TSTP Solution File: SCT169+6 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT169+6 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 259.08s 259.47s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SCT169+6 : TPTP v8.1.0. Released v5.3.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n024.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 : Fri Jul 1 22:18:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.21/1.54 ============================== Prover9 ===============================
% 1.21/1.54 Prover9 (32) version 2009-11A, November 2009.
% 1.21/1.54 Process 24852 was started by sandbox on n024.cluster.edu,
% 1.21/1.54 Fri Jul 1 22:18:16 2022
% 1.21/1.54 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_24699_n024.cluster.edu".
% 1.21/1.54 ============================== end of head ===========================
% 1.21/1.54
% 1.21/1.54 ============================== INPUT =================================
% 1.21/1.54
% 1.21/1.54 % Reading from file /tmp/Prover9_24699_n024.cluster.edu
% 1.21/1.54
% 1.21/1.54 set(prolog_style_variables).
% 1.21/1.54 set(auto2).
% 1.21/1.54 % set(auto2) -> set(auto).
% 1.21/1.54 % set(auto) -> set(auto_inference).
% 1.21/1.54 % set(auto) -> set(auto_setup).
% 1.21/1.54 % set(auto_setup) -> set(predicate_elim).
% 1.21/1.54 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.21/1.54 % set(auto) -> set(auto_limits).
% 1.21/1.54 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.21/1.54 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.21/1.54 % set(auto) -> set(auto_denials).
% 1.21/1.54 % set(auto) -> set(auto_process).
% 1.21/1.54 % set(auto2) -> assign(new_constants, 1).
% 1.21/1.54 % set(auto2) -> assign(fold_denial_max, 3).
% 1.21/1.54 % set(auto2) -> assign(max_weight, "200.000").
% 1.21/1.54 % set(auto2) -> assign(max_hours, 1).
% 1.21/1.54 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.21/1.54 % set(auto2) -> assign(max_seconds, 0).
% 1.21/1.54 % set(auto2) -> assign(max_minutes, 5).
% 1.21/1.54 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.21/1.54 % set(auto2) -> set(sort_initial_sos).
% 1.21/1.54 % set(auto2) -> assign(sos_limit, -1).
% 1.21/1.54 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.21/1.54 % set(auto2) -> assign(max_megs, 400).
% 1.21/1.54 % set(auto2) -> assign(stats, some).
% 1.21/1.54 % set(auto2) -> clear(echo_input).
% 1.21/1.54 % set(auto2) -> set(quiet).
% 1.21/1.54 % set(auto2) -> clear(print_initial_clauses).
% 1.21/1.54 % set(auto2) -> clear(print_given).
% 1.21/1.54 assign(lrs_ticks,-1).
% 1.21/1.54 assign(sos_limit,10000).
% 1.21/1.54 assign(order,kbo).
% 1.21/1.54 set(lex_order_vars).
% 1.21/1.54 clear(print_given).
% 1.21/1.54
% 1.21/1.54 % formulas(sos). % not echoed (644 formulas)
% 1.21/1.54
% 1.21/1.54 ============================== end of input ==========================
% 1.21/1.54
% 1.21/1.54 % From the command line: assign(max_seconds, 300).
% 1.21/1.54
% 1.21/1.54 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.21/1.54
% 1.21/1.54 % Formulas that are not ordinary clauses:
% 1.21/1.54 1 (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].
% 1.21/1.54 2 (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].
% 1.21/1.54 3 (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].
% 1.21/1.54 4 (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].
% 1.21/1.54 5 (all X_a (minus(X_a) -> ti(fun(X_a,fun(X_a,X_a)),minus_minus(X_a)) = minus_minus(X_a))) # label(tsy_c_Groups_Ominus__class_Ominus_res) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 6 (all X_a (one(X_a) -> ti(X_a,one_one(X_a)) = one_one(X_a))) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 7 (all X_a (monoid_add(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 8 (all X_a (ab_semigroup_add(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 9 (all X_a (cancel_semigroup_add(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_2_res) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 10 (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].
% 1.21/1.54 11 (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].
% 1.21/1.54 12 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 13 (all X_a (number_ring(X_a) -> ti(fun(int,X_a),number_number_of(X_a)) = number_number_of(X_a))) # label(tsy_c_Int_Onumber__class_Onumber__of_0_res) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 14 (all X_a (ring_1(X_a) -> ti(fun(X_a,bool),ring_1_Ints(X_a)) = ring_1_Ints(X_a))) # label(tsy_c_Int_Oring__1__class_OInts_res) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 15 (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].
% 1.21/1.54 16 (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].
% 1.21/1.54 17 (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].
% 1.21/1.54 18 (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].
% 1.21/1.54 19 (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].
% 1.21/1.54 20 (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].
% 1.21/1.54 21 (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].
% 1.21/1.54 22 (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].
% 1.21/1.54 23 (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].
% 1.21/1.54 24 (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].
% 1.21/1.54 25 (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].
% 1.21/1.54 26 (all X_a (linorder(X_a) -> ti(fun(fun(X_a,bool),list(X_a)),linord467138063of_set(X_a)) = linord467138063of_set(X_a))) # label(tsy_c_List_Olinorder__class_Osorted__list__of__set_res) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 27 (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].
% 1.21/1.54 28 (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].
% 1.21/1.54 29 (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].
% 1.21/1.54 30 (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].
% 1.21/1.54 31 (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].
% 1.21/1.54 32 (all X_a ti(fun(fun(X_a,bool),fun(list(X_a),bool)),list_ex(X_a)) = list_ex(X_a)) # label(tsy_c_List_Olist__ex_res) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 33 (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].
% 1.21/1.54 34 (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].
% 1.21/1.54 35 (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].
% 1.21/1.54 36 (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].
% 1.21/1.54 37 (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].
% 1.21/1.54 38 (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].
% 1.21/1.54 39 (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].
% 1.21/1.54 40 (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].
% 1.21/1.54 41 (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].
% 1.21/1.54 42 (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].
% 1.21/1.54 43 (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].
% 1.21/1.54 44 (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].
% 1.21/1.54 45 (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].
% 1.21/1.54 46 (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].
% 1.21/1.54 47 (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].
% 1.21/1.54 48 (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].
% 1.21/1.54 49 (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_res) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 50 (all X_b (bot(X_b) -> ti(X_b,bot_bot(X_b)) = bot_bot(X_b))) # label(tsy_c_Orderings_Obot__class_Obot_res) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 51 (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].
% 1.21/1.54 52 (all X_a (ordere236663937imp_le(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_0_res) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 53 (all X_a (linorder(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_1_res) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 54 (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].
% 1.21/1.54 55 (all X_a ti(fun(X_a,fun(X_a,bool)),fequal(X_a)) = fequal(X_a)) # label(tsy_c_fequal_res) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 56 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_arg1) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 57 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 58 (all X_c all X_a all B_1_1 all B_2_1 ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_res) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 59 (all B_1_1 (hBOOL(ti(bool,B_1_1)) <-> hBOOL(B_1_1))) # label(tsy_c_hBOOL_arg1) # label(hypothesis) # label(non_clause). [assumption].
% 1.21/1.54 60 (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].
% 1.21/1.54 61 (exists A_4 exists B_2 exists C hBOOL(hAPP(list(arrow_490897120le_alt),bool,distinct(arrow_490897120le_alt),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),A_4),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),B_2),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),C),nil(arrow_490897120le_alt))))))) # label(fact_0_alt3) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 62 (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].
% 1.21/1.54 63 (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].
% 1.21/1.54 64 (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].
% 1.21/1.54 65 (all X_a all Xs_1 (Xs_1 != nil(X_a) <-> (exists Y_1 exists Ys_2 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_2)))) # label(fact_4_neq__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 66 (all X_a all Y (Y != nil(X_a) -> -(all A_4 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_4),List_3)))) # label(fact_5_list_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 67 (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].
% 1.21/1.54 68 (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].
% 1.21/1.54 69 (all X_a all Aa all List all A_3 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) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_3),List_2) <-> ti(X_a,Aa) = ti(X_a,A_3) & List = List_2)) # label(fact_8_list_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 70 (all X_a all V 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),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),Va)) # label(fact_9_splice_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 71 (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].
% 1.21/1.54 72 (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].
% 1.21/1.54 73 (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].
% 1.21/1.54 74 (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].
% 1.21/1.54 75 (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].
% 1.21/1.54 76 (all X_a all X all Xs all Y all Ys 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)) = 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)))) # label(fact_15_splice_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 77 (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].
% 1.21/1.54 78 (all X_a all Ys 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) = Ys) # label(fact_17_splice_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 79 (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].
% 1.21/1.54 80 (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].
% 1.21/1.54 81 (all X_b all X_a all F1 all F2 all Aa all List 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)) = hAPP(list(X_b),X_a,hAPP(X_b,fun(list(X_b),X_a),F2,Aa),List)) # label(fact_20_list_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 82 (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].
% 1.21/1.54 83 (all X_b all X_a all F1 all F2 all Aa all List 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)) = 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),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))) # label(fact_22_list_Orecs_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 84 (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].
% 1.21/1.54 85 (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].
% 1.21/1.54 86 (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].
% 1.21/1.54 87 (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].
% 1.21/1.54 88 (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].
% 1.21/1.54 89 (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].
% 1.21/1.54 90 (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].
% 1.21/1.54 91 (all X_a (linorder(X_a) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),nil(X_a))))) # label(fact_30_sorted_ONil) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 92 (all X_a all Xs all Ys 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)),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),Zs_2))) # label(fact_31_append__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 93 (all X_a all Xs_1 all Ys_1 all Zs 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_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs),Ts) <-> (exists Us_1 (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs),Us_1) & hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us_1),Ys_1) = 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_1) = Zs & Ys_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us_1),Ts))))) # label(fact_32_append__eq__append__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 94 (all X_a all Xs_1 all Ys_1 all Zs (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Zs) <-> Ys_1 = Zs)) # label(fact_33_same__append__eq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 95 (all X_a all Ys_1 all Xs_1 all Zs (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs),Xs_1) <-> Ys_1 = Zs)) # label(fact_34_append__same__eq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 96 (all X_a all Ys all Us 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 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs1),Us) -> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs_2),Us)))) # label(fact_35_append__eq__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 97 (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_36_maps__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 98 (all X_a all X all Xs all 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)),cons(X_a),X),Xs)),Ys) = 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))) # label(fact_37_append__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 99 (all X_a all Xs all Zs_2 all X all Xs1 all Ys (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs1) = Ys -> (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),Zs_2)))) # label(fact_38_Cons__eq__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 100 (all X_a all Ys 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) = Ys) # label(fact_39_append__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 101 (all X_a all Xs_1 all Ys_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),Xs_1),Ys_1) <-> Xs_1 = nil(X_a) & Ys_1 = nil(X_a))) # label(fact_40_Nil__is__append__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 102 (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_41_append__Nil2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 103 (all X_a all Xs_1 all Ys_1 (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_1) <-> Ys_1 = nil(X_a))) # label(fact_42_self__append__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 104 (all X_a all Ys_1 all Xs_1 (Ys_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_1) <-> Xs_1 = nil(X_a))) # label(fact_43_self__append__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 105 (all X_a all Xs_1 all Ys_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_1) = nil(X_a) <-> Xs_1 = nil(X_a) & Ys_1 = nil(X_a))) # label(fact_44_append__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 106 (all X_a all Xs_1 all Ys_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_1) = Xs_1 <-> Ys_1 = nil(X_a))) # label(fact_45_append__self__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 107 (all X_a all Xs_1 all Ys_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_1) = Ys_1 <-> Xs_1 = nil(X_a))) # label(fact_46_append__self__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 108 (all X_a all Xs all Ys (Xs = Ys -> 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))) # label(fact_47_eq__Nil__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 109 (all X_a all Ys_1 all Zs 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_1),Zs) = 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_1 = nil(X_a) & Zs = 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_3 (Ys_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Ys_3) & hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),Zs) = Xs_1)))) # label(fact_48_append__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 110 (all X_a all X_1 all Xs_1 all Ys_1 all Zs (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_1),Zs) <-> Ys_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),Xs_1) = Zs | (exists Ys_3 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Ys_3) = Ys_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_3),Zs))))) # label(fact_49_Cons__eq__append__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 111 (all X_a all Xs_1 all X_1 all Ys_1 all Y_2 (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_1),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))) <-> Xs_1 = Ys_1 & ti(X_a,X_1) = ti(X_a,Y_2))) # label(fact_50_append1__eq__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 112 (all X_a all Xs all Ys ((Ys = 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)) = hAPP(list(X_a),list(X_a),butlast(X_a),Xs)) & (Ys != 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)) = 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))))) # label(fact_51_butlast__append) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 113 (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_52_sorted__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 114 (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_53_rev__induct) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 115 (all X_a all Xs (Xs != nil(X_a) -> -(all Ys_2 all Y_1 Xs != hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_2),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_54_rev__cases) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 116 (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_55_equal__Nil__null) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 117 (all X_a all Xs_1 all X_1 all Ys_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))) = Ys_1 <-> Ys_1 != nil(X_a) & hAPP(list(X_a),list(X_a),butlast(X_a),Ys_1) = Xs_1 & hAPP(list(X_a),X_a,last(X_a),Ys_1) = ti(X_a,X_1))) # label(fact_56_snoc__eq__iff__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 118 (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_57_append__butlast__last__id) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 119 (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_58_rotate__simps) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.54 120 (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_59_last__snoc) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 121 (all X_a all Ws (-hBOOL(hAPP(list(X_a),bool,distinct(X_a),Ws)) -> (exists Xs_2 exists Ys_2 exists Zs_1 exists Y_1 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_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_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_1),nil(X_a))),Zs_1))))))) # label(fact_60_not__distinct__decomp) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 122 (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_61_replicate__append__same) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 123 (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_62_rev_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 124 (all X_a all Xs_1 all Ys_1 (hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) = hAPP(list(X_a),list(X_a),rev(X_a),Ys_1) <-> Xs_1 = Ys_1)) # label(fact_63_rev__is__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 125 (all X_a all Xs_1 all Ys_1 (hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) = Ys_1 <-> Xs_1 = hAPP(list(X_a),list(X_a),rev(X_a),Ys_1))) # label(fact_64_rev__swap) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 126 (all X_a all N 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),X)) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)) # label(fact_65_rev__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 127 (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_66_rev__rev__ident) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 128 (all X_a all X_1 all Y_2 (hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),equal_equal(list(X_a)),X_1),Y_2)) <-> X_1 = Y_2)) # label(fact_67_equal__list__def) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 129 (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_68_rev__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 130 (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_69_Nil__is__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 131 (all X_a hAPP(list(X_a),list(X_a),rev(X_a),nil(X_a)) = nil(X_a)) # label(fact_70_rev_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 132 (all X_a all Xs all Ys 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)) = 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),rev(X_a),Xs))) # label(fact_71_rev__append) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 133 (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_72_distinct__rev) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 134 (all X_a all N 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),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),X))) # label(fact_73_append__replicate__commute) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 135 (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_74_rotate1__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 136 (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].
% 1.21/1.55 137 (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].
% 1.21/1.55 138 (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].
% 1.21/1.55 139 (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_78_distinct1__rotate) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 140 (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_79_singleton__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 141 (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_80_rev__singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 142 (all X_a all N 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),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),X)),Xs))) # label(fact_81_replicate__app__Cons__same) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 143 (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_82_last__ConsL) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 144 (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_83_last__ConsR) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 145 (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_84_last_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 146 (all X_a all Xs all Ys ((Ys = 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)) = hAPP(list(X_a),X_a,last(X_a),Xs)) & (Ys != 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)) = hAPP(list(X_a),X_a,last(X_a),Ys)))) # label(fact_85_last__append) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 147 (all X_a all Xs all Ys (Ys != 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)) = hAPP(list(X_a),X_a,last(X_a),Ys))) # label(fact_86_last__appendR) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 148 (all X_a all Xs all Ys (Ys = 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)) = hAPP(list(X_a),X_a,last(X_a),Xs))) # label(fact_87_last__appendL) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 149 (all X_a all Xs_1 all Y_2 all Ys_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),Y_2),Ys_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(list(X_a),list(X_a),rev(X_a),Ys_1)),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_88_rev__eq__Cons__iff) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 150 (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_89_last__rev) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 151 (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_90_hd__rev) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 152 (all X_a (cl_HOL_Oequal(X_a) -> equal_equal(X_a) = fequal(X_a))) # label(fact_91_equal) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 153 (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_92_equal__refl) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 154 (all X_a (cl_HOL_Oequal(X_a) -> (all X_1 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),equal_equal(X_a),X_1),Y_2)) <-> ti(X_a,X_1) = ti(X_a,Y_2))))) # label(fact_93_equal__eq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 155 (all X_a (cl_HOL_Oequal(X_a) -> fequal(X_a) = equal_equal(X_a))) # label(fact_94_eq__equal) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 156 (all X_a all Ys 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)) = hAPP(list(X_a),X_a,hd(X_a),Ys)) & (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)) = hAPP(list(X_a),X_a,hd(X_a),Xs)))) # label(fact_95_hd__append) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 157 (all X_a all Ys 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)) = hAPP(list(X_a),X_a,hd(X_a),Xs))) # label(fact_96_hd__append2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 158 (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_97_rotate1__hd__tl) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 159 (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_98_tl_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 160 (all X_a hAPP(list(X_a),list(X_a),tl(X_a),nil(X_a)) = nil(X_a)) # label(fact_99_tl_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 161 (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_100_hd_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 162 (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_101_distinct__tl) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 163 (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_102_sorted__tl) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 164 (all X_a all Ys 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)) = 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))) # label(fact_103_tl__append2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 165 (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].
% 1.21/1.55 166 (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_105_member__rec_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 167 (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_106_list__ex1__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 168 (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_107_elem) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 169 (all X_a all X_1 all Xs_1 all Y_2 (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_2)) <-> ti(X_a,X_1) = ti(X_a,Y_2) | hBOOL(hAPP(X_a,bool,hAPP(list(X_a),fun(X_a,bool),member_1(X_a),Xs_1),Y_2)))) # label(fact_108_member__rec_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 170 (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_109_insert) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 171 (all X_a all X all N (N != 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),X)) = ti(X_a,X))) # label(fact_110_hd__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 172 (all X_a all X all N (N != 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),X)) = ti(X_a,X))) # label(fact_111_last__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 173 (all X_a all M_1 all X_1 all N_2 all Y_2 (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),M_1),X_1) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_2),Y_2) <-> M_1 = N_2 & (M_1 != zero_zero(nat) -> ti(X_a,X_1) = ti(X_a,Y_2)))) # label(fact_112_replicate__eq__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 174 (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_113_dropWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 175 (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_114_dropWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 176 (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_115_distinct__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 177 (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_116_sorted__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 178 (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_117_replicate__0) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 179 (all X_a all N_2 all X_1 (nil(X_a) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_2),X_1) <-> N_2 = zero_zero(nat))) # label(fact_118_empty__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 180 (all X_a all N_2 all X_1 (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_2),X_1) = nil(X_a) <-> N_2 = zero_zero(nat))) # label(fact_119_replicate__empty) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 181 (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_120_sublist__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 182 (all X_a all P_1 all Xs_1 all Y_2 all Ys_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(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_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(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_2),Ys_1)) & -hBOOL(hAPP(X_a,bool,P_1,Y_2)))) # label(fact_121_dropWhile__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 183 (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_122_list_Osize_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 184 (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_1 (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_1),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_123_ListMem_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 185 (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_124_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 186 (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_125_hd__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 187 (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_126_takeWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 188 (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_127_distinct__takeWhile) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 189 (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_128_sorted__takeWhile) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 190 (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_129_sublist__nil) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 191 (all X_a all I_4 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_4))))) # label(fact_130_distinct__sublistI) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 192 (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_131_nth__Cons__0) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 193 (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_132_takeWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 194 (all X_a all Xs_1 all L_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(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_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))) # label(fact_133_takeWhile__tail) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 195 (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_134_takeWhile__dropWhile__id) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 196 (all X_a all Xs all X all Ys 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))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)) = ti(X_a,X)) # label(fact_135_nth__append__length) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 197 (all X_a (linorder(X_a) -> (all Y_2 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_2) = ti(X_a,Y_2)) & (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_2) = 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_2)))))) # label(fact_136_foldr__max__sorted) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 198 (all X_b all X_a all Xs_1 all Ys_1 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_1 all Ys_2 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_1),Ys_2)))) -> ((all X_2 all Xs_2 all Y_1 all Ys_2 (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,Xs_2),Ys_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)),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Y_1),Ys_2))))) -> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,Xs_1),Ys_1))))))) # label(fact_137_list__induct2_H) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 199 (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_138_map__filter__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 200 (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_139_listrelp_ONil) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 201 (all X_a all Xs_1 all Ys_1 all R_1 all X_1 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,X_1),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_1),Ys_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),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_2),Ys_1)))))) # label(fact_140_listrelp_OCons) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 202 (all X_a all 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),bot_bot(fun(nat,bool))) = nil(X_a)) # label(fact_141_sublist__empty) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 203 (all X_a all Xs all Ys (hAPP(list(X_a),nat,size_size(list(X_a)),Xs) != hAPP(list(X_a),nat,size_size(list(X_a)),Ys) -> Xs != Ys)) # label(fact_142_neq__if__length__neq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 204 (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_143_length__rev) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 205 (all X_a all N 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),X)) = N) # label(fact_144_length__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 206 (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_145_length__rotate1) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 207 (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_146_foldr_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.55 208 (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_147_foldr_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 209 (all X_a all X_b all F all Xs_1 all Ys_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(list(X_b),fun(list(X_b),list(X_b)),append(X_b),Xs_1),Ys_1)),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_1),Aa))) # label(fact_148_foldr__append) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 210 (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_149_length__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 211 (all X_a hAPP(list(X_a),nat,size_size(list(X_a)),nil(X_a)) = zero_zero(nat)) # label(fact_150_list_Osize_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 212 (all X_a all X_b all P_1 all Xs_1 all Ys_1 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(list(X_b),nat,size_size(list(X_b)),Ys_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 all Y_1 all Ys_2 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_2) = hAPP(list(X_b),nat,size_size(list(X_b)),Ys_2) -> (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,Xs_2),Ys_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)),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Y_1),Ys_2)))))) -> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,Xs_1),Ys_1)))))) # label(fact_151_list__induct2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 213 (all X_a all Aa -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),bot_bot(fun(X_a,bool))))) # label(fact_152_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 214 (all X_a all X_b (bot(X_b) -> (all X_2 hAPP(X_a,X_b,bot_bot(fun(X_a,X_b)),X_2) = bot_bot(X_b)))) # label(fact_153_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 215 (all X_b all X_a (bot(X_a) -> (all X_1 hAPP(X_b,X_a,bot_bot(fun(X_b,X_a)),X_1) = bot_bot(X_a)))) # label(fact_154_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 216 (all X_a all N exists Xs_2 hAPP(list(X_a),nat,size_size(list(X_a)),Xs_2) = N) # label(fact_155_Ex__list__of__length) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 217 (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_1 exists Xs_2 exists Ys_2 (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_1),Ys_2) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,X_2),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_2),Ys_2)))))) # label(fact_156_listrelp_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 218 (all X_a all Aa all A_1 (ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),A_1)))) # label(fact_157_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 219 (all X_a all P_1 (hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1) = bot_bot(fun(X_a,bool)) <-> (all X_2 -hBOOL(hAPP(X_a,bool,P_1,X_2))))) # label(fact_158_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 220 (all X_a all C_1 -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),bot_bot(fun(X_a,bool))))) # label(fact_159_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 221 (all X_a all P_1 (bot_bot(fun(X_a,bool)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1) <-> (all X_2 -hBOOL(hAPP(X_a,bool,P_1,X_2))))) # label(fact_160_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 222 (all X_a all A_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),A_1))) <-> ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)))) # label(fact_161_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 223 (all X_a 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))) <-> ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)))) # label(fact_162_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 224 (all X_a bot_bot(fun(X_a,bool)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(bool,fun(X_a,bool),combk(bool,X_a),fFalse))) # label(fact_163_empty__def) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 225 (all X_a all A_1 ((all Y_1 -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1))) -> ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)))) # label(fact_164_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 226 (all X_a (linorder(X_a) -> hAPP(fun(X_a,bool),list(X_a),linord467138063of_set(X_a),bot_bot(fun(X_a,bool))) = nil(X_a))) # label(fact_165_sorted__list__of__set__empty) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 227 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z))))) # label(fact_166_min__max_Osup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 228 (all X_a (linorder(X_a) -> (all A_2 all B_1 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_1)),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_1),C_2))))) # label(fact_167_min__max_Osup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 229 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z))))) # label(fact_168_min__max_Osup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 230 (all X_a (linorder(X_a) -> (all B_1 all A_2 all C_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_1),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_1),C_2))))) # label(fact_169_min__max_Osup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 231 (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_170_min__max_Osup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 232 (all X_a (linorder(X_a) -> (all A_2 all B_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_1),A_2)))) # label(fact_171_min__max_Osup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 233 (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_172_min__max_Osup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 234 (all X_a (linorder(X_a) -> (all A_2 all B_1 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_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_1)))) # label(fact_173_min__max_Osup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 235 (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_174_min__max_Osup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 236 (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_175_Max_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 237 (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_176_dropWhile__eq__drop) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 238 (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_177_nth__length__takeWhile) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 239 (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_178_takeWhile__nth) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 240 (all X_a all Xs all X all Ys 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))),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))) # label(fact_179_list__update__length) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 241 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),zero_zero(nat)),N) = N) # label(fact_180_max__0L) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 242 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_181_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 243 (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_182_list__update__overwrite) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 244 (all X_a all Xs all X all X_3 all I_1 all I_3 (I_1 != I_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_1),X)),I_3),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_3),X_3)),I_1),X))) # label(fact_183_list__update__swap) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 245 (all P_1 all M_1 all N_2 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),M_1))) -> ((M_1 = N_2 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),M_1))) -> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),M_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),M_1)))))) # label(fact_184_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 246 (all S all T_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3)) -> S != T_3)) # label(fact_185_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 247 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> M != N)) # label(fact_186_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 248 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))) # label(fact_187_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 249 (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_188_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 250 (all M_1 all N_2 (M_1 != N_2 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1)))) # label(fact_189_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 251 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))) # label(fact_190_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 252 (all N (N != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_191_gr0I) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 253 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> N != zero_zero(nat))) # label(fact_192_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 254 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_193_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 255 (all N_2 (N_2 != zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)))) # label(fact_194_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 256 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_195_not__less0) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 257 (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_196_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 258 (all X_a (linorder(X_a) -> (all X_1 all Y_2 (ti(X_a,X_1) != ti(X_a,Y_2) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1)))))) # label(fact_197_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 259 (all X_a (linorder(X_a) -> (all X_1 all Y_2 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1)) | ti(X_a,X_1) = ti(X_a,Y_2))))) # label(fact_198_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 260 (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_199_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 261 (all X_a (linorder(X_a) -> (all Y_2 all X_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2)) <-> ti(X_a,X_1) = ti(X_a,Y_2)))))) # label(fact_200_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 262 (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_201_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 263 (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)) -> X != Y)))) # label(fact_202_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 264 (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_203_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 265 (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_204_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 266 (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)) -> X != Y)))) # label(fact_205_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 267 (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)) -> Y != X)))) # label(fact_206_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 268 (all X_a (preorder(X_a) -> (all P_1 all X_1 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1)) -> hBOOL(P_1)))))) # label(fact_207_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 269 (all X_a (preorder(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)))))) # label(fact_208_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 270 (all X_a (order(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)))))) # label(fact_209_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 271 (all X_a (ord(X_a) -> (all C_2 all A_2 all B_1 (A_2 = B_1 -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C_2))))))) # label(fact_210_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 272 (all X_a (order(X_a) -> (all C_2 all A_2 all B_1 (A_2 = B_1 -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_2),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_2),A_2))))))) # label(fact_211_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 273 (all X_a (ord(X_a) -> (all C_2 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> (B_1 = C_2 -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C_2))))))) # label(fact_212_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 274 (all X_a (order(X_a) -> (all C_2 all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) -> (B_1 = C_2 -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_2),A_2))))))) # label(fact_213_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 275 (all X_a (preorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))))))) # label(fact_214_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 276 (all X_a (order(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))))))) # label(fact_215_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 277 (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_216_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 278 (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_217_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 279 (all X_a all Ys 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)),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))) # label(fact_218_list__update__append1) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 280 (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_219_nth__list__update) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 281 (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_220_list__update__same__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 282 (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_221_nth__list__update__eq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 283 (all X_a all N all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),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),Xs)) = hAPP(list(X_a),X_a,last(X_a),Xs))) # label(fact_222_last__drop) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 284 (all X_a (bot(X_a) -> (all A_2 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),bot_bot(X_a)))))) # label(fact_223_not__less__bot) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 285 (all X_a (bot(X_a) -> (all Aa (ti(X_a,Aa) != bot_bot(X_a) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),bot_bot(X_a)),Aa)))))) # label(fact_224_bot__less) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 286 (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_225_drop__0) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 287 (all X_a all N hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),nil(X_a)) = nil(X_a)) # label(fact_226_drop__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 288 (all X_a (linorder(X_a) -> (all Z_1 all X_1 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y_2)))))) # label(fact_227_less__max__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 289 (all X_a (linorder(X_a) -> (all X_1 all Y_2 all Z_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),ord_max(X_a),X_1),Y_2)),Z_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),Z_1)))))) # label(fact_228_max__less__iff__conj) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 290 (all X_a (linorder(X_a) -> (all B_1 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_1))))))) # label(fact_229_min__max_Oless__supI1) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 291 (all X_a (linorder(X_a) -> (all A_2 all X all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),B_1)) -> 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_1))))))) # label(fact_230_min__max_Oless__supI2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 292 (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_231_distinct__drop) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 293 (all X_a (linorder(X_a) -> (all N 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),Xs))))))) # label(fact_232_sorted__drop) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 294 (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_233_list__update__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 295 (all X_a all I_1 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),nil(X_a)),I_1),V) = nil(X_a)) # label(fact_234_list__update_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 296 (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_235_list__update__code_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 297 (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_236_length__list__update) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 298 (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_237_list__update__id) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 299 (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_238_nth__list__update__neq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 300 (all X_a all N all Xs 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),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),Xs))) # label(fact_239_drop__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 301 (all X_a all N 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),Xs)) = 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),butlast(X_a),Xs))) # label(fact_240_butlast__drop) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 302 (all X_a all N 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),Xs)) = 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),tl(X_a),Xs))) # label(fact_241_tl__drop) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 303 (all X_a all N all Xs 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),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),Xs))) # label(fact_242_drop__tl) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 304 (all X_a all N all Xs (Xs != nil(X_a) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),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),Xs)) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),N)))) # label(fact_243_hd__drop__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 305 (all X_a all N all Xs all Y all Ys (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Ys) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),N) = ti(X_a,Y))) # label(fact_244_nth__via__drop) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 306 (all X_a all Xs_1 all Ys_1 (Xs_1 = Ys_1 <-> hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = 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_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_1),I_2))))) # label(fact_245_list__eq__iff__nth__eq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 307 (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_246_list__update__code_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 308 (all X_a all X all I_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),N)) -> 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),X)),I_1) = ti(X_a,X))) # label(fact_247_nth__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 309 (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_248_length__greater__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 310 (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_249_distinct__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 311 (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_250_nth__eq__iff__index__eq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 312 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N),zero_zero(nat)) = N) # label(fact_252_max__0R) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 313 (all X_a all Xs all Ys (hAPP(list(X_a),nat,size_size(list(X_a)),Xs) = 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))) -> 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),I_2))) -> Xs = Ys))) # label(fact_253_nth__equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 314 (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_254_Skolem__list__nth) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 315 (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_255_dropWhile__nth) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 316 (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_256_nth__drop_H) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 317 (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_ex(X_a),P_1),Xs_1)) <-> (exists 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_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_1))))))) # label(fact_257_list__ex__length) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 318 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,N)))) # label(fact_258_lessI) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 319 (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),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))))) # label(fact_259_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 320 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N)))) # label(fact_260_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 321 (all X all Y (hAPP(nat,nat,suc,X) = hAPP(nat,nat,suc,Y) -> X = Y)) # label(fact_261_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.56 322 (all M_1 all K_1 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K_1) <-> M_1 = N_2)) # label(fact_262_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 323 (all K_1 all M_1 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2) <-> M_1 = N_2)) # label(fact_263_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 324 (all M all N 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),N)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K))) # label(fact_264_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 325 (all Nat_4 all Nat_3 (hAPP(nat,nat,suc,Nat_4) = hAPP(nat,nat,suc,Nat_3) <-> Nat_4 = Nat_3)) # label(fact_265_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 326 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N))) # label(fact_266_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 327 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) # label(fact_267_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 328 (all X all Y all Z 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)) = 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))) # label(fact_268_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 329 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) # label(fact_269_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 330 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)) # label(fact_270_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 331 (all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)) <-> (exists K_2 N_2 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2))))) # label(fact_271_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 332 (all I_1 all M 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),I_1))))) # label(fact_272_less__add__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 333 (all I_1 all M 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))))) # label(fact_273_less__add__Suc1) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 334 (all N hAPP(nat,nat,suc,N) != N) # label(fact_274_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 335 (all N N != hAPP(nat,nat,suc,N)) # label(fact_275_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 336 (all M_1 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2) = hAPP(nat,nat,suc,zero_zero(nat)) <-> M_1 = hAPP(nat,nat,suc,zero_zero(nat)) & N_2 = zero_zero(nat) | M_1 = zero_zero(nat) & N_2 = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_276_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 337 (all M_1 all N_2 (hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2) <-> M_1 = hAPP(nat,nat,suc,zero_zero(nat)) & N_2 = zero_zero(nat) | M_1 = zero_zero(nat) & N_2 = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_277_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 338 (all X_a (cancel_semigroup_add(X_a) -> (all B_1 all A_2 all C_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),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_1) = ti(X_a,C_2))))) # label(fact_278_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 339 (all X_a (cancel146912293up_add(X_a) -> (all A_2 all B_1 all C_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1) = 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_1) = ti(X_a,C_2))))) # label(fact_279_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 340 (all X_a (cancel_semigroup_add(X_a) -> (all A_2 all B_1 all C_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1) = 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_1) = ti(X_a,C_2))))) # label(fact_280_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 341 (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_281_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 342 (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_282_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 343 (all X_a (ab_semigroup_add(X_a) -> (all A_2 all B_1 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_1)),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_1),C_2))))) # label(fact_283_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 344 (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_284_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 345 (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_285_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 346 (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_286_double__zero__sym) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 347 (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_287_add__0) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 348 (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_288_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 349 (all X_a (ordere236663937imp_le(X_a) -> (all C_2 all A_2 all B_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),C_2),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),B_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)))))) # label(fact_289_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 350 (all X_a (ordere236663937imp_le(X_a) -> (all A_2 all C_2 all B_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_1),C_2))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)))))) # label(fact_290_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 351 (all X_a (ordere223160158up_add(X_a) -> (all C_2 all D_2 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_2),D_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_1),D_2)))))))) # label(fact_291_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 352 (all X_a (ordere223160158up_add(X_a) -> (all C_2 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_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),C_2),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),B_1))))))) # label(fact_292_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 353 (all X_a (ordere223160158up_add(X_a) -> (all C_2 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_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_1),C_2))))))) # label(fact_293_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 354 (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_294_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 355 (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_295_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 356 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_296_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 357 (all Nat_2 zero_zero(nat) != hAPP(nat,nat,suc,Nat_2)) # label(fact_297_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 358 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_298_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 359 (all Nat_1 hAPP(nat,nat,suc,Nat_1) != zero_zero(nat)) # label(fact_299_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 360 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_300_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 361 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_301_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 362 (all M_1 all N_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_1))))) # label(fact_302_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 363 (all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)) | M_1 = N_2)) # label(fact_303_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 364 (all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)))) # label(fact_304_Suc__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 365 (all N_2 all M_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_1))) <-> N_2 = M_1))) # label(fact_305_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 366 (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))) -> M = N))) # label(fact_306_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 367 (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),M),hAPP(nat,nat,suc,N))))) # label(fact_307_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 368 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> (hAPP(nat,nat,suc,M) != N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N))))) # label(fact_308_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 369 (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_309_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 370 (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_310_less__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 371 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_311_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 372 (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_312_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 373 (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(fun(X_a,bool)),A_1),bot_bot(fun(X_a,bool))))) # label(fact_313_not__psubset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 374 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N) = N) # label(fact_314_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 375 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),zero_zero(nat)) = M) # label(fact_315_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 376 (all M_1 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2) = zero_zero(nat) <-> M_1 = zero_zero(nat) & N_2 = zero_zero(nat))) # label(fact_316_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 377 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = M -> N = zero_zero(nat))) # label(fact_317_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 378 (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_318_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 379 (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_319_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 380 (all K_1 all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)))) # label(fact_320_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 381 (all M 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))))) # label(fact_321_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 382 (all M 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),J))))) # label(fact_322_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 383 (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_323_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 384 (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_324_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 385 (all M all N 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),L) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))))) # label(fact_325_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 386 (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_326_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 387 (all X_a (ordere236663937imp_le(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z))))) # label(fact_327_max__add__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 388 (all X_a all N all M all Xs 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(nat,fun(list(X_a),list(X_a)),drop(X_a),M),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),M)),Xs)) # label(fact_328_drop__drop) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 389 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),M),N))) # label(fact_329_max__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 390 (all X_a all A_2 all List_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)),cons(X_a),A_2),List_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),List_1)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_330_list_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 391 (all X_a all Fa all Aa all List 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)) = 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))),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_331_list_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 392 (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_ex(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_ex(X_a),P_1),Xs_1)))) # label(fact_332_list__ex__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 393 (all X_a all P_1 -hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),nil(X_a)))) # label(fact_333_list__ex__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 394 (all X_a all P_1 all Xs_1 all Ys_1 (hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(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_1))) <-> hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),Xs_1)) | hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),Ys_1)))) # label(fact_334_list__ex__append) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 395 (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_335_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 396 (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_336_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 397 (all X_a (ordere216010020id_add(X_a) -> (all B_1 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_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)))))))) # label(fact_337_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 398 (all X_a (ordere216010020id_add(X_a) -> (all B_1 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_1),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_1)),zero_zero(X_a)))))))) # label(fact_338_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 399 (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_ex(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_ex(X_a),P_1),Xs_1)))) # label(fact_339_list__ex__rev) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 400 (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)) <-> (exists M_2 N_2 = hAPP(nat,nat,suc,M_2)))) # label(fact_340_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 401 (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,zero_zero(nat)))) <-> N_2 = zero_zero(nat))) # label(fact_341_less__Suc0) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 402 (all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2))) <-> M_1 = zero_zero(nat) | (exists J_2 (M_1 = hAPP(nat,nat,suc,J_2) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),N_2)))))) # label(fact_342_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 403 (all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)))) # label(fact_343_add__gr__0) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 404 (all X_a all X all Xs 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),Xs)),hAPP(nat,nat,suc,N)) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),N)) # label(fact_344_nth__Cons__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 405 (all X_a all Xs all Ys 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)) = 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))) # label(fact_345_length__append) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 406 (all X_a all N 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)),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),Xs)) # label(fact_346_drop__Suc__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 407 (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_347_list__update__code_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 408 (all X_a all N all X hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(nat,nat,suc,N)),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),X))) # label(fact_348_replicate__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 409 (all X_a all N all M 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),M)),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),X)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),M),X))) # label(fact_349_replicate__add) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 410 (all X_a all N 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)),Xs) = 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),tl(X_a),Xs))) # label(fact_350_drop__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 411 (all X_a all Xs all Ys 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)) = 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))) # label(fact_351_length__splice) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 412 (all X_a all Xs all Ys 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(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),N)) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys),N)) # label(fact_352_nth__append__length__plus) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 413 (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_353_less__imp__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 414 (all X_a all Xs_1 all N_2 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(nat,nat,suc,N_2) <-> (exists Y_1 exists Ys_2 (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_2) & hAPP(list(X_a),nat,size_size(list(X_a)),Ys_2) = N_2)))) # label(fact_354_length__Suc__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 415 (all X_a all N_2 all Xs_1 (hAPP(nat,nat,suc,N_2) = hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) <-> (exists Y_1 exists Ys_2 (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_2) & hAPP(list(X_a),nat,size_size(list(X_a)),Ys_2) = N_2)))) # label(fact_355_Suc__length__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 416 (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_356_less__imp__add__positive) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 417 (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_357_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 418 (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_358_psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 419 (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_359_gr0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 420 (all X_a (order(X_a) -> (all N_2 all N_3 all F ((all N_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_1)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_1))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),N_3)) -> 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,N_3)))))))) # label(fact_360_lift__Suc__mono__less) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 421 (all X_a (order(X_a) -> (all N_2 all M_1 all F ((all N_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_1)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_1))))) -> (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,M_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1))))))) # label(fact_361_lift__Suc__mono__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 422 (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_362_even__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 423 (all X_a (linordered_semidom(X_a) -> (all B_1 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_1),C_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)))))))) # label(fact_363_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 424 (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_364_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 425 (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_365_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 426 (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_366_lessE) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 427 (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_367_Suc__lessE) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 428 (all Y (Y != zero_zero(nat) -> -(all Nat Y != hAPP(nat,nat,suc,Nat)))) # label(fact_368_nat_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 429 (all N (N != zero_zero(nat) -> (exists M_2 N = hAPP(nat,nat,suc,M_2)))) # label(fact_369_not0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 430 (all N_2 all P_1 (hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> ((all N_1 (hBOOL(hAPP(nat,bool,P_1,N_1)) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_1))))) -> hBOOL(hAPP(nat,bool,P_1,N_2))))) # label(fact_370_nat__induct) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 431 (all P_1 all K_1 (hBOOL(hAPP(nat,bool,P_1,K_1)) -> ((all N_1 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_1))) -> hBOOL(hAPP(nat,bool,P_1,N_1)))) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))))) # label(fact_371_zero__induct) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 432 (all X_a all N all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),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),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),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)),Xs))) # label(fact_372_take__hd__drop) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 433 (all X_a all N all Xs 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),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)),Xs))) # label(fact_373_take__tl) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 434 (all X_a all N hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),nil(X_a)) = nil(X_a)) # label(fact_374_take__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 435 (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_375_distinct__take) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 436 (all X_a (linorder(X_a) -> (all N 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),Xs))))))) # label(fact_376_sorted__take) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 437 (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_377_takeWhile__eq__take) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 438 (all X_a all N 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),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs)) = Xs) # label(fact_378_append__take__drop__id) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 439 (all X_a all N all M all Xs 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(nat,fun(list(X_a),list(X_a)),drop(X_a),M),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),M),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),M)),Xs))) # label(fact_379_take__drop) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 440 (all X_a all Xs all I_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),N)) -> 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),Xs)),I_1) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_1))) # label(fact_380_nth__take) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 441 (all X_a all N 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)),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),Xs))) # label(fact_381_take__Suc__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 442 (all X_a all N_2 all Xs_1 (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_2),Xs_1) = nil(X_a) <-> N_2 = zero_zero(nat) | Xs_1 = nil(X_a))) # label(fact_382_take__eq__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 443 (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_383_take__0) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 444 (all X_a all Xs_1 all Ys_1 all Zs (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1) = Zs <-> 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) & Ys_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)),Xs_1)),Zs))) # label(fact_384_append__eq__conv__conj) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 445 (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_385_take__add) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 446 (all X_a all N all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),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),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),Xs))) # label(fact_386_take__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 447 (all X_a all N 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)),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),hAPP(list(X_a),list(X_a),tl(X_a),Xs))))) # label(fact_387_take__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 448 (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_388_take__Suc__conv__app__nth) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 449 (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_389_id__take__nth__drop) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 450 (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_390_upd__conv__take__nth__drop) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 451 (all X_a all P_1 all Xs_1 all N_2 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N_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(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)))) -> 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_2),Xs_1)))) # label(fact_391_takeWhile__eq__take__P__nth) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 452 (all Z 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))))) # label(fact_392_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 453 (all Y all X all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z)) -> 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))))) # label(fact_393_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 454 (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_394_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 455 (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_395_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 456 (all X_a (comm_semiring_1(X_a) -> (all A_2 all B_1 all C_2 all D_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_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),D_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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D_2))))) # label(fact_396_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 457 (all X_a (comm_semiring_1(X_a) -> (all A_2 all B_1 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_1)),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_1)))) # label(fact_397_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 458 (all X_a (comm_semiring_1(X_a) -> (all A_2 all B_1 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_1)),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_1),C_2))))) # label(fact_398_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 459 (all X_a (comm_semiring_1(X_a) -> (all A_2 all C_2 all D_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),C_2),D_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)),D_2)))) # label(fact_399_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 460 (all X_a (comm_semiring_1(X_a) -> (all A_2 all C_2 all D_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),C_2),D_2)) = 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_2))))) # label(fact_400_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 461 (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_401_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 462 (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_402_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 463 (all X_a all N all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),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) = 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))))) # label(fact_403_rev__nth) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 464 (all X_a all Xs all Ys ((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)) -> Xs = Ys)) # label(fact_404_take__equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 465 (all X_a all N all M all Xs 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(nat,fun(list(X_a),list(X_a)),take(X_a),M),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),N)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))) # label(fact_405_drop__take) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 466 (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_406_drop__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 467 (all M all K all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) # label(fact_407_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 468 (all K all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) # label(fact_408_diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.57 469 (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_409_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 470 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),N) = M) # label(fact_410_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 471 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),N) = M) # label(fact_411_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 472 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba all C_1 all D_1 (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_1) -> (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_1))))))) # label(fact_412_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 473 (all X_a (group_add(X_a) -> (all A_2 all B_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),plus_plus(X_a),A_2),B_1)),B_1) = ti(X_a,A_2)))) # label(fact_413_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 474 (all X_a (group_add(X_a) -> (all A_2 all B_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),minus_minus(X_a),A_2),B_1)),B_1) = ti(X_a,A_2)))) # label(fact_414_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 475 (all N 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)),K)))) # label(fact_415_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 476 (all L 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),M),L)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M)))))) # label(fact_416_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 477 (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_417_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 478 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),M))))) # label(fact_418_diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 479 (all N_2 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),M_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)))) # label(fact_419_zero__less__diff) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 480 (all M all 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),N)),hAPP(nat,nat,suc,M)))) # label(fact_420_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 481 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)) = zero_zero(nat)) # label(fact_421_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 482 (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_422_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 483 (all M all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = M)) # label(fact_423_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 484 (all X_a all N 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),Xs)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),N)) # label(fact_424_length__drop) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 485 (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_425_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 486 (all X_a (ordered_ab_group_add(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z))))) # label(fact_426_max__diff__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 487 (all X_a (ab_group_add(X_a) -> (all Aa all Ba all C_1 all D_1 (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_1) -> (ti(X_a,Aa) = ti(X_a,Ba) <-> ti(X_a,C_1) = ti(X_a,D_1)))))) # label(fact_427_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 488 (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_428_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 489 (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_429_diff__self) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 490 (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_430_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 491 (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_431_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 492 (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_432_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 493 (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_433_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 494 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = zero_zero(nat) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M) = zero_zero(nat) -> M = N))) # label(fact_434_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 495 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M) = zero_zero(nat)) # label(fact_435_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 496 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat)) = M) # label(fact_436_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 497 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N) = zero_zero(nat)) # label(fact_437_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 498 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) # label(fact_438_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 499 (all M all N 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)),N)),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),N)),K)) # label(fact_439_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 500 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M)),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N),M)) # label(fact_440_nat__minus__add__max) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 501 (all I_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,I_1))),N)))) # label(fact_441_diff__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 502 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))) = N)) # label(fact_442_Suc__pred) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 503 (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_443_nat__diff__split) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 504 (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_444_nat__diff__split__asm) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 505 (all X_a all N all Xs all Ys 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(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),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(nat,fun(list(X_a),list(X_a)),take(X_a),N),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),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))),Ys))) # label(fact_445_take__append) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 506 (all X_a all N all Xs all Ys 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(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),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(nat,fun(list(X_a),list(X_a)),drop(X_a),N),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),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))),Ys))) # label(fact_446_drop__append) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 507 (all X_a all Ys all N all Xs ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),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)),N) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),N)) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),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)),N) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))))) # label(fact_447_nth__append) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 508 (all X_a all Ys all X all N all Xs ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),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)),N),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),X)),Ys)) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),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)),N),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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))),X))))) # label(fact_448_list__update__append) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 509 (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_449_rev__drop) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 510 (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_450_rev__take) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 511 (all I all P_1 all K_1 (hBOOL(hAPP(nat,bool,P_1,K_1)) -> ((all N_1 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_1))) -> hBOOL(hAPP(nat,bool,P_1,N_1)))) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K_1),I)))))) # label(fact_451_zero__induct__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 512 (all X_a all X all K all Xs (Xs != nil(X_a) -> (K = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat)) -> hAPP(list(X_a),X_a,last(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),K),X)) = ti(X_a,X)) & (K != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat)) -> hAPP(list(X_a),X_a,last(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),K),X)) = hAPP(list(X_a),X_a,last(X_a),Xs)))) # label(fact_452_last__list__update) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 513 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),bot_bot(fun(X_a,bool))),A_1) = bot_bot(fun(X_a,bool))) # label(fact_453_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 514 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),bot_bot(fun(X_a,bool))) = ti(fun(X_a,bool),A_1)) # label(fact_454_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 515 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),A_1) = bot_bot(fun(X_a,bool))) # label(fact_455_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 516 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N)),one_one(nat)) = N) # label(fact_456_diff__Suc__1) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 517 (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(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N)) # label(fact_457_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 518 (all N hAPP(nat,nat,suc,N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N)) # label(fact_458_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 519 (all N hAPP(nat,nat,suc,N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))) # label(fact_459_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 520 (all X_a all X all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),one_one(nat)),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_460_drop__1__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 521 (all X_a (one(X_a) -> (all X_1 (one_one(X_a) = ti(X_a,X_1) <-> ti(X_a,X_1) = one_one(X_a))))) # label(fact_461_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 522 (all X_a (linordered_semidom(X_a) -> (all A_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),one_one(X_a))))))) # label(fact_463_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 523 (all X_a (linordered_semidom(X_a) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a))))) # label(fact_464_not__one__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 524 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),one_one(X_a))))) # label(fact_465_zero__less__one) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 525 (all X_a (zero_neq_one(X_a) -> one_one(X_a) != zero_zero(X_a))) # label(fact_466_one__neq__zero) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 526 (all X_a (zero_neq_one(X_a) -> zero_zero(X_a) != one_one(X_a))) # label(fact_467_zero__neq__one) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 527 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)))))) # label(fact_468_zero__less__two) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 528 (all X_a all X all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),one_one(nat)),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),nil(X_a))) # label(fact_469_take__1__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 529 (all X_a all Xs hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),butlast(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)),one_one(nat))) # label(fact_470_length__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 530 (all X_a all Xs hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),tl(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)),one_one(nat))) # label(fact_471_length__tl) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 531 (all X_a all N 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)),take(X_a),N),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),one_one(nat))),hAPP(list(X_a),list(X_a),tl(X_a),Xs))) # label(fact_472_tl__take) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 532 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))))) # label(fact_473_Suc__pred_H) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 533 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))) = N)) # label(fact_474_Suc__diff__1) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 534 (all N all M ((M = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = N) & (M != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N))))) # label(fact_475_add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 535 (all X_a all X all Xs all N ((N = zero_zero(nat) -> 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)),N) = ti(X_a,X)) & (N != zero_zero(nat) -> 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)),N) = 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),N),one_one(nat)))))) # label(fact_476_nth__Cons_H) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 536 (all X_a all X all Xs all N ((N = zero_zero(nat) -> 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),Xs)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) & (N != zero_zero(nat) -> 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),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),one_one(nat))),Xs)))) # label(fact_477_drop__Cons_H) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 537 (all X_a all Xs 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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat))),Xs)) # label(fact_478_butlast__conv__take) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 538 (all X_a all X all K all Xs ((K = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat)) -> hAPP(list(X_a),list(X_a),butlast(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),K),X)) = hAPP(list(X_a),list(X_a),butlast(X_a),Xs)) & (K != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat)) -> hAPP(list(X_a),list(X_a),butlast(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),K),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),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)),K),X)))) # label(fact_479_butlast__list__update) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 539 (all X_a all X all N (N != zero_zero(nat) -> hAPP(list(X_a),list(X_a),tl(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),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),N),one_one(nat))),X))) # label(fact_480_tl__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 540 (all X_a all X all Xs all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),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),Xs)),N) = 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),N),one_one(nat))))) # label(fact_481_nth__Cons__pos) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 541 (all X_a all X all Xs all N ((N = zero_zero(nat) -> 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),Xs)) = nil(X_a)) & (N != zero_zero(nat) -> 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),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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),Xs))))) # label(fact_482_take__Cons_H) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 542 (all X_a all Y all K all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(list(X_a),list(X_a),rev(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),K),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),rev(X_a),Xs)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),K)),one_one(nat))),Y))) # label(fact_483_rev__update) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 543 (all X_a all Xs (Xs != nil(X_a) -> hAPP(list(X_a),X_a,last(X_a),Xs) = 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)),one_one(nat))))) # label(fact_484_last__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 544 (all X_a all X all Xs all V ((hAPP(int,nat,number_number_of(nat),V) = zero_zero(nat) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(int,nat,number_number_of(nat),V)),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)) & (hAPP(int,nat,number_number_of(nat),V) != zero_zero(nat) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(int,nat,number_number_of(nat),V)),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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))),Xs))))) # label(fact_485_take__Cons__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 545 (all X_a (linordered_idom(X_a) -> (all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(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_486_Ints__odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 546 (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_487_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 547 (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_488_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 548 (all X_a (ring_1(X_a) -> (all Ba all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),ring_1_Ints(X_a)))))))) # label(fact_489_Ints__diff) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 549 (all X_a (number_ring(X_a) -> (all V all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),V),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_490_number__of__diff) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 550 (all X_a (number_ring(X_a) -> (all V all W all C_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),W)),C_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))),C_2)))) # label(fact_491_add__number__of__diff1) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 551 (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_492_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 552 (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_493_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 553 (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_494_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 554 (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_495_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 555 (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_496_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 556 (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].
% 1.21/1.58 557 (all T_2 all T_1 (preorder(T_1) -> preorder(fun(T_2,T_1)))) # label(arity_fun___Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 558 (all T_2 all T_1 (order(T_1) -> order(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oorder) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 559 (all T_2 all T_1 (ord(T_1) -> ord(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oord) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 560 (all T_2 all T_1 (bot(T_1) -> bot(fun(T_2,T_1)))) # label(arity_fun___Orderings_Obot) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 561 (all T_2 all T_1 (minus(T_1) -> minus(fun(T_2,T_1)))) # label(arity_fun___Groups_Ominus) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 562 (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].
% 1.21/1.58 563 (all T_1 cl_HOL_Oequal(list(T_1))) # label(arity_List_Olist___HOL_Oequal) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 564 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 565 (all P (-hBOOL(hAPP(bool,bool,fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 566 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 567 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R) = hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R))) # label(help_COMBB_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 568 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q)) # label(help_COMBC_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 569 (all X_b all X_a all P all Q hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P)) # label(help_COMBK_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 570 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c)),combs(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R))) # label(help_COMBS_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 571 (all Q all P (-hBOOL(P) | -hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 572 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 573 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 574 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 575 (all X_a all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) | ti(X_a,X) = ti(X_a,Y))) # label(help_fequal_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 576 (all X_a all X all Y (ti(X_a,X) != ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)))) # label(help_fequal_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.58 577 -(exists C hBOOL(hAPP(list(arrow_490897120le_alt),bool,distinct(arrow_490897120le_alt),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),a),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),b),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),C),nil(arrow_490897120le_alt))))))) # label(conj_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.44/1.70
% 1.44/1.70 ============================== end of process non-clausal formulas ===
% 1.44/1.70
% 1.44/1.70 ============================== PROCESS INITIAL CLAUSES ===============
% 1.44/1.70
% 1.44/1.70 ============================== PREDICATE ELIMINATION =================
% 1.44/1.70 578 one(int) # label(arity_Int_Oint___Groups_Oone) # label(axiom). [assumption].
% 1.44/1.70 579 -one(A) | one_one(A) = ti(A,one_one(A)) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom). [clausify(6)].
% 1.44/1.70 Derived: one_one(int) = ti(int,one_one(int)). [resolve(578,a,579,a)].
% 1.44/1.70 580 one(nat) # label(arity_Nat_Onat___Groups_Oone) # label(axiom). [assumption].
% 1.44/1.70 Derived: one_one(nat) = ti(nat,one_one(nat)). [resolve(580,a,579,a)].
% 1.44/1.70 581 monoid_add(int) # label(arity_Int_Oint___Groups_Omonoid__add) # label(axiom). [assumption].
% 1.44/1.70 582 -monoid_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom). [clausify(7)].
% 1.44/1.70 583 -monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_285_add__0__right) # label(axiom). [clausify(345)].
% 1.44/1.70 584 -monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_288_add__0__left) # label(axiom). [clausify(348)].
% 1.44/1.70 Derived: plus_plus(int) = ti(fun(int,fun(int,int)),plus_plus(int)). [resolve(581,a,582,a)].
% 1.44/1.70 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),zero_zero(int)) = ti(int,A). [resolve(581,a,583,a)].
% 1.44/1.70 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),A) = ti(int,A). [resolve(581,a,584,a)].
% 1.44/1.70 585 monoid_add(nat) # label(arity_Nat_Onat___Groups_Omonoid__add) # label(axiom). [assumption].
% 1.44/1.70 Derived: plus_plus(nat) = ti(fun(nat,fun(nat,nat)),plus_plus(nat)). [resolve(585,a,582,a)].
% 1.44/1.70 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),zero_zero(nat)) = ti(nat,A). [resolve(585,a,583,a)].
% 1.44/1.70 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),A) = ti(nat,A). [resolve(585,a,584,a)].
% 1.44/1.70 586 ab_semigroup_add(int) # label(arity_Int_Oint___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 1.44/1.70 587 -ab_semigroup_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom). [clausify(8)].
% 1.44/1.70 588 -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_283_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom). [clausify(343)].
% 1.44/1.70 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)). [resolve(586,a,588,a)].
% 1.44/1.70 589 ab_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 1.44/1.70 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(589,a,588,a)].
% 1.44/1.70 590 cancel_semigroup_add(int) # label(arity_Int_Oint___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.44/1.70 591 -cancel_semigroup_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_2_res) # label(axiom). [clausify(9)].
% 1.44/1.70 592 -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_278_add__right__imp__eq) # label(axiom). [clausify(338)].
% 1.52/1.76 593 -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_280_add__left__imp__eq) # label(axiom). [clausify(340)].
% 1.52/1.76 594 -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_281_add__right__cancel) # label(axiom). [clausify(341)].
% 1.52/1.76 595 -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_281_add__right__cancel) # label(axiom). [clausify(341)].
% 1.52/1.76 596 -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_282_add__left__cancel) # label(axiom). [clausify(342)].
% 1.52/1.76 597 -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_282_add__left__cancel) # label(axiom). [clausify(342)].
% 1.52/1.76 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B) | ti(int,A) = ti(int,C). [resolve(590,a,592,a)].
% 1.52/1.76 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C) | ti(int,B) = ti(int,C). [resolve(590,a,593,a)].
% 1.52/1.76 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B) | ti(int,A) != ti(int,C). [resolve(590,a,595,a)].
% 1.52/1.76 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C) | ti(int,B) != ti(int,C). [resolve(590,a,597,a)].
% 1.52/1.76 598 cancel_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.52/1.76 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(598,a,592,a)].
% 1.52/1.76 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(598,a,593,a)].
% 1.52/1.76 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(598,a,595,a)].
% 1.52/1.76 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(598,a,597,a)].
% 1.52/1.76 599 zero(int) # label(arity_Int_Oint___Groups_Ozero) # label(axiom). [assumption].
% 1.52/1.76 600 -zero(A) | zero_zero(A) = ti(A,zero_zero(A)) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom). [clausify(10)].
% 1.52/1.76 Derived: zero_zero(int) = ti(int,zero_zero(int)). [resolve(599,a,600,a)].
% 1.52/1.76 601 zero(nat) # label(arity_Nat_Onat___Groups_Ozero) # label(axiom). [assumption].
% 1.52/1.76 Derived: zero_zero(nat) = ti(nat,zero_zero(nat)). [resolve(601,a,600,a)].
% 1.52/1.76 602 number_ring(int) # label(arity_Int_Oint___Int_Onumber__ring) # label(axiom). [assumption].
% 1.52/1.76 603 -number_ring(A) | number_number_of(A) = ti(fun(int,A),number_number_of(A)) # label(tsy_c_Int_Onumber__class_Onumber__of_0_res) # label(axiom). [clausify(13)].
% 1.52/1.76 604 -number_ring(A) | hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C)) # label(fact_490_number__of__diff) # label(axiom). [clausify(549)].
% 1.52/1.76 605 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),C)),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C))),D) # label(fact_491_add__number__of__diff1) # label(axiom). [clausify(550)].
% 1.52/1.81 Derived: number_number_of(int) = ti(fun(int,int),number_number_of(int)). [resolve(602,a,603,a)].
% 1.52/1.81 Derived: hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B)). [resolve(602,a,604,a)].
% 1.52/1.81 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,number_number_of(int),B)),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),C). [resolve(602,a,605,a)].
% 1.52/1.81 606 ring_1(int) # label(arity_Int_Oint___Rings_Oring__1) # label(axiom). [assumption].
% 1.52/1.81 607 -ring_1(A) | ring_1_Ints(A) = ti(fun(A,bool),ring_1_Ints(A)) # label(tsy_c_Int_Oring__1__class_OInts_res) # label(axiom). [clausify(14)].
% 1.52/1.81 608 -ring_1(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),ring_1_Ints(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),ring_1_Ints(A))) # label(fact_489_Ints__diff) # label(axiom). [clausify(548)].
% 1.52/1.81 Derived: ring_1_Ints(int) = ti(fun(int,bool),ring_1_Ints(int)). [resolve(606,a,607,a)].
% 1.52/1.81 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),ring_1_Ints(int))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),ring_1_Ints(int))). [resolve(606,a,608,a)].
% 1.52/1.81 609 linorder(int) # label(arity_Int_Oint___Orderings_Olinorder) # label(axiom). [assumption].
% 1.52/1.81 610 -linorder(A) | linorder_sorted(A) = ti(fun(list(A),bool),linorder_sorted(A)) # label(tsy_c_List_Olinorder__class_Osorted_res) # label(axiom). [clausify(25)].
% 1.52/1.81 611 -linorder(A) | linord467138063of_set(A) = ti(fun(fun(A,bool),list(A)),linord467138063of_set(A)) # label(tsy_c_List_Olinorder__class_Osorted__list__of__set_res) # label(axiom). [clausify(26)].
% 1.52/1.81 612 -linorder(A) | ord_max(A) = ti(fun(A,fun(A,A)),ord_max(A)) # label(tsy_c_Orderings_Oord__class_Omax_1_res) # label(axiom). [clausify(53)].
% 1.52/1.81 613 -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(90)].
% 1.52/1.81 614 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),nil(A))) # label(fact_30_sorted_ONil) # label(axiom). [clausify(91)].
% 1.52/1.81 615 -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_52_sorted__butlast) # label(axiom). [clausify(113)].
% 1.52/1.81 616 -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_102_sorted__tl) # label(axiom). [clausify(163)].
% 1.52/1.81 617 -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_116_sorted__dropWhile) # label(axiom). [clausify(177)].
% 1.52/1.81 618 -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_128_sorted__takeWhile) # label(axiom). [clausify(189)].
% 1.52/1.81 619 -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_136_foldr__max__sorted) # label(axiom). [clausify(197)].
% 1.52/1.81 620 -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_136_foldr__max__sorted) # label(axiom). [clausify(197)].
% 1.52/1.81 621 -linorder(A) | hAPP(fun(A,bool),list(A),linord467138063of_set(A),bot_bot(fun(A,bool))) = nil(A) # label(fact_165_sorted__list__of__set__empty) # label(axiom). [clausify(226)].
% 1.52/1.81 622 -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_166_min__max_Osup__assoc) # label(axiom). [clausify(227)].
% 1.52/1.81 623 -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_167_min__max_Osup_Oassoc) # label(axiom). [clausify(228)].
% 1.52/1.81 624 -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_168_min__max_Osup__left__commute) # label(axiom). [clausify(229)].
% 1.52/1.81 625 -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_169_min__max_Osup_Oleft__commute) # label(axiom). [clausify(230)].
% 1.52/1.81 626 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),B) = ti(A,B) # label(fact_170_min__max_Osup_Oidem) # label(axiom). [clausify(231)].
% 1.52/1.81 627 -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_171_min__max_Osup_Ocommute) # label(axiom). [clausify(232)].
% 1.52/1.81 628 -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_172_min__max_Osup__commute) # label(axiom). [clausify(233)].
% 1.52/1.81 629 -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_173_min__max_Osup_Oleft__idem) # label(axiom). [clausify(234)].
% 1.52/1.81 630 -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_174_min__max_Osup__left__idem) # label(axiom). [clausify(235)].
% 1.52/1.81 631 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),B) = ti(A,B) # label(fact_175_Max_Oidem) # label(axiom). [clausify(236)].
% 1.52/1.81 632 -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_197_linorder__neq__iff) # label(axiom). [clausify(258)].
% 1.52/1.81 633 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_197_linorder__neq__iff) # label(axiom). [clausify(258)].
% 1.52/1.81 634 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_197_linorder__neq__iff) # label(axiom). [clausify(258)].
% 1.52/1.81 635 -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_198_not__less__iff__gr__or__eq) # label(axiom). [clausify(259)].
% 1.52/1.81 636 -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_198_not__less__iff__gr__or__eq) # label(axiom). [clausify(259)].
% 1.52/1.81 637 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_198_not__less__iff__gr__or__eq) # label(axiom). [clausify(259)].
% 1.52/1.81 638 -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_199_linorder__less__linear) # label(axiom). [clausify(260)].
% 1.52/1.81 639 -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_200_linorder__antisym__conv3) # label(axiom). [clausify(261)].
% 1.52/1.81 640 -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_200_linorder__antisym__conv3) # label(axiom). [clausify(261)].
% 1.52/1.81 641 -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_201_linorder__neqE) # label(axiom). [clausify(262)].
% 1.52/1.81 642 -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_217_linorder__cases) # label(axiom). [clausify(278)].
% 1.52/1.81 643 -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_227_less__max__iff__disj) # label(axiom). [clausify(288)].
% 1.52/1.81 644 -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_227_less__max__iff__disj) # label(axiom). [clausify(288)].
% 1.52/1.81 645 -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_227_less__max__iff__disj) # label(axiom). [clausify(288)].
% 1.52/1.81 646 -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_228_max__less__iff__conj) # label(axiom). [clausify(289)].
% 1.52/1.81 647 -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_228_max__less__iff__conj) # label(axiom). [clausify(289)].
% 1.52/1.81 648 -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_228_max__less__iff__conj) # label(axiom). [clausify(289)].
% 1.52/1.81 649 -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_229_min__max_Oless__supI1) # label(axiom). [clausify(290)].
% 1.52/1.81 650 -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_230_min__max_Oless__supI2) # label(axiom). [clausify(291)].
% 1.52/1.81 651 -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_232_sorted__drop) # label(axiom). [clausify(293)].
% 1.52/1.81 652 -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_376_sorted__take) # label(axiom). [clausify(436)].
% 1.52/1.81 Derived: linorder_sorted(int) = ti(fun(list(int),bool),linorder_sorted(int)). [resolve(609,a,610,a)].
% 1.52/1.81 Derived: linord467138063of_set(int) = ti(fun(fun(int,bool),list(int)),linord467138063of_set(int)). [resolve(609,a,611,a)].
% 1.52/1.81 Derived: ord_max(int) = ti(fun(int,fun(int,int)),ord_max(int)). [resolve(609,a,612,a)].
% 1.52/1.81 Derived: hBOOL(hAPP(list(int),bool,linorder_sorted(int),hAPP(list(int),list(int),hAPP(int,fun(list(int),list(int)),cons(int),A),nil(int)))). [resolve(609,a,613,a)].
% 1.52/1.81 Derived: hBOOL(hAPP(list(int),bool,linorder_sorted(int),nil(int))). [resolve(609,a,614,a)].
% 1.52/1.81 Derived: nil(int) = A | -hBOOL(hAPP(list(int),bool,linorder_sorted(int),A)) | hBOOL(hAPP(list(int),bool,linorder_sorted(int),hAPP(list(int),list(int),butlast(int),A))). [resolve(609,a,615,a)].
% 1.52/1.82 Derived: -hBOOL(hAPP(list(int),bool,linorder_sorted(int),A)) | hBOOL(hAPP(list(int),bool,linorder_sorted(int),hAPP(list(int),list(int),tl(int),A))). [resolve(609,a,616,a)].
% 1.52/1.82 Derived: -hBOOL(hAPP(list(int),bool,linorder_sorted(int),A)) | hBOOL(hAPP(list(int),bool,linorder_sorted(int),hAPP(list(int),list(int),hAPP(fun(int,bool),fun(list(int),list(int)),dropWhile(int),B),A))). [resolve(609,a,617,a)].
% 1.52/1.82 Derived: -hBOOL(hAPP(list(int),bool,linorder_sorted(int),A)) | hBOOL(hAPP(list(int),bool,linorder_sorted(int),hAPP(list(int),list(int),hAPP(fun(int,bool),fun(list(int),list(int)),takeWhile(int),B),A))). [resolve(609,a,618,a)].
% 1.52/1.82 Derived: -hBOOL(hAPP(list(int),bool,linorder_sorted(int),hAPP(list(int),list(int),rev(int),A))) | nil(int) != A | hAPP(int,int,hAPP(list(int),fun(int,int),hAPP(fun(int,fun(int,int)),fun(list(int),fun(int,int)),foldr(int,int),ord_max(int)),A),B) = ti(int,B). [resolve(609,a,619,a)].
% 1.52/1.82 Derived: -hBOOL(hAPP(list(int),bool,linorder_sorted(int),hAPP(list(int),list(int),rev(int),A))) | nil(int) = A | hAPP(int,int,hAPP(list(int),fun(int,int),hAPP(fun(int,fun(int,int)),fun(list(int),fun(int,int)),foldr(int,int),ord_max(int)),A),B) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(nat,int,hAPP(list(int),fun(nat,int),nth(int),A),zero_zero(nat))),B). [resolve(609,a,620,a)].
% 1.52/1.82 Derived: hAPP(fun(int,bool),list(int),linord467138063of_set(int),bot_bot(fun(int,bool))) = nil(int). [resolve(609,a,621,a)].
% 1.52/1.82 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)). [resolve(609,a,622,a)].
% 1.52/1.82 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)). [resolve(609,a,624,a)].
% 1.52/1.82 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),A) = ti(int,A). [resolve(609,a,626,a)].
% 1.52/1.82 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),A). [resolve(609,a,627,a)].
% 1.52/1.82 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B). [resolve(609,a,629,a)].
% 1.52/1.82 Derived: ti(int,A) = ti(int,B) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(609,a,632,a)].
% 1.52/1.82 Derived: ti(int,A) != ti(int,B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)). [resolve(609,a,633,a)].
% 1.52/1.82 Derived: ti(int,A) != ti(int,B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(609,a,634,a)].
% 1.52/1.82 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)). [resolve(609,a,636,a)].
% 1.52/1.82 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(609,a,643,a)].
% 1.52/1.82 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(609,a,644,a)].
% 1.52/1.82 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(609,a,645,a)].
% 1.52/1.82 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(609,a,646,a)].
% 1.52/1.82 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(609,a,647,a)].
% 1.52/1.82 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(609,a,648,a)].
% 1.52/1.82 Derived: -hBOOL(hAPP(list(int),bool,linorder_sorted(int),A)) | hBOOL(hAPP(list(int),bool,linorder_sorted(int),hAPP(list(int),list(int),hAPP(nat,fun(list(int),list(int)),drop(int),B),A))). [resolve(609,a,651,a)].
% 1.52/1.82 Derived: -hBOOL(hAPP(list(int),bool,linorder_sorted(int),A)) | hBOOL(hAPP(list(int),bool,linorder_sorted(int),hAPP(list(int),list(int),hAPP(nat,fun(list(int),list(int)),take(int),B),A))). [resolve(609,a,652,a)].
% 1.52/1.82 653 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom). [assumption].
% 1.52/1.82 Derived: linorder_sorted(nat) = ti(fun(list(nat),bool),linorder_sorted(nat)). [resolve(653,a,610,a)].
% 1.52/1.82 Derived: linord467138063of_set(nat) = ti(fun(fun(nat,bool),list(nat)),linord467138063of_set(nat)). [resolve(653,a,611,a)].
% 1.52/1.82 Derived: ord_max(nat) = ti(fun(nat,fun(nat,nat)),ord_max(nat)). [resolve(653,a,612,a)].
% 1.52/1.82 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(653,a,613,a)].
% 1.52/1.82 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),nil(nat))). [resolve(653,a,614,a)].
% 1.52/1.82 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(653,a,615,a)].
% 1.52/1.82 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(653,a,616,a)].
% 1.52/1.82 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(653,a,617,a)].
% 1.52/1.82 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(653,a,618,a)].
% 1.52/1.82 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(653,a,619,a)].
% 1.52/1.82 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(653,a,620,a)].
% 1.52/1.82 Derived: hAPP(fun(nat,bool),list(nat),linord467138063of_set(nat),bot_bot(fun(nat,bool))) = nil(nat). [resolve(653,a,621,a)].
% 1.52/1.82 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(653,a,622,a)].
% 1.52/1.82 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(653,a,624,a)].
% 1.52/1.82 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),A) = ti(nat,A). [resolve(653,a,626,a)].
% 1.52/1.82 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(653,a,627,a)].
% 1.52/1.82 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(653,a,629,a)].
% 1.59/1.85 Derived: ti(nat,A) = ti(nat,B) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(653,a,632,a)].
% 1.59/1.85 Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(653,a,633,a)].
% 1.59/1.85 Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(653,a,634,a)].
% 1.59/1.85 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(653,a,636,a)].
% 1.59/1.85 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(653,a,643,a)].
% 1.59/1.85 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(653,a,644,a)].
% 1.59/1.85 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(653,a,645,a)].
% 1.59/1.85 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(653,a,646,a)].
% 1.59/1.85 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(653,a,647,a)].
% 1.59/1.85 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(653,a,648,a)].
% 1.59/1.85 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(653,a,651,a)].
% 1.59/1.85 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(653,a,652,a)].
% 1.59/1.85 654 ordere236663937imp_le(int) # label(arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.59/1.85 655 -ordere236663937imp_le(A) | ord_max(A) = ti(fun(A,fun(A,A)),ord_max(A)) # label(tsy_c_Orderings_Oord__class_Omax_0_res) # label(axiom). [clausify(52)].
% 1.59/1.85 656 -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_289_add__less__imp__less__left) # label(axiom). [clausify(349)].
% 1.59/1.85 657 -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_290_add__less__imp__less__right) # label(axiom). [clausify(350)].
% 1.59/1.85 658 -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_294_add__less__cancel__left) # label(axiom). [clausify(354)].
% 1.59/1.85 659 -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_294_add__less__cancel__left) # label(axiom). [clausify(354)].
% 1.59/1.85 660 -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_295_add__less__cancel__right) # label(axiom). [clausify(355)].
% 1.63/1.87 661 -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_295_add__less__cancel__right) # label(axiom). [clausify(355)].
% 1.63/1.87 662 -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_327_max__add__distrib__left) # label(axiom). [clausify(387)].
% 1.63/1.87 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(654,a,656,a)].
% 1.63/1.87 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(654,a,657,a)].
% 1.63/1.87 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(654,a,659,a)].
% 1.63/1.87 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(654,a,661,a)].
% 1.63/1.87 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)),B). [resolve(654,a,662,a)].
% 1.63/1.87 663 ordere236663937imp_le(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.63/1.87 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(663,a,656,a)].
% 1.63/1.87 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(663,a,657,a)].
% 1.63/1.87 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(663,a,659,a)].
% 1.63/1.87 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(663,a,661,a)].
% 1.63/1.87 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(663,a,662,a)].
% 1.63/1.87 664 cancel146912293up_add(int) # label(arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.63/1.87 665 -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_279_add__imp__eq) # label(axiom). [clausify(339)].
% 1.70/1.95 666 cancel146912293up_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.70/1.95 667 comm_monoid_add(int) # label(arity_Int_Oint___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.70/1.95 668 -comm_monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_284_add_Ocomm__neutral) # label(axiom). [clausify(344)].
% 1.70/1.95 669 -comm_monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_287_add__0) # label(axiom). [clausify(347)].
% 1.70/1.95 670 comm_monoid_add(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.70/1.95 671 linord219039673up_add(int) # label(arity_Int_Oint___Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 1.70/1.95 672 -linord219039673up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_286_double__zero__sym) # label(axiom). [clausify(346)].
% 1.70/1.95 673 -linord219039673up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) = zero_zero(A) | zero_zero(A) != ti(A,B) # label(fact_286_double__zero__sym) # label(axiom). [clausify(346)].
% 1.70/1.95 674 -linord219039673up_add(A) | -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),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_335_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(395)].
% 1.70/1.95 675 -linord219039673up_add(A) | 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),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_335_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(395)].
% 1.70/1.95 676 -linord219039673up_add(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),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_336_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(396)].
% 1.70/1.95 677 -linord219039673up_add(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),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_336_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(396)].
% 1.70/1.95 678 -linord219039673up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_365_double__eq__0__iff) # label(axiom). [clausify(425)].
% 1.70/1.95 679 -linord219039673up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) = zero_zero(A) | zero_zero(A) != ti(A,B) # label(fact_365_double__eq__0__iff) # label(axiom). [clausify(425)].
% 1.70/1.95 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) != zero_zero(int) | zero_zero(int) = ti(int,A). [resolve(671,a,672,a)].
% 1.70/1.95 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) = zero_zero(int) | zero_zero(int) != ti(int,A). [resolve(671,a,673,a)].
% 1.70/1.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(671,a,674,a)].
% 1.70/1.95 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(671,a,675,a)].
% 1.70/1.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(671,a,676,a)].
% 1.70/1.95 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(671,a,677,a)].
% 1.70/1.95 680 ordere223160158up_add(int) # label(arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.70/1.97 681 -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_291_add__strict__mono) # label(axiom). [clausify(351)].
% 1.70/1.97 682 -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_292_add__strict__left__mono) # label(axiom). [clausify(352)].
% 1.70/1.97 683 -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_293_add__strict__right__mono) # label(axiom). [clausify(353)].
% 1.70/1.97 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D))). [resolve(680,a,681,a)].
% 1.70/1.97 684 ordere223160158up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.70/1.97 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(684,a,681,a)].
% 1.70/1.97 685 ordere216010020id_add(int) # label(arity_Int_Oint___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 1.70/1.97 686 -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_337_add__pos__pos) # label(axiom). [clausify(397)].
% 1.70/1.97 687 -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_338_add__neg__neg) # label(axiom). [clausify(398)].
% 1.70/1.97 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))). [resolve(685,a,686,a)].
% 1.70/1.97 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),zero_zero(int))). [resolve(685,a,687,a)].
% 1.70/1.97 688 ordere216010020id_add(nat) # label(arity_Nat_Onat___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 1.70/1.97 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(688,a,686,a)].
% 1.70/1.97 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(688,a,687,a)].
% 1.74/2.00 689 linordered_idom(int) # label(arity_Int_Oint___Rings_Olinordered__idom) # label(axiom). [assumption].
% 1.74/2.00 690 -linordered_idom(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),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_362_even__less__0__iff) # label(axiom). [clausify(422)].
% 1.74/2.00 691 -linordered_idom(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),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_362_even__less__0__iff) # label(axiom). [clausify(422)].
% 1.74/2.00 692 -linordered_idom(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_364_linorder__neqE__linordered__idom) # label(axiom). [clausify(424)].
% 1.74/2.00 693 -linordered_idom(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),B)),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_486_Ints__odd__less__0) # label(axiom). [clausify(545)].
% 1.74/2.00 694 -linordered_idom(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),B)),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_486_Ints__odd__less__0) # label(axiom). [clausify(545)].
% 1.74/2.00 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),A)),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(689,a,693,a)].
% 1.74/2.00 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),A)),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(689,a,694,a)].
% 1.74/2.00 695 linordered_semidom(int) # label(arity_Int_Oint___Rings_Olinordered__semidom) # label(axiom). [assumption].
% 1.74/2.00 696 -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_363_pos__add__strict) # label(axiom). [clausify(423)].
% 1.74/2.00 697 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A)))) # label(fact_463_less__add__one) # label(axiom). [clausify(522)].
% 1.74/2.00 698 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),zero_zero(A))) # label(fact_464_not__one__less__zero) # label(axiom). [clausify(523)].
% 1.74/2.00 699 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),one_one(A))) # label(fact_465_zero__less__one) # label(axiom). [clausify(524)].
% 1.74/2.00 700 -linordered_semidom(A) | 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),one_one(A)),one_one(A)))) # label(fact_468_zero__less__two) # label(axiom). [clausify(527)].
% 1.74/2.00 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))). [resolve(695,a,696,a)].
% 1.74/2.02 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int)))). [resolve(695,a,697,a)].
% 1.74/2.02 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),zero_zero(int))). [resolve(695,a,698,a)].
% 1.74/2.02 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))). [resolve(695,a,699,a)].
% 1.74/2.02 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int)))). [resolve(695,a,700,a)].
% 1.74/2.02 701 linordered_semidom(nat) # label(arity_Nat_Onat___Rings_Olinordered__semidom) # label(axiom). [assumption].
% 1.74/2.02 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(701,a,696,a)].
% 1.74/2.02 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat)))). [resolve(701,a,697,a)].
% 1.74/2.02 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),zero_zero(nat))). [resolve(701,a,698,a)].
% 1.74/2.02 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),one_one(nat))). [resolve(701,a,699,a)].
% 1.74/2.02 Derived: 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),one_one(nat)),one_one(nat)))). [resolve(701,a,700,a)].
% 1.74/2.02 702 comm_semiring_1(int) # label(arity_Int_Oint___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.74/2.02 703 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_394_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom). [clausify(454)].
% 1.74/2.02 704 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_395_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom). [clausify(455)].
% 1.74/2.02 705 -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_396_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom). [clausify(456)].
% 1.74/2.02 706 -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_397_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom). [clausify(457)].
% 1.74/2.02 707 -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_398_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom). [clausify(458)].
% 1.74/2.02 708 -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_399_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom). [clausify(459)].
% 1.74/2.02 709 -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_400_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom). [clausify(460)].
% 1.74/2.02 710 -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_401_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom). [clausify(461)].
% 1.74/2.02 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D)). [resolve(702,a,705,a)].
% 1.82/2.06 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),B). [resolve(702,a,706,a)].
% 1.82/2.06 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)). [resolve(702,a,709,a)].
% 1.82/2.06 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A). [resolve(702,a,710,a)].
% 1.82/2.06 711 comm_semiring_1(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.82/2.06 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(711,a,705,a)].
% 1.82/2.06 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(711,a,706,a)].
% 1.82/2.06 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(711,a,709,a)].
% 1.82/2.06 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(711,a,710,a)].
% 1.82/2.06 712 semiri456707255roduct(int) # label(arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption].
% 1.82/2.06 713 -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_402_add__0__iff) # label(axiom). [clausify(462)].
% 1.82/2.06 714 -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_402_add__0__iff) # label(axiom). [clausify(462)].
% 1.82/2.06 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != ti(int,A) | zero_zero(int) = ti(int,B). [resolve(712,a,713,a)].
% 1.82/2.06 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = ti(int,A) | zero_zero(int) != ti(int,B). [resolve(712,a,714,a)].
% 1.82/2.06 715 semiri456707255roduct(nat) # label(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption].
% 1.82/2.06 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != ti(nat,A) | zero_zero(nat) = ti(nat,B). [resolve(715,a,713,a)].
% 1.82/2.06 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = ti(nat,A) | zero_zero(nat) != ti(nat,B). [resolve(715,a,714,a)].
% 1.82/2.06 716 ordered_ab_group_add(int) # label(arity_Int_Oint___Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 1.82/2.06 717 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | -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),B),C)) # label(fact_412_diff__eq__diff__less) # label(axiom). [clausify(472)].
% 1.82/2.06 718 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | 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),B),C)) # label(fact_412_diff__eq__diff__less) # label(axiom). [clausify(472)].
% 1.82/2.06 719 -ordered_ab_group_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),minus_minus(A),B),C)),zero_zero(A))) # label(fact_417_less__iff__diff__less__0) # label(axiom). [clausify(477)].
% 1.82/2.09 720 -ordered_ab_group_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),minus_minus(A),B),C)),zero_zero(A))) # label(fact_417_less__iff__diff__less__0) # label(axiom). [clausify(477)].
% 1.82/2.09 721 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C) # label(fact_426_max__diff__distrib__left) # label(axiom). [clausify(486)].
% 1.82/2.09 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(716,a,717,a)].
% 1.82/2.09 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(716,a,718,a)].
% 1.82/2.09 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),zero_zero(int))). [resolve(716,a,719,a)].
% 1.82/2.09 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),zero_zero(int))). [resolve(716,a,720,a)].
% 1.82/2.09 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)),B). [resolve(716,a,721,a)].
% 1.82/2.09 722 group_add(int) # label(arity_Int_Oint___Groups_Ogroup__add) # label(axiom). [assumption].
% 1.82/2.09 723 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),C) = ti(A,B) # label(fact_413_add__diff__cancel) # label(axiom). [clausify(473)].
% 1.82/2.09 724 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),C) = ti(A,B) # label(fact_414_diff__add__cancel) # label(axiom). [clausify(474)].
% 1.82/2.09 725 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),zero_zero(A)) = ti(A,B) # label(fact_428_diff__0__right) # label(axiom). [clausify(488)].
% 1.82/2.09 726 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),B) = zero_zero(A) # label(fact_429_diff__self) # label(axiom). [clausify(489)].
% 1.82/2.09 727 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != zero_zero(A) | ti(A,C) = ti(A,B) # label(fact_431_right__minus__eq) # label(axiom). [clausify(491)].
% 1.82/2.09 728 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) = zero_zero(A) | ti(A,C) != ti(A,B) # label(fact_431_right__minus__eq) # label(axiom). [clausify(491)].
% 1.82/2.09 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),B) = ti(int,A). [resolve(722,a,723,a)].
% 1.82/2.09 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),B) = ti(int,A). [resolve(722,a,724,a)].
% 1.82/2.09 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),zero_zero(int)) = ti(int,A). [resolve(722,a,725,a)].
% 1.82/2.09 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),A) = zero_zero(int). [resolve(722,a,726,a)].
% 1.82/2.09 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != zero_zero(int) | ti(int,B) = ti(int,A). [resolve(722,a,727,a)].
% 1.82/2.09 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) = zero_zero(int) | ti(int,B) != ti(int,A). [resolve(722,a,728,a)].
% 1.82/2.09 729 ab_group_add(int) # label(arity_Int_Oint___Groups_Oab__group__add) # label(axiom). [assumption].
% 3.29/3.55 730 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | ti(A,E) != ti(A,D) | ti(A,C) = ti(A,B) # label(fact_427_diff__eq__diff__eq) # label(axiom). [clausify(487)].
% 3.29/3.55 731 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | ti(A,E) = ti(A,D) | ti(A,C) != ti(A,B) # label(fact_427_diff__eq__diff__eq) # label(axiom). [clausify(487)].
% 3.29/3.55 732 -ab_group_add(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B) = zero_zero(A) # label(fact_430_eq__iff__diff__eq__0) # label(axiom). [clausify(490)].
% 3.29/3.55 733 -ab_group_add(A) | ti(A,B) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B) != zero_zero(A) # label(fact_430_eq__iff__diff__eq__0) # label(axiom). [clausify(490)].
% 3.29/3.55 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | ti(int,D) != ti(int,C) | ti(int,B) = ti(int,A). [resolve(729,a,730,a)].
% 3.29/3.55 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | ti(int,D) = ti(int,C) | ti(int,B) != ti(int,A). [resolve(729,a,731,a)].
% 3.29/3.55 734 zero_neq_one(int) # label(arity_Int_Oint___Rings_Ozero__neq__one) # label(axiom). [assumption].
% 3.29/3.55 735 -zero_neq_one(A) | zero_zero(A) != one_one(A) # label(fact_466_one__neq__zero) # label(axiom). [clausify(525)].
% 3.29/3.55 736 -zero_neq_one(A) | zero_zero(A) != one_one(A) # label(fact_467_zero__neq__one) # label(axiom). [clausify(526)].
% 3.29/3.55 Derived: zero_zero(int) != one_one(int). [resolve(734,a,735,a)].
% 3.29/3.55 737 zero_neq_one(nat) # label(arity_Nat_Onat___Rings_Ozero__neq__one) # label(axiom). [assumption].
% 3.29/3.55 Derived: zero_zero(nat) != one_one(nat). [resolve(737,a,735,a)].
% 3.29/3.55
% 3.29/3.55 ============================== end predicate elimination =============
% 3.29/3.55
% 3.29/3.55 Auto_denials: (non-Horn, no changes).
% 3.29/3.55
% 3.29/3.55 Term ordering decisions:
% 3.29/3.55 Function symbol KB weights: nat=1. bool=1. int=1. suc=1. arrow_490897120le_alt=1. fconj=1. fFalse=1. fNot=1. fTrue=1. a=1. b=1. c1=1. c2=1. c3=1. fun=1. ti=1. foldr=1. list_rec=1. maps=1. combk=1. list_case=1. map_filter=1. f1=1. f2=1. f3=1. f4=1. f13=1. f14=1. f15=1. f16=1. f17=1. f18=1. f37=1. f42=1. f43=1. f44=1. f45=1. f46=1. f48=1. f49=1. f56=1. f58=1. f59=1. f64=1. f68=1. f69=1. f72=1. f73=1. list=1. ord_less=1. nil=1. plus_plus=1. zero_zero=1. cons=1. append=1. minus_minus=1. size_size=1. nth=1. ord_max=1. take=1. drop=1. rev=1. one_one=1. list_update=1. replicate=1. distinct=1. linorder_sorted=1. member=1. last=1. butlast=1. takeWhile=1. bot_bot=1. tl=1. list_ex=1. hd=1. listrelp=1. dropWhile=1. listMem=1. number_number_of=1. equal_equal=1. rotate1=1. null=1. splice=1. collect=1. member_1=1. ring_1_Ints=1. sublist=1. fequal=1. linord467138063of_set=1. list_size=1. insert=1. list_ex1=1. option=1. undefined=1. f57=1. f65=1. f70=1. f71=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. f47=1. f50=1. f51=1. f52=1. f55=1. f60=1. f61=1. f62=1. f63=1. f75=1. f76=1. f77=1. f78=1. hAPP=1. f19=1. f38=1. f39=1. f40=1. f41=1. f53=1. f54=1. f66=1. f67=1. f74=1. f8=1. f9=1. f10=1. f25=1. f26=1. f27=1. f28=1. f29=1. f30=1. f31=1. f32=1. f33=1. f34=1. f35=1. f36=1.
% 3.29/3.55
% 3.29/3.55 ============================== end of process initial clauses ========
% 3.29/3.55
% 3.29/3.55 ============================== CLAUSES FOR SEARCH ====================
% 3.29/3.55
% 3.29/3.55 ============================== end of clauses for search =============
% 3.29/3.55
% 3.29/3.55 ============================== SEARCH ================================
% 3.29/3.55
% 3.29/3.55 % Starting search at 0.88 seconds.
% 3.29/3.55
% 3.29/3.55 Low Water (keep): wt=194.000, iters=3708
% 3.29/3.55
% 3.29/3.55 Low Water (keep): wt=185.000, iters=3665
% 3.29/3.55
% 3.29/3.55 Low Water (keep): wt=184.000, iters=3661
% 3.29/3.55
% 3.29/3.55 Low Water (keep): wt=153.000, iters=3397
% 3.29/3.55
% 3.29/3.55 Low Water (keep): wt=145.000, iters=3637
% 3.29/3.55
% 3.29/3.55 Low Water (keep): wt=128.000, iters=3388
% 3.29/3.55
% 3.29/3.55 Low Water (keep): wt=127.000, iters=3491
% 3.29/3.55
% 3.29/3.55 Low Water (keep): wt=121.000, iters=3380
% 3.29/3.55
% 3.29/3.55 Low Water (keep): wt=118.000, iters=3372
% 3.29/3.55
% 3.29/3.55 Low Water (keep): wt=116.000, iters=3481
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=112.000, iters=3430
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=110.000, iters=3363
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=109.000, iters=3424
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% 259.08/259.46 Low Water (keep): wt=106.000, iters=3335
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=104.000, iters=3397
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=100.000, iters=3511
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=99.000, iters=3471
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=98.000, iters=3423
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=96.000, iters=3402
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=92.000, iters=3353
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=91.000, iters=3371
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=90.000, iters=3382
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=89.000, iters=3344
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=88.000, iters=3343
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=87.000, iters=3558
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=86.000, iters=3486
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=84.000, iters=3374
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=83.000, iters=3350
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=81.000, iters=3354
% 259.08/259.46
% 259.08/259.46 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 62 (0.00 of 2.76 sec).
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=80.000, iters=3342
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=79.000, iters=3345
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=78.000, iters=3360
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=77.000, iters=3349
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=76.000, iters=3357
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=75.000, iters=3375
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=74.000, iters=3362
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=73.000, iters=3373
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=72.000, iters=3349
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=71.000, iters=3584
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=68.000, iters=3490
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=67.000, iters=3457
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=66.000, iters=3395
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=65.000, iters=3420
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=64.000, iters=3392
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=62.000, iters=3383
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=61.000, iters=3340
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=60.000, iters=3341
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=59.000, iters=3342
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=58.000, iters=3403
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=57.000, iters=3373
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=56.000, iters=3387
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=55.000, iters=3380
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=54.000, iters=3433
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=53.000, iters=3416
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=52.000, iters=3337
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=51.000, iters=3741
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=46.000, iters=3639
% 259.08/259.46
% 259.08/259.46 Low Water (keep): wt=40.000, iters=3466
% 259.08/259.47
% 259.08/259.47 Low Water (displace): id=3968, wt=200.000
% 259.08/259.47
% 259.08/259.47 Low Water (displace): id=12443, wt=44.000
% 259.08/259.47
% 259.08/259.47 Low Water (displace): id=12457, wt=34.000
% 259.08/259.47
% 259.08/259.47 Low Water (displace): id=12477, wt=32.000
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=38.000, iters=3395
% 259.08/259.47
% 259.08/259.47 Low Water (displace): id=12532, wt=21.000
% 259.08/259.47
% 259.08/259.47 Low Water (displace): id=12541, wt=19.000
% 259.08/259.47
% 259.08/259.47 Low Water (displace): id=12854, wt=17.000
% 259.08/259.47
% 259.08/259.47 Low Water (displace): id=13011, wt=16.000
% 259.08/259.47
% 259.08/259.47 Low Water (displace): id=13046, wt=15.000
% 259.08/259.47
% 259.08/259.47 Low Water (displace): id=13998, wt=14.000
% 259.08/259.47
% 259.08/259.47 Low Water (displace): id=14099, wt=12.000
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=37.000, iters=3368
% 259.08/259.47
% 259.08/259.47 Low Water (displace): id=17048, wt=11.000
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=36.000, iters=3479
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=35.000, iters=3337
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=34.000, iters=3623
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=33.000, iters=3407
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=32.000, iters=3361
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=31.000, iters=3354
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=30.000, iters=3345
% 259.08/259.47
% 259.08/259.47 Low Water (displace): id=50327, wt=10.000
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=29.000, iters=3361
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=28.000, iters=3422
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=27.000, iters=3333
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=26.000, iters=3340
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=25.000, iters=3373
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=24.000, iters=3333
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=23.000, iters=3335
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=22.000, iters=3360
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=21.000, iters=3342
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=20.000, iters=3333
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=19.000, iters=3333
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=18.000, iters=3334
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=17.000, iters=3339
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=16.000, iters=3334
% 259.08/259.47
% 259.08/259.47 Low Water (keep): wt=15.000, iters=3358
% 259.08/259.47
% 259.08/259.47 ============================== STATISTICS ============================
% 259.08/259.47
% 259.08/259.47 Given=19394. Generated=5592012. Kept=270975. proofs=0.
% 259.08/259.47 Usable=19070. Sos=9997. Demods=527. Limbo=104, Disabled=242813. Hints=0.
% 259.08/259.47 Kept_by_rule=0, Deleted_by_rule=35193.
% 259.08/259.47 Forward_subsumed=705390. Back_subsumed=99.
% 259.08/259.47 Sos_limit_deleted=4580454. Sos_displaced=240816. Sos_removed=0.
% 259.08/259.47 New_demodulators=1345 (0 lex), Back_demodulated=811. Back_unit_deleted=78.
% 259.08/259.47 Demod_attempts=274705480. Demod_rewrites=1325016.
% 259.08/259.47 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
% 259.08/259.47 Nonunit_fsub_feature_tests=2370639. Nonunit_bsub_feature_tests=12576.
% 259.08/259.47 Megabytes=419.43.
% 259.08/259.47 User_CPU=254.69, System_CPU=3.24, Wall_clock=258.
% 259.08/259.47
% 259.08/259.47 Megs malloced by palloc(): 400.
% 259.08/259.47 type (bytes each) gets frees in use bytes
% 259.08/259.47 chunk ( 104) 35898 35898 0 0.0 K
% 259.08/259.47 string_buf ( 8) 32325 32325 0 0.0 K
% 259.08/259.47 token ( 20) 81872 81872 0 0.0 K
% 259.08/259.47 pterm ( 16) 54805 54805 0 0.0 K
% 259.08/259.47 hashtab ( 8) 577 577 0 0.0 K
% 259.08/259.47 hashnode ( 8) 1883 1883 0 0.0 K
% 259.08/259.47 term ( 20) 480099934 469780624 10319310 201549.0 K
% 259.08/259.47 term arg arrays: 43799.6 K
% 259.08/259.47 attribute ( 12) 4647 162 4485 52.6 K
% 259.08/259.47 ilist ( 8) 1585248374 1583555530 1692844 13225.3 K
% 259.08/259.47 plist ( 8) 11184420 10870390 314030 2453.4 K
% 259.08/259.47 i2list ( 12) 30744178 30744178 0 0.0 K
% 259.08/259.47 just ( 12) 7397524 7043285 354239 4151.2 K
% 259.08/259.47 parajust ( 16) 3804393 3570504 233889 3654.5 K
% 259.08/259.47 instancejust ( 8) 0 0 0 0.0 K
% 259.08/259.47 ivyjust ( 24) 0 0 0 0.0 K
% 259.08/259.47 formula ( 28) 19978 12772 7206 197.0 K
% 259.08/259.47 formula arg arrays: 23.6 K
% 259.08/259.47 topform ( 52) 5593668 5321037 272631 13844.5 K
% 259.08/259.47 clist_pos ( 20) 807112 534601 272511 5322.5 K
% 259.08/259.47 clist ( 16) 8 1 7 0.1 K
% 259.08/259.47 context ( 808) 37303959 37303957 2 1.6 K
% 259.08/259.47 trail ( 12) 31857466 31857465 1 0.0 K
% 259.08/259.47 ac_match_pos (70044) 0 0 0 0.0 K
% 259.08/259.47 ac_match_free_vars_pos (20020)
% 259.08/259.47 0 0 0 0.0 K
% 259.08/259.47 btm_state ( 60) 0 0 0 0.0 K
% 259.08/259.47 btu_state ( 60) 0 0 0 0.0 K
% 259.08/259.47 ac_position (285432) 0 0 0 0.0 K
% 259.08/259.47 fpa_trie ( 20) 2690015 2136264 553751 10815.4 K
% 259.08/259.47 fpa_state ( 28) 21900270 21900270 0 0.0 K
% 259.08/259.47 fpa_index ( 12) 10 0 10 0.1 K
% 259.08/259.47 fpa_chunk ( 20) 3643932 3510235 133697 2611.3 K
% 259.08/259.47 fpa_list ( 16) 2207995 0 2207995 34499.9 K
% 259.08/259.47 fpa_list chunks: 12070.8 K
% 259.08/259.47 discrim ( 12) 3372220 3264589 107631 1261.3 K
% 259.08/259.47 discrim_pos ( 16) 1577686 1577686 0 0.0 K
% 259.08/259.47 flat2 ( 32) 208005255 208005255 0 0.0 K
% 259.08/259.47 flat ( 48) 0 0 0 0.0 K
% 259.08/259.47 flatterm ( 32) 347553619 347553619 0 0.0 K
% 259.08/259.47 mindex ( 28) 13 0 13 0.4 K
% 259.08/259.47 mindex_pos ( 56) 26066259 26066259 0 0.0 K
% 259.08/259.47 lindex ( 12) 5 0 5 0.1 K
% 259.08/259.47 clash ( 40) 0 0 0 0.0 K
% 259.08/259.47 di_tree ( 12) 27487115 22958883 4528232 53065.2 K
% 259.08/259.47 avl_node ( 20) 540952 520958 19994 390.5 K
% 259.08/259.47
% 259.08/259.47 Memory report, 20 @ 20 = 400 megs (400.00 megs used).
% 259.08/259.47 List 1, length 5, 0.0 K
% 259.08/259.47 List 2, length 612, 4.8 K
% 259.08/259.47 List 3, length 103988, 1218.6 K
% 259.08/259.47 List 7, length 65, 1.8 K
% 259.08/259.47 List 8, length 3340, 104.4 K
% 259.08/259.47 List 10, length 8, 0.3 K
% 259.08/259.47 List 14, length 2, 0.1 K
% 259.08/259.47 List 16, length 2445, 152.8 K
% 259.08/259.47 List 26, length 253, 25.7 K
% 259.08/259.47 List 32, length 2100, 262.5 K
% 259.08/259.47 List 64, length 1338, 334.5 K
% 259.08/259.47 List 128, length 408, 204.0 K
% 259.08/259.47 List 202, length 2, 1.6 K
% 259.08/259.47
% 259.08/259.47 ============================== SELECTOR REPORT =======================
% 259.08/259.47 Sos_deleted=4580454, Sos_displaced=240816, Sos_size=9997
% 259.08/259.47 SELECTOR PART PRIORITY ORDER SIZE SELECTED
% 259.08/259.47 I 2147483647 high age 0 745
% 259.08/259.47 H 1 high weight 0 0
% 259.08/259.47 A 1 low age 9997 2073
% 259.08/259.47 F 4 low weight 980 8288
% 259.08/259.47 T 4 low weight 9017 8288
% 259.08/259.47 ============================== end of selector report ================
% 259.08/259.47
% 259.08/259.47 ============================== end of statistics =====================
% 259.08/259.47
% 259.08/259.47 Exiting with failure.
% 259.08/259.47
% 259.08/259.47 Process 24852 exit (max_megs) Fri Jul 1 22:22:34 2022
% 259.08/259.47 Prover9 interrupted
%------------------------------------------------------------------------------