4 K
% 227.56/227.87 mindex_pos ( 56) 19257981 19257981 0 0.0 K
% 227.56/227.87 lindex ( 12) 5 0 5 0.1 K
% 227.56/227.87 clash ( 40) 0 0 0 0.0 K
% 227.56/227.87 di_tree ( 12) 124715274 111476106 13239168 155146.5 K
% 227.56/227.87 avl_node ( 20) 452731 432733 19998 390.6 K
% 227.56/227.87
% 227.56/227.87 Memory report, 20 @ 20 = 400 megs (400.00 megs used).
% 227.56/227.87 List 1, length 5, 0.0 K
% 227.56/227.87 List 2, length 1398, 10.9 K
% 227.56/227.87 List 3, length 1286740, 15079.0 K
% 227.56/227.87 List 8, length 545, 17.0 K
% 227.56/227.87 List 10, length 12, 0.5 K
% 227.56/227.87 List 11, length 18, 0.8 K
% 227.56/227.87 List 12, length 9, 0.4 K
% 227.56/227.87 List 14, length 2, 0.1 K
% 227.56/227.87 List 16, length 147, 9.2 K
% 227.56/227.87 List 26, length 1203, 122.2 K
% 227.56/227.87 List 64, length 64, 16.0 K
% 227.56/227.87 List 128, length 133, 66.5 K
% 227.56/227.87 List 202, length 2, 1.6 K
% 227.56/227.87 List 256, length 7, 7.0 K
% 227.56/227.87
% 227.56/227.87 ============================== SELECTOR REPORT =======================
% 227.56/227.87 Sos_deleted=2834544, Sos_displaced=205648, Sos_size=9999
% 227.56/227.87 SELECTOR PART PRIORITY ORDER SIZE SELECTED
% 227.56/227.87 I 2147483647 high age 0 1385
% 227.56/227.87 H 1 high weight 0 0
% 227.56/227.87 A 1 low age 9999 1053
% 227.56/227.87 F 4 low weight 131 4210
% 227.56/227.87 T 4 low weight 9868 4208
% 227.56/227.87 ============================== end of selector report ================
% 227.56/227.87
% 227.56/227.87 ============================== end of statistics =====================
% 227.56/227.87
% 227.56/227.87 Exiting with failure.
% 227.56/227.87
% 227.56/227.87 Process 20609 exit (max_megs) Sat Jul 2 02:38:36 2022
% 227.56/227.87 Prover9 interrupted
%------------------------------------------------------------------------------