TSTP Solution File: SCT170+6 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT170+6 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 22:04:25 EDT 2022
% Result : Unknown 104.86s 105.16s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SCT170+6 : TPTP v8.1.0. Released v5.3.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sat Jul 2 06:17:22 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.47/1.77 ============================== Prover9 ===============================
% 1.47/1.77 Prover9 (32) version 2009-11A, November 2009.
% 1.47/1.77 Process 15777 was started by sandbox on n009.cluster.edu,
% 1.47/1.77 Sat Jul 2 06:17:23 2022
% 1.47/1.77 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15623_n009.cluster.edu".
% 1.47/1.77 ============================== end of head ===========================
% 1.47/1.77
% 1.47/1.77 ============================== INPUT =================================
% 1.47/1.77
% 1.47/1.77 % Reading from file /tmp/Prover9_15623_n009.cluster.edu
% 1.47/1.77
% 1.47/1.77 set(prolog_style_variables).
% 1.47/1.77 set(auto2).
% 1.47/1.77 % set(auto2) -> set(auto).
% 1.47/1.77 % set(auto) -> set(auto_inference).
% 1.47/1.77 % set(auto) -> set(auto_setup).
% 1.47/1.77 % set(auto_setup) -> set(predicate_elim).
% 1.47/1.77 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.47/1.77 % set(auto) -> set(auto_limits).
% 1.47/1.77 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.47/1.77 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.47/1.77 % set(auto) -> set(auto_denials).
% 1.47/1.77 % set(auto) -> set(auto_process).
% 1.47/1.77 % set(auto2) -> assign(new_constants, 1).
% 1.47/1.77 % set(auto2) -> assign(fold_denial_max, 3).
% 1.47/1.77 % set(auto2) -> assign(max_weight, "200.000").
% 1.47/1.77 % set(auto2) -> assign(max_hours, 1).
% 1.47/1.77 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.47/1.77 % set(auto2) -> assign(max_seconds, 0).
% 1.47/1.77 % set(auto2) -> assign(max_minutes, 5).
% 1.47/1.77 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.47/1.77 % set(auto2) -> set(sort_initial_sos).
% 1.47/1.77 % set(auto2) -> assign(sos_limit, -1).
% 1.47/1.77 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.47/1.77 % set(auto2) -> assign(max_megs, 400).
% 1.47/1.77 % set(auto2) -> assign(stats, some).
% 1.47/1.77 % set(auto2) -> clear(echo_input).
% 1.47/1.77 % set(auto2) -> set(quiet).
% 1.47/1.77 % set(auto2) -> clear(print_initial_clauses).
% 1.47/1.77 % set(auto2) -> clear(print_given).
% 1.47/1.77 assign(lrs_ticks,-1).
% 1.47/1.77 assign(sos_limit,10000).
% 1.47/1.77 assign(order,kbo).
% 1.47/1.77 set(lex_order_vars).
% 1.47/1.77 clear(print_given).
% 1.47/1.77
% 1.47/1.77 % formulas(sos). % not echoed (617 formulas)
% 1.47/1.77
% 1.47/1.77 ============================== end of input ==========================
% 1.47/1.77
% 1.47/1.77 % From the command line: assign(max_seconds, 300).
% 1.47/1.77
% 1.47/1.77 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.47/1.77
% 1.47/1.77 % Formulas that are not ordinary clauses:
% 1.47/1.77 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].
% 1.47/1.77 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].
% 1.47/1.77 3 (all X_a ti(fun(X_a,X_a),combi(X_a)) = combi(X_a)) # label(tsy_c_COMBI_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 4 (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].
% 1.47/1.77 5 (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].
% 1.47/1.77 6 (all X_a all X_b ti(fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),in_rel(X_a,X_b)) = in_rel(X_a,X_b)) # label(tsy_c_FunDef_Oin__rel_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 7 (all X_a all X_b ti(fun(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool))),pi(X_a,X_b)) = pi(X_a,X_b)) # label(tsy_c_FuncSet_OPi_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 8 (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].
% 1.47/1.77 9 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 10 (all X_a ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a)) = if(X_a)) # label(tsy_c_If_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 11 (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].
% 1.47/1.77 12 (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].
% 1.47/1.77 13 (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].
% 1.47/1.77 14 (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].
% 1.47/1.77 15 (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].
% 1.47/1.77 16 (all X_a all X_b ti(fun(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a))),foldl(X_a,X_b)) = foldl(X_a,X_b)) # label(tsy_c_List_Ofoldl_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 17 (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].
% 1.47/1.77 18 (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].
% 1.47/1.77 19 (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].
% 1.47/1.77 20 (all X_a ti(fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool)),lex(X_a)) = lex(X_a)) # label(tsy_c_List_Olex_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 21 (all X_a ti(fun(fun(product_prod(X_a,X_a),bool),fun(nat,fun(product_prod(list(X_a),list(X_a)),bool))),lexn(X_a)) = lexn(X_a)) # label(tsy_c_List_Olexn_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 22 (all X_a ti(fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool)),lexord(X_a)) = lexord(X_a)) # label(tsy_c_List_Olexord_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 23 (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].
% 1.47/1.77 24 (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].
% 1.47/1.77 25 (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].
% 1.47/1.77 26 (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].
% 1.47/1.77 27 (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].
% 1.47/1.77 28 (all X_a ti(fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool)),listrel(X_a)) = listrel(X_a)) # label(tsy_c_List_Olistrel_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 29 (all X_a ti(fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool)),listrel1(X_a)) = listrel1(X_a)) # label(tsy_c_List_Olistrel1_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 30 (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].
% 1.47/1.77 31 (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].
% 1.47/1.77 32 (all X_b ti(fun(list(X_b),bool),null(X_b)) = null(X_b)) # label(tsy_c_List_Onull_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 33 (all X_a ti(fun(fun(X_a,bool),fun(list(X_a),product_prod(list(X_a),list(X_a)))),partition(X_a)) = partition(X_a)) # label(tsy_c_List_Opartition_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 34 (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].
% 1.47/1.77 35 (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].
% 1.47/1.77 36 (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].
% 1.47/1.77 37 (all X_a ti(fun(list(X_a),fun(X_a,bool)),set(X_a)) = set(X_a)) # label(tsy_c_List_Oset_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 38 (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].
% 1.47/1.77 39 (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].
% 1.47/1.77 40 (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].
% 1.47/1.77 41 (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].
% 1.47/1.77 42 (all X_a ti(fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),nat_case(X_a)) = nat_case(X_a)) # label(tsy_c_Nat_Onat_Onat__case_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 43 (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].
% 1.47/1.77 44 (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].
% 1.47/1.77 45 (all X_b (ord(X_b) -> ti(fun(X_b,fun(X_b,bool)),ord_less_eq(X_b)) = ord_less_eq(X_b))) # label(tsy_c_Orderings_Oord__class_Oless__eq_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 46 (all X_a (top(X_a) -> ti(X_a,top_top(X_a)) = top_top(X_a))) # label(tsy_c_Orderings_Otop__class_Otop_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 47 (all X_a all X_b ti(fun(X_a,fun(X_b,product_prod(X_a,X_b))),product_Pair(X_a,X_b)) = product_Pair(X_a,X_b)) # label(tsy_c_Product__Type_OPair_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 48 (all X_a all X_b all X_c ti(fun(fun(product_prod(X_a,X_b),X_c),fun(X_a,fun(X_b,X_c))),product_curry(X_a,X_b,X_c)) = product_curry(X_a,X_b,X_c)) # label(tsy_c_Product__Type_Ocurry_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 49 (all X_b all X_c all X_a ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),produc1605651328_split(X_b,X_c,X_a)) = produc1605651328_split(X_b,X_c,X_a)) # label(tsy_c_Product__Type_Ointernal__split_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 50 (all X_b all X_c all X_a ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),product_prod_case(X_b,X_c,X_a)) = product_prod_case(X_b,X_c,X_a)) # label(tsy_c_Product__Type_Oprod_Oprod__case_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 51 (all X_b all X_c all X_a ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),product_prod_rec(X_b,X_c,X_a)) = product_prod_rec(X_b,X_c,X_a)) # label(tsy_c_Product__Type_Oprod_Oprod__rec_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 52 (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].
% 1.47/1.77 53 (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].
% 1.47/1.77 54 (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].
% 1.47/1.77 55 (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].
% 1.47/1.77 56 (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].
% 1.47/1.77 57 (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].
% 1.47/1.77 58 (all X_b ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b)) = member(X_b)) # label(tsy_c_member_res) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 59 (all I (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I))) <-> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p_1,I))))) # label(fact_5_iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 60 -(all C_2 -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_2),nil(arrow_490897120le_alt))))))) # label(fact_6__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 61 (all X_1 all Y_1 all L_1 all Z_2 (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,L_1),Z_2))) <-> ti(arrow_490897120le_alt,Y_1) != ti(arrow_490897120le_alt,Z_2) & (ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Z_2) -> ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_1)) & (ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Z_2) -> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_1)),L_1))))) # label(fact_10_in__mkbot) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 62 (all X_1 all Y_1 all L_1 all Z_2 (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,L_1),Z_2))) <-> ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Z_2) & (ti(arrow_490897120le_alt,Y_1) = ti(arrow_490897120le_alt,Z_2) -> ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_1)) & (ti(arrow_490897120le_alt,Y_1) != ti(arrow_490897120le_alt,Z_2) -> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_1)),L_1))))) # label(fact_11_in__mktop) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 63 (all X_1 all Y_1 all L_1 all Aa all Ba (ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba) -> (hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)) -> (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,L_1),Aa),Ba))) <-> ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_1) & (ti(arrow_490897120le_alt,Y_1) = ti(arrow_490897120le_alt,Aa) -> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Ba)),L_1))) & (ti(arrow_490897120le_alt,Y_1) != ti(arrow_490897120le_alt,Aa) -> (ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Aa) -> ti(arrow_490897120le_alt,Y_1) = ti(arrow_490897120le_alt,Ba) | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Y_1)),L_1))) & (ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Aa) -> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_1)),L_1)))))))) # label(fact_12_in__below) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 64 (all X_a all X_b all Pa ((all X1 hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,X1))) <-> (all A_4 all B_2 hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_2)))))) # label(fact_13_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 65 (all X_b all X_a all Aa all Ba all A_5 all B_3 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_5),B_3) <-> ti(X_a,Aa) = ti(X_a,A_5) & ti(X_b,Ba) = ti(X_b,B_3))) # label(fact_14_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 66 (all X_b all X_a all A_2 all B_1 all A_6 all B_4 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_6),B_4) -> -(ti(X_a,A_2) = ti(X_a,A_6) -> ti(X_b,B_1) != ti(X_b,B_4)))) # label(fact_15_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 67 (all X_b all X_a all R_1 all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),in_rel(X_a,X_b),R_1),X_1),Y_1)) <-> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y_1)),R_1)))) # label(fact_16_in__rel__def) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 68 (all L_1 all X_1 all Y_1 (ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_1) -> (hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)) -> hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,L_1),X_1),Y_1)),arrow_2064824852le_Lin))))) # label(fact_17_below__Lin) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 69 (all P_a all Pa all A_5 all B_3 all Aa all Ba (ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba) -> (ti(arrow_490897120le_alt,A_5) != ti(arrow_490897120le_alt,B_3) -> (ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,B_3) -> (ti(arrow_490897120le_alt,Ba) != ti(arrow_490897120le_alt,A_5) -> (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Pa),arrow_1111136790e_Prof)) -> (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),P_a),arrow_1111136790e_Prof)) -> ((all I (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I))) <-> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_a,I))))) -> (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa))) -> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_a)))))))))))) # label(fact_19__C1_C) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 70 (all P_a all Pa all A_5 all B_3 all Aa all Ba (ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba) -> (ti(arrow_490897120le_alt,A_5) != ti(arrow_490897120le_alt,B_3) -> (ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,B_3) -> (ti(arrow_490897120le_alt,Ba) != ti(arrow_490897120le_alt,A_5) -> (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Pa),arrow_1111136790e_Prof)) -> (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),P_a),arrow_1111136790e_Prof)) -> ((all I (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I))) <-> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_a,I))))) -> (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa))) <-> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_a)))))))))))) # label(fact_20__C2_C) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 71 (all L_1 (hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)) -> hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),combk(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),arrow_660593299e_indi),L_1)),arrow_1111136790e_Prof)))) # label(fact_22_const__Lin__Prof) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 72 (all X_1 all L_1 (hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)) -> hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,L_1),X_1)),arrow_2064824852le_Lin)))) # label(fact_23_mkbot__Lin) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 73 (all X_1 all L_1 (hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)) -> hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,L_1),X_1)),arrow_2064824852le_Lin)))) # label(fact_24_mktop__Lin) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.77 74 (all Aa all Ba all L_1 (hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)) -> (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),L_1)) -> -hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Aa)),L_1))))) # label(fact_25_Lin__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 75 (all X_1 all Y_1 all L_1 (hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)) -> (ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_1) -> (-hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_1)),L_1)) <-> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Y_1),X_1)),L_1)))))) # label(fact_26_notin__Lin__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 76 (all A_2 all B_1 (ti(arrow_490897120le_alt,A_2) != ti(arrow_490897120le_alt,B_1) -> (exists C_2 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_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),B_1),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_2),nil(arrow_490897120le_alt))))))))) # label(fact_27_third__alt) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 77 (all Fa (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,Fa)) <-> (all X_2 (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof)) -> (all Xa (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Xa),arrow_1111136790e_Prof)) -> (all A_4 all B_2 ((all I (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_4),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I))) <-> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_4),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Xa,I))))) -> (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_4),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2))) <-> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_4),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,Xa)))))))))))) # label(fact_28_IIA__def) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 78 (all Fa (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,Fa)) <-> (all X_2 (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof)) -> (all A_4 all B_2 ((all I hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_4),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I)))) -> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_4),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2))))))))) # label(fact_29_unanimity__def) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 79 (all Aa all Ba (ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba) -> (exists X_2 (hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X_2),arrow_2064824852le_Lin)) & hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),X_2)))))) # label(fact_30_complete__Lin) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 80 (all X_1 all Y_1 all L_1 all Aa all Ba (ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba) -> (hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)) -> (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,L_1),Aa),Ba))) <-> ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_1) & (ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Ba) -> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Y_1)),L_1))) & (ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Ba) -> (ti(arrow_490897120le_alt,Y_1) = ti(arrow_490897120le_alt,Ba) -> ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Aa) | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Aa)),L_1))) & (ti(arrow_490897120le_alt,Y_1) != ti(arrow_490897120le_alt,Ba) -> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_1)),L_1)))))))) # label(fact_31_in__above) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 81 (all X_b all X_c all X_a all F1 all Aa all Ba hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_rec(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,Aa),Ba)) # label(fact_32_prod_Orecs) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 82 (all X_a hBOOL(hAPP(list(X_a),bool,distinct(X_a),nil(X_a)))) # label(fact_33_distinct_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 83 (all X_a all A_6 all List_3 nil(X_a) != hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_6),List_3)) # label(fact_34_list_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 84 (all X_a all A_6 all List_3 hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_6),List_3) != nil(X_a)) # label(fact_35_list_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 85 (exists A_4 exists B_2 exists C_2 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_2),nil(arrow_490897120le_alt))))))) # label(fact_36_alt3) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 86 (exists L_2 hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_2),arrow_2064824852le_Lin))) # label(fact_37_linear__alt) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 87 (all X_a all Aa all List all A_5 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_5),List_2) <-> ti(X_a,Aa) = ti(X_a,A_5) & List = List_2)) # label(fact_38_list_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 88 (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_39_not__Cons__self2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 89 (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_40_not__Cons__self) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 90 (all L_1 all X_1 all Y_1 (ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_1) -> (hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)) -> hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,L_1),X_1),Y_1)),arrow_2064824852le_Lin))))) # label(fact_41_above__Lin) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 91 (all I_2 all Fa (hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Fa),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) -> ((all X_2 (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof)) -> (all A_4 all B_2 (ti(arrow_490897120le_alt,A_4) != ti(arrow_490897120le_alt,B_2) -> (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_4),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_2))) -> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_4),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2)))))))) -> hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,Fa),I_2))))) # label(fact_42_dictatorI) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 92 (all X_a all X_b all X_1 all F all A_1 all B (hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,fun(X_b,bool),B,X_1))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))))) # label(fact_43_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 93 (all X_a all Y (Y != nil(X_a) -> -(all A_4 all List_1 Y != hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_4),List_1)))) # label(fact_44_list_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 94 (all X_a all Xs_1 (Xs_1 != nil(X_a) <-> (exists Y_2 exists Ys 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)))) # label(fact_45_neq__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 95 (all Fa all I_2 (hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,Fa),I_2)) <-> (all X_2 (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof)) -> hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2) = hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_2))))) # label(fact_46_dictator__def) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 96 (all X_a all A_1 hBOOL(hAPP(fun(fun(X_a,X_a),bool),bool,hAPP(fun(X_a,X_a),fun(fun(fun(X_a,X_a),bool),bool),member(fun(X_a,X_a)),combi(X_a)),hAPP(fun(X_a,fun(X_a,bool)),fun(fun(X_a,X_a),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_a,bool)),fun(fun(X_a,X_a),bool)),pi(X_a,X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),combk(fun(X_a,bool),X_a),A_1))))) # label(fact_47_funcset__id) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.78 97 (all X_a all X_b all X_1 all F all A_1 all B (hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B)))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),B))))) # label(fact_48_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 98 (all X_a all V_1 all Va hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),V_1),Va)),nil(X_a)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),V_1),Va)) # label(fact_49_splice_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 99 (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_50_list_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 100 (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_51_list_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 101 (all X_a all X all Xs all Y all Ys_2 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_2)) = 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_2)))) # label(fact_52_splice_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 102 (all X_a all Ys_2 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_2) = Ys_2) # label(fact_53_splice_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 103 (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_54_splice__Nil2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 104 (all X_a all X_b all X_1 all F all A_1 all B (hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,fun(X_b,bool),B,X_1)))))) # label(fact_55_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 105 (all X_b all X_a all F all B all A_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,fun(X_b,bool),B,X_2))))) -> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))))) # label(fact_56_Pi__I) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 106 (all X_b all X_a all F all B all A_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),B)))) -> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B)))))) # label(fact_57_funcsetI) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 107 (all X_b all X_a all F all B all A_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,fun(X_b,bool),B,X_2))))) -> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))))) # label(fact_58_Pi__I_H) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 108 (all X_b all X_a all B all F all G all A_1 ((all W (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),W),A_1)) -> hAPP(X_a,X_b,F,W) = hAPP(X_a,X_b,G,W))) -> (hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) <-> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),G),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)))))) # label(fact_59_Pi__cong) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 109 (all X_a all X_b all S_1 all R_1 ((all X_2 all Xa (hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Xa)),R_1)) <-> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Xa)),S_1)))) <-> ti(fun(product_prod(X_a,X_b),bool),R_1) = ti(fun(product_prod(X_a,X_b),bool),S_1))) # label(fact_60_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 110 (all X_a all X_b all Y -(all A_4 all B_2 ti(product_prod(X_a,X_b),Y) != hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_2))) # label(fact_61_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 111 (all X_a all X_b all P_2 -(all X_2 all Y_2 ti(product_prod(X_a,X_b),P_2) != hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2))) # label(fact_62_PairE) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 112 (all X_a all X_b all X_c all Y -(all A_4 all B_2 all C_2 ti(product_prod(X_a,product_prod(X_b,X_c)),Y) != hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_4),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B_2),C_2)))) # label(fact_63_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 113 (all X_a all X_b all X_c all X_1 all Pa ((all A_4 all B_2 all C_2 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,Pa,hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_4),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B_2),C_2))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,Pa,X_1)))) # label(fact_64_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 114 (all X_a all X_b all X_c all X_d all X_e all X_f all X_1 all Pa ((all A_4 all B_2 all C_2 all D all E all F_1 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,Pa,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),A_4),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),B_2),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),C_2),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),D),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),E),F_1)))))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,Pa,X_1)))) # label(fact_65_prod__induct6) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 115 (all X_a all X_b all X_c all X_d all X_e all X_f all Y -(all A_4 all B_2 all C_2 all D all E all F_1 ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),Y) != hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),A_4),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),B_2),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),C_2),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),D),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),E),F_1))))))) # label(fact_66_prod__cases6) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 116 (all X_a all X_b all X_c all X_d all X_e all X_1 all Pa ((all A_4 all B_2 all C_2 all D all E hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,Pa,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),A_4),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),B_2),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),C_2),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),D),E))))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,Pa,X_1)))) # label(fact_67_prod__induct5) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 117 (all X_a all X_b all X_c all X_d all X_e all Y -(all A_4 all B_2 all C_2 all D all E ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),Y) != hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),A_4),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),B_2),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),C_2),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),D),E)))))) # label(fact_68_prod__cases5) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 118 (all X_a all X_b all X_c all X_d all X_1 all Pa ((all A_4 all B_2 all C_2 all D hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,Pa,hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),A_4),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),B_2),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),C_2),D)))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,Pa,X_1)))) # label(fact_69_prod__induct4) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 119 (all X_a all X_b all X_c all X_d all Y -(all A_4 all B_2 all C_2 all D ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),Y) != hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),A_4),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),B_2),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),C_2),D))))) # label(fact_70_prod__cases4) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 120 (all X_a all X_b all Pa ((exists X1 hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,X1))) <-> (exists A_4 exists B_2 hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_2)))))) # label(fact_71_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 121 (all X_b all X_c all X_a all Ca all Aa all Ba hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),produc1605651328_split(X_b,X_c,X_a),Ca),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),Ca,Aa),Ba)) # label(fact_72_internal__split__conv) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 122 (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_73_insert__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 123 (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_74_distinct__insert) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 124 (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].
% 1.56/1.78 125 (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].
% 1.56/1.78 126 (all X_a all Pa hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa) = ti(fun(X_a,bool),Pa)) # label(fact_77_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 127 (all X_a all Pa all Xs_1 (Xs_1 != nil(X_a) -> ((all X_2 hBOOL(hAPP(list(X_a),bool,Pa,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,Pa,Xs_2)) -> hBOOL(hAPP(list(X_a),bool,Pa,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,Pa,Xs_1)))))) # label(fact_78_list__nonempty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 128 (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_79_list_Orecs_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 129 (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_80_list_Orecs_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 130 (all X_b all X_c all X_a all X_2 all Xa all Xb hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),hAPP(fun(product_prod(X_a,X_b),X_c),fun(X_a,fun(X_b,X_c)),product_curry(X_a,X_b,X_c),X_2),Xa),Xb) = hAPP(product_prod(X_a,X_b),X_c,X_2,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Xa),Xb))) # label(fact_81_curry__def) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 131 (all X_a all X_b all F all Aa all Ba (hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba)))) # label(fact_82_curryI) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 132 (all X_b hBOOL(hAPP(list(X_b),bool,null(X_b),nil(X_b)))) # label(fact_83_null__rec_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 133 (all X_a all Xs_1 (hBOOL(hAPP(list(X_a),bool,null(X_a),Xs_1)) <-> Xs_1 = nil(X_a))) # label(fact_84_List_Onull__def) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 134 (all X_a all Xs_1 (Xs_1 = nil(X_a) <-> hBOOL(hAPP(list(X_a),bool,null(X_a),Xs_1)))) # label(fact_85_eq__Nil__null) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 135 (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_86_null__rec_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 136 (all X_b all X_a all F all Aa all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))))) # label(fact_87_curryD) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 137 (all X_b all X_a all F all Aa all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))))) # label(fact_88_curryE) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 138 (all X_c all X_a all X_b all F all Aa all Ba hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),hAPP(fun(product_prod(X_b,X_c),X_a),fun(X_b,fun(X_c,X_a)),product_curry(X_b,X_c,X_a),F),Aa),Ba) = hAPP(product_prod(X_b,X_c),X_a,F,hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba))) # label(fact_89_curry__conv) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 139 (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_90_equal__Nil__null) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 140 (all X_a all Aa all X_1 all Ba all Y_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Aa),X_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Ba),Y_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))) <-> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),Aa),Ba)),R_2)) | ti(X_a,Aa) = ti(X_a,Ba) & hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),X_1),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))))) # label(fact_92_lexord__cons__cons) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 141 (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_93_maps__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 142 (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_94_sorted__single) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 143 (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_95_distinct__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 144 (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)) = ti(X_a,X))) # label(fact_96_last__ConsL) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 145 (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)) = hAPP(list(X_a),X_a,last(X_a),Xs))) # label(fact_97_last__ConsR) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 146 (all X_a all X_1 hBOOL(hAPP(X_a,bool,top_top(fun(X_a,bool)),X_1))) # label(fact_98_top1I) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 147 (all X_a (linorder(X_a) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),nil(X_a))))) # label(fact_99_sorted_ONil) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 148 (all X_a all X_1 all Y_1 (hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),equal_equal(list(X_a)),X_1),Y_1)) <-> X_1 = Y_1)) # label(fact_100_equal__list__def) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 149 (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_101_sorted__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 150 (all X_a all X_b all A_1 hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),top_top(fun(X_b,bool)))) = top_top(fun(fun(X_a,X_b),bool))) # label(fact_102_Pi__UNIV) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 151 (all X_a hAPP(list(X_a),list(X_a),butlast(X_a),nil(X_a)) = nil(X_a)) # label(fact_103_butlast_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 152 (all X_a all X_1 all R_2 -hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),X_1),nil(X_a))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2)))) # label(fact_104_lexord__Nil__right) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 153 (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_105_butlast_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 154 (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_106_last_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 155 (all X_a all Y_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),nil(X_a)),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))) <-> (exists A_4 exists X_2 Y_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_4),X_2)))) # label(fact_107_lexord__Nil__left) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 156 (all X_a all Xs_1 all R_2 ((all X_2 -hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),X_2)),R_2))) -> -hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Xs_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))))) # label(fact_108_lexord__irreflexive) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 157 (all X_a all X_1 all Y_1 all R_2 ((all A_4 all B_2 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),A_4),B_2)),R_2)) | ti(X_a,A_4) = ti(X_a,B_2) | hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),B_2),A_4)),R_2)))) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),X_1),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))) | X_1 = Y_1 | hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Y_1),X_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))))) # label(fact_109_lexord__linear) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 158 (all X_a all X_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),top_top(fun(X_a,bool))))) # label(fact_110_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 159 (all X_a all X_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),top_top(fun(X_a,bool))))) # label(fact_111_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 160 (all X_b all X_a (top(X_a) -> (all X_1 hAPP(X_b,X_a,top_top(fun(X_b,X_a)),X_1) = top_top(X_a)))) # label(fact_112_top__apply) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 161 (all X_a all Xs_1 (Xs_1 != nil(X_a) -> (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),hAPP(list(X_a),X_a,last(X_a),Xs_1)))),Xs_1) = hAPP(list(X_a),list(X_a),butlast(X_a),Xs_1)))) # label(fact_113_takeWhile__not__last) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 162 (all X_a all Pa hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(fun(X_a,bool),fun(list(X_a),product_prod(list(X_a),list(X_a))),partition(X_a),Pa),nil(X_a)) = hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),nil(X_a)),nil(X_a))) # label(fact_114_partition_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 163 (all X_a all Pa hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),nil(X_a)) = nil(X_a)) # label(fact_115_takeWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 164 (all X_a all Pa 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),Pa),Xs_1))))) # label(fact_116_distinct__takeWhile) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 165 (all X_a (linorder(X_a) -> (all Pa 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),Pa),Xs_1))))))) # label(fact_117_sorted__takeWhile) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 166 (all X_a all Xs_1 all Pa all X_1 ((hBOOL(hAPP(X_a,bool,Pa,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),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),Pa),Xs_1))) & (-hBOOL(hAPP(X_a,bool,Pa,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),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_118_takeWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 167 (all X_a top_top(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),fTrue))) # label(fact_119_UNIV__def) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 168 (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))) -> top_top(fun(X_a,bool)) = ti(fun(X_a,bool),A_1))) # label(fact_120_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 169 (all X_a exists X_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),top_top(fun(X_a,bool))))) # label(fact_121_UNIV__witness) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 170 (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_123_append__butlast__last__id) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 171 (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_124_snoc__eq__iff__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 172 (all X_a all Xs_1 all R_2 -hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),nil(X_a))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lex(X_a),R_2)))) # label(fact_125_Nil2__notin__lex) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 173 (all X_a all Ys_1 all R_2 -hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),nil(X_a)),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lex(X_a),R_2)))) # label(fact_126_Nil__notin__lex) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 174 (all X_a all Ys_2 all Us_2 all Xs all Xs1 all Zs_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Xs1) = Zs_1 -> (Ys_2 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs1),Us_2) -> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_2) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs_1),Us_2)))) # label(fact_127_append__eq__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 175 (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_128_append__same__eq) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 176 (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_129_same__append__eq) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 177 (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 (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) & hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us),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) = 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),Ts))))) # label(fact_130_append__eq__append__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 178 (all X_a all Xs all Ys_2 all Zs_1 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_2)),Zs_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_2),Zs_1))) # label(fact_131_append__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 179 (all X_a all X all Xs all 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),X),Xs)),Ys_2) = 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_2))) # label(fact_132_append__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 180 (all X_a all Xs all Zs_1 all X all Xs1 all Ys_2 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs1) = Ys_2 -> (Xs = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs1),Zs_1) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_2),Zs_1)))) # label(fact_133_Cons__eq__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 181 (all X_a all Ys_2 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_2) = Ys_2) # label(fact_134_append__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 182 (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_135_Nil__is__append__conv) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 183 (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_136_append__Nil2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 184 (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_137_self__append__conv) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 185 (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_138_self__append__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 186 (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_139_append__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 187 (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_140_append__self__conv) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 188 (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_141_append__self__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 189 (all X_a all Xs all Ys_2 (Xs = Ys_2 -> 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_2))) # label(fact_142_eq__Nil__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 190 (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_143_append__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 191 (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_144_Cons__eq__append__conv) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 192 (all X_a all Xs_1 all X_1 all Ys_1 all Y_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),nil(X_a))) <-> Xs_1 = Ys_1 & ti(X_a,X_1) = ti(X_a,Y_1))) # label(fact_145_append1__eq__conv) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 193 (all X_a all Xs_1 all L all Pa all X_1 (-hBOOL(hAPP(X_a,bool,Pa,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),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))) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1))) # label(fact_146_takeWhile__tail) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 194 (all X_a all Xs all Ys_2 ((Ys_2 = 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_2)) = hAPP(list(X_a),list(X_a),butlast(X_a),Xs)) & (Ys_2 != 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_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),butlast(X_a),Ys_2))))) # label(fact_147_butlast__append) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 195 (all X_a all Xs all Ys_2 ((Ys_2 = 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_2)) = hAPP(list(X_a),X_a,last(X_a),Xs)) & (Ys_2 != 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_2)) = hAPP(list(X_a),X_a,last(X_a),Ys_2)))) # label(fact_148_last__append) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 196 (all X_a all Xs all Ys_2 (Ys_2 != 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_2)) = hAPP(list(X_a),X_a,last(X_a),Ys_2))) # label(fact_149_last__appendR) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 197 (all X_a all Xs all Ys_2 (Ys_2 = 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_2)) = hAPP(list(X_a),X_a,last(X_a),Xs))) # label(fact_150_last__appendL) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 198 (all X_a all X_1 all U all V all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),U),V)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),X_1),U)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),X_1),V))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))))) # label(fact_151_lexord__append__leftI) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 199 (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_152_maps__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 200 (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_153_butlast__snoc) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 201 (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_154_last__snoc) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 202 (all X_a all U all X_1 all Y_1 all Aa all Ba all R_2 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),Aa),Ba)),R_2)) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),U),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Aa),X_1))),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),U),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Ba),Y_1)))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))))) # label(fact_155_lexord__append__left__rightI) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 203 (all X_a all X_1 all R_2 all Y_1 ((exists B_2 exists Z_1 Y_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),B_2),Z_1)) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),X_1),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),X_1),Y_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))))) # label(fact_156_lexord__append__rightI) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 204 (all X_a all X_1 all U all V all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),X_1),U)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),X_1),V))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))) -> ((all A_4 -hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),A_4),A_4)),R_2))) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),U),V)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2)))))) # label(fact_157_lexord__append__leftD) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 205 (all X_a all Xs_1 all Pa (hBOOL(hAPP(list(X_a),bool,Pa,nil(X_a))) -> ((all X_2 all Xs_2 (hBOOL(hAPP(list(X_a),bool,Pa,Xs_2)) -> hBOOL(hAPP(list(X_a),bool,Pa,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,Pa,Xs_1))))) # label(fact_158_rev__induct) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 206 (all X_a all Xs (Xs != nil(X_a) -> -(all Ys all Y_2 Xs != hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),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_159_rev__cases) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 207 (all X_a all Xs_1 all X_1 all Ys_1 all Y_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),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_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_1),nil(X_a))))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))) <-> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))) & ti(X_a,X_1) = ti(X_a,Y_1) | Xs_1 = Ys_1 & hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),R_2)))) # label(fact_160_snoc__listrel1__snoc__iff) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 208 (all X_a all Xs_1 hAPP(list(X_a),list(X_a),rotate1(X_a),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),list(X_a)),hAPP(list(X_a),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),list(X_a))),list_case(list(X_a),X_a),nil(X_a)),hAPP(fun(X_a,list(X_a)),fun(X_a,fun(list(X_a),list(X_a))),hAPP(fun(list(X_a),fun(list(X_a),list(X_a))),fun(fun(X_a,list(X_a)),fun(X_a,fun(list(X_a),list(X_a)))),combb(list(X_a),fun(list(X_a),list(X_a)),X_a),hAPP(fun(list(X_a),fun(list(X_a),list(X_a))),fun(list(X_a),fun(list(X_a),list(X_a))),combc(list(X_a),list(X_a),list(X_a)),append(X_a))),hAPP(list(X_a),fun(X_a,list(X_a)),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),fun(X_a,list(X_a))),combc(X_a,list(X_a),list(X_a)),cons(X_a)),nil(X_a)))),Xs_1)) # label(fact_161_rotate1__def) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 209 (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_162_rotate__simps) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 210 (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_163_rotate1__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 211 (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_164_distinct1__rotate) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 212 (all X_a all X_1 all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Ys_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))))) # label(fact_165_listrel1I2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 213 (all X_a all Xs_1 all R_2 -hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),nil(X_a))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2)))) # label(fact_166_not__listrel1__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 214 (all X_a all Xs_1 all R_2 -hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),nil(X_a)),Xs_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2)))) # label(fact_167_not__Nil__listrel1) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 215 (all X_a all Us_1 all Vs_1 all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))) & Us_1 = Vs_1 | Xs_1 = Ys_1 & hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Us_1),Vs_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),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_1),Us_1)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Vs_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))))) # label(fact_168_append__listrel1I) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 216 (all X_a all X_1 all Xs_1 all Y_1 all Ys_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))) <-> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),R_2)) & Xs_1 = Ys_1 | ti(X_a,X_1) = ti(X_a,Y_1) & hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))))) # label(fact_169_Cons__listrel1__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 217 (all X_a all Xs_1 all X_1 all Y_1 all R_2 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),R_2)) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Xs_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))))) # label(fact_170_listrel1I1) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 218 (all X_a all Ys_1 all Xs_1 all Us_1 all Vs_1 all X_1 all Y_1 all R_2 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),R_2)) -> (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Vs_1)) -> (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),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Vs_1)) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))))))) # label(fact_171_listrel1I) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 219 (all X_a all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))) -> -(all X_2 all Y_2 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Y_2)),R_2)) -> (all Us all Vs (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Vs)) -> Ys_1 != hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Vs)))))))) # label(fact_172_listrel1E) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 220 (all X_a all X_1 all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))) -> ((all Y_2 (Ys_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Xs_1) -> -hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_2)),R_2)))) -> -(all Zs_2 (Ys_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs_2) -> -hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Zs_2)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2)))))))) # label(fact_173_Cons__listrel1E1) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 221 (all X_a all Xs_1 all Y_1 all Ys_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))) -> ((all X_2 (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Ys_1) -> -hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Y_1)),R_2)))) -> -(all Zs_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),Zs_2) -> -hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Zs_2),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2)))))))) # label(fact_174_Cons__listrel1E2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 222 (all X_a all X_1 all Xs_1 all Y_1 all Ys_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lex(X_a),R_2))) <-> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),R_2)) & hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1) | ti(X_a,X_1) = ti(X_a,Y_1) & hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lex(X_a),R_2))))) # label(fact_175_Cons__in__lex) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 223 (all X_a all Pa all Xs_1 all Y_1 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),Pa),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_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),Pa),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_1)) & -hBOOL(hAPP(X_a,bool,Pa,Y_1)))) # label(fact_176_dropWhile__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 224 (all X_a all Pa all X_1 all Xs_1 hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(fun(X_a,bool),fun(list(X_a),product_prod(list(X_a),list(X_a))),partition(X_a),Pa),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(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a)),hAPP(fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a))),product_prod_case(list(X_a),list(X_a),product_prod(list(X_a),list(X_a))),hAPP(fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),hAPP(fun(list(X_a),fun(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),product_prod(list(X_a),list(X_a))))),fun(fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))))),combs(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),product_prod(list(X_a),list(X_a)))),hAPP(fun(list(X_a),fun(list(X_a),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a))))),fun(list(X_a),fun(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),product_prod(list(X_a),list(X_a))))),hAPP(fun(fun(list(X_a),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a)))),fun(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),product_prod(list(X_a),list(X_a))))),fun(fun(list(X_a),fun(list(X_a),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a))))),fun(list(X_a),fun(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),product_prod(list(X_a),list(X_a)))))),combb(fun(list(X_a),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a)))),fun(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),product_prod(list(X_a),list(X_a)))),list(X_a)),combs(list(X_a),product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a)))),hAPP(fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),fun(list(X_a),fun(list(X_a),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a))))),hAPP(fun(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a))))),fun(fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),fun(list(X_a),fun(list(X_a),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a)))))),combb(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a)))),list(X_a)),hAPP(fun(product_prod(list(X_a),list(X_a)),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a)))),fun(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a))))),combb(product_prod(list(X_a),list(X_a)),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a))),list(X_a)),hAPP(bool,fun(product_prod(list(X_a),list(X_a)),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a)))),if(product_prod(list(X_a),list(X_a))),hAPP(X_a,bool,Pa,X_1)))),hAPP(fun(list(X_a),list(X_a)),fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),hAPP(fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),fun(fun(list(X_a),list(X_a)),fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))))),combb(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),list(X_a)),product_Pair(list(X_a),list(X_a))),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1))))),hAPP(fun(list(X_a),list(X_a)),fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),hAPP(fun(list(X_a),fun(fun(list(X_a),list(X_a)),fun(list(X_a),product_prod(list(X_a),list(X_a))))),fun(fun(list(X_a),list(X_a)),fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))))),combc(list(X_a),fun(list(X_a),list(X_a)),fun(list(X_a),product_prod(list(X_a),list(X_a)))),hAPP(fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),fun(list(X_a),fun(fun(list(X_a),list(X_a)),fun(list(X_a),product_prod(list(X_a),list(X_a))))),hAPP(fun(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(fun(list(X_a),list(X_a)),fun(list(X_a),product_prod(list(X_a),list(X_a))))),fun(fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),fun(list(X_a),fun(fun(list(X_a),list(X_a)),fun(list(X_a),product_prod(list(X_a),list(X_a)))))),combb(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(fun(list(X_a),list(X_a)),fun(list(X_a),product_prod(list(X_a),list(X_a)))),list(X_a)),combb(list(X_a),product_prod(list(X_a),list(X_a)),list(X_a))),product_Pair(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),product_prod(list(X_a),list(X_a)),hAPP(fun(X_a,bool),fun(list(X_a),product_prod(list(X_a),list(X_a))),partition(X_a),Pa),Xs_1))) # label(fact_177_partition_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 225 (all X_b all X_c all X_a all X_d all X_e all F all G all P_1 hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F),hAPP(product_prod(X_d,X_e),product_prod(X_b,X_c),hAPP(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(product_prod(X_d,X_e),product_prod(X_b,X_c)),product_prod_case(X_d,X_e,product_prod(X_b,X_c)),G),P_1)) = hAPP(product_prod(X_d,X_e),X_a,hAPP(fun(X_d,fun(X_e,X_a)),fun(product_prod(X_d,X_e),X_a),product_prod_case(X_d,X_e,X_a),hAPP(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(X_d,fun(X_e,X_a)),hAPP(fun(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a)),fun(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(X_d,fun(X_e,X_a))),combb(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a),X_d),hAPP(fun(product_prod(X_b,X_c),X_a),fun(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a)),combb(product_prod(X_b,X_c),X_a,X_e),hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F))),G)),P_1)) # label(fact_178_split__twice) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 226 (all X_a all Xs all Ys_2 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs) != hAPP(list(X_a),nat,size_size(list(X_a)),Ys_2) -> Xs != Ys_2)) # label(fact_179_neq__if__length__neq) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 227 (all X_c all X_a all X_b all Ca all P_1 all Q_2 (ti(product_prod(X_a,X_b),P_1) = ti(product_prod(X_a,X_b),Q_2) -> hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),Ca),P_1) = hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),Ca),Q_2))) # label(fact_180_split__weak__cong) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 228 (all X_b all X_c all X_a all F1 all Aa all Ba hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,Aa),Ba)) # label(fact_181_prod_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 229 (all X_b all X_c all X_a all F all Aa all Ba hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F,Aa),Ba)) # label(fact_182_split__conv) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 230 (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_183_length__rotate1) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 231 (all X_a all Xs_1 all Pa all X_1 ((hBOOL(hAPP(X_a,bool,Pa,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),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),Pa),Xs_1)) & (-hBOOL(hAPP(X_a,bool,Pa,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),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_184_dropWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 232 (all X_a all Pa hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),nil(X_a)) = nil(X_a)) # label(fact_185_dropWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 233 (all X_a all Pa 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),Pa),Xs_1))))) # label(fact_186_distinct__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 234 (all X_a (linorder(X_a) -> (all Pa 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),Pa),Xs_1))))))) # label(fact_187_sorted__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 235 (all X_a all X_b all X_c all F hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,X_c)),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,X_c)),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,X_c))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,X_c),X_a),hAPP(fun(product_prod(X_a,X_b),X_c),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,X_c)),combb(product_prod(X_a,X_b),X_c,X_b),F)),product_Pair(X_a,X_b))) = ti(fun(product_prod(X_a,X_b),X_c),F)) # label(fact_188_split__eta) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 236 (all X_a all X_b all X_c all F hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),hAPP(fun(product_prod(X_a,X_b),X_c),fun(X_a,fun(X_b,X_c)),product_curry(X_a,X_b,X_c),F)) = ti(fun(product_prod(X_a,X_b),X_c),F)) # label(fact_189_split__curry) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 237 (all X_a all X_b all X_c all F hAPP(fun(product_prod(X_a,X_b),X_c),fun(X_a,fun(X_b,X_c)),product_curry(X_a,X_b,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),F)) = ti(fun(X_a,fun(X_b,X_c)),F)) # label(fact_190_curry__split) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 238 (all X_a all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))) -> hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1))) # label(fact_191_listrel1__eq__len) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 239 (all X_a all X_b all X_c produc1605651328_split(X_a,X_b,X_c) = product_prod_case(X_a,X_b,X_c)) # label(fact_192_internal__split__def) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 240 (all X_a all Pa 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),Pa),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),Xs_1)) = Xs_1) # label(fact_193_takeWhile__dropWhile__id) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 241 (all X_a all X_1 all Y_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),X_1),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lex(X_a),R_2))) <-> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),X_1),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))) & hAPP(list(X_a),nat,size_size(list(X_a)),X_1) = hAPP(list(X_a),nat,size_size(list(X_a)),Y_1))) # label(fact_194_lexord__lex) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 242 (all X_a all X_b all Pa 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),Pa,nil(X_a)),nil(X_b))) -> ((all X_2 all Xs_2 all Y_2 all Ys (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_2) = hAPP(list(X_b),nat,size_size(list(X_b)),Ys) -> (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),Pa,Xs_2),Ys)) -> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),Pa,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2)),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Y_2),Ys)))))) -> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),Pa,Xs_1),Ys_1)))))) # label(fact_195_list__induct2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 243 (all X_b all X_c all X_a all F all G ((all X_2 all Y_2 hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),F,X_2),Y_2) = hAPP(product_prod(X_a,X_b),X_c,G,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2))) -> hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),F) = ti(fun(product_prod(X_a,X_b),X_c),G))) # label(fact_196_cond__split__eta) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 244 (all X_c all X_b all X_a all P_1 all F all G all Q_2 ((all X_2 all Y_2 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2) = ti(product_prod(X_a,X_b),Q_2) -> hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),F,X_2),Y_2) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),G,X_2),Y_2))) -> (ti(product_prod(X_a,X_b),P_1) = ti(product_prod(X_a,X_b),Q_2) -> hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),F),P_1) = hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),G),Q_2)))) # label(fact_197_split__cong) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 245 (all X_a all X_b all X_c all Q_1 all Pa all Z_2 (hBOOL(hAPP(X_a,bool,Q_1,hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),Pa),Z_2))) -> -(all X_2 all Y_2 (ti(product_prod(X_b,X_c),Z_2) = hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),X_2),Y_2) -> -hBOOL(hAPP(X_a,bool,Q_1,hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),Pa,X_2),Y_2))))))) # label(fact_198_splitE2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 246 (all X_a all Xs_1 all Ys_1 all R_2 all N (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(nat,fun(product_prod(list(X_a),list(X_a)),bool),hAPP(fun(product_prod(X_a,X_a),bool),fun(nat,fun(product_prod(list(X_a),list(X_a)),bool)),lexn(X_a),R_2),N))) -> hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = N & hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1) = N)) # label(fact_199_lexn__length) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 247 (all X_b all X_a all F all Aa all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F,Aa),Ba)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),F),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))))) # label(fact_200_splitI) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 248 (all X_b all X_a all F1 all Aa all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F1,Aa),Ba)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),F1),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))))) # label(fact_201_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.79 249 (all X_a all X_c all X_b all Z_2 all Ca all Aa all Ba (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z_2),hAPP(X_c,fun(X_a,bool),hAPP(X_b,fun(X_c,fun(X_a,bool)),Ca,Aa),Ba))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z_2),hAPP(product_prod(X_b,X_c),fun(X_a,bool),hAPP(fun(X_b,fun(X_c,fun(X_a,bool))),fun(product_prod(X_b,X_c),fun(X_a,bool)),product_prod_case(X_b,X_c,fun(X_a,bool)),Ca),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)))))) # label(fact_202_mem__splitI) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 250 (all X_a all X_b all F all Aa all Ba (hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),F),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F,Aa),Ba)))) # label(fact_203_splitD) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 251 (all X_c all X_a all X_b all R_1 all Aa all Ba all Ca (hBOOL(hAPP(X_c,bool,hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),R_1),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba)),Ca)) -> hBOOL(hAPP(X_c,bool,hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),R_1,Aa),Ba),Ca)))) # label(fact_204_splitD_H) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 252 (all X_a all X_b all Ca all P_1 ((all A_4 all B_2 (ti(product_prod(X_a,X_b),P_1) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_2) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Ca,A_4),B_2)))) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),Ca),P_1)))) # label(fact_205_splitI2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 253 (all X_a all X_b all Ca all P_1 (hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),Ca),P_1)) -> -(all X_2 all Y_2 (ti(product_prod(X_a,X_b),P_1) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2) -> -hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Ca,X_2),Y_2)))))) # label(fact_206_splitE) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 254 (all X_c all X_a all X_b all Z_2 all Ca all P_1 ((all A_4 all B_2 (ti(product_prod(X_a,X_b),P_1) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_2) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Z_2),hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),Ca,A_4),B_2))))) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Z_2),hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),Ca),P_1))))) # label(fact_207_mem__splitI2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 255 (all X_c all X_b all X_a all Ca all X_1 all P_1 ((all A_4 all B_2 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_2) = ti(product_prod(X_a,X_b),P_1) -> hBOOL(hAPP(X_c,bool,hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),Ca,A_4),B_2),X_1)))) -> hBOOL(hAPP(X_c,bool,hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),Ca),P_1),X_1)))) # label(fact_208_splitI2_H) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 256 (all X_a all X_b all X_c all Z_2 all Ca all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z_2),hAPP(product_prod(X_b,X_c),fun(X_a,bool),hAPP(fun(X_b,fun(X_c,fun(X_a,bool))),fun(product_prod(X_b,X_c),fun(X_a,bool)),product_prod_case(X_b,X_c,fun(X_a,bool)),Ca),P_1))) -> -(all X_2 all Y_2 (ti(product_prod(X_b,X_c),P_1) = hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),X_2),Y_2) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z_2),hAPP(X_c,fun(X_a,bool),hAPP(X_b,fun(X_c,fun(X_a,bool)),Ca,X_2),Y_2))))))) # label(fact_209_mem__splitE) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 257 (all X_a all X_b all Pa all Q_1 all X_2 (hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fconj,Pa))),Q_1)),X_2)) <-> hBOOL(Pa) & hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),Q_1),X_2)))) # label(fact_210_split__part) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 258 (all X_c all X_a all X_b all Ca all P_1 all Z_2 (hBOOL(hAPP(X_c,bool,hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),Ca),P_1),Z_2)) -> -(all X_2 all Y_2 (ti(product_prod(X_a,X_b),P_1) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2) -> -hBOOL(hAPP(X_c,bool,hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),Ca,X_2),Y_2),Z_2)))))) # label(fact_211_splitE_H) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 259 (all X_a all N_1 exists Xs_2 hAPP(list(X_a),nat,size_size(list(X_a)),Xs_2) = N_1) # label(fact_212_Ex__list__of__length) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 260 (all X_a all Ws (-hBOOL(hAPP(list(X_a),bool,distinct(X_a),Ws)) -> (exists Xs_2 exists Ys exists Zs_2 exists Y_2 Ws = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_2),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),nil(X_a))),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),nil(X_a))),Zs_2))))))) # label(fact_213_not__distinct__decomp) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 261 (all X_a all Xs_1 all Ys_1 all X_1 all Y_1 all R_2 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),R_2)) -> (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2))) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2)))))) # label(fact_214_listrel_OCons) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 262 (all X_a all Xs_1 all Ys_1 hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),list(X_a)),hAPP(list(X_a),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),list(X_a))),list_case(list(X_a),X_a),hAPP(list(X_a),list(X_a),tl(X_a),Ys_1)),hAPP(fun(list(X_a),list(X_a)),fun(X_a,fun(list(X_a),list(X_a))),combk(fun(list(X_a),list(X_a)),X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),hAPP(fun(list(X_a),fun(list(X_a),list(X_a))),fun(list(X_a),fun(list(X_a),list(X_a))),combc(list(X_a),list(X_a),list(X_a)),append(X_a)),Ys_1))),Xs_1)) # label(fact_215_tl__append) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 263 (all X_a all Xs_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),nil(X_a))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2))) -> Xs_1 = nil(X_a))) # label(fact_216_listrel__Nil2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 264 (all X_a all Xs_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),nil(X_a)),Xs_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2))) -> Xs_1 = nil(X_a))) # label(fact_217_listrel__Nil1) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 265 (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_218_tl_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 266 (all X_a hAPP(list(X_a),list(X_a),tl(X_a),nil(X_a)) = nil(X_a)) # label(fact_219_tl_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 267 (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_220_distinct__tl) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 268 (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_221_sorted__tl) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 269 (all X_a all R_2 hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),nil(X_a)),nil(X_a))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2)))) # label(fact_222_listrel_ONil) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 270 (all X_a all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2))) -> hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1))) # label(fact_223_listrel__eq__len) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.80 271 (all X_a all Ys_2 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_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),tl(X_a),Xs)),Ys_2))) # label(fact_224_tl__append2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 272 (all X_a all Xs_1 all Y_1 all Ys_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2))) -> -(all X_2 all Xs_2 (Xs_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(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Y_1)),R_2)) -> -hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_2),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2)))))))) # label(fact_225_listrel__Cons2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 273 (all X_a all Y_1 all Ys_1 all Xs_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_1)),Xs_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2))) -> -(all Y_2 all Ys (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) -> (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),Y_1),Y_2)),R_2)) -> -hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Ys_1),Ys)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2)))))))) # label(fact_226_listrel__Cons1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 274 (all X_a all R_2 all X_2 all Xa (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),hAPP(fun(product_prod(X_a,X_a),bool),fun(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_a),bool),fun(X_a,bool))),fun(fun(product_prod(X_a,X_a),bool),fun(X_a,fun(X_a,bool))),combc(X_a,fun(product_prod(X_a,X_a),bool),fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,fun(fun(product_prod(X_a,X_a),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_a),bool),fun(X_a,bool))),hAPP(fun(fun(X_a,fun(fun(product_prod(X_a,X_a),bool),bool)),fun(fun(product_prod(X_a,X_a),bool),fun(X_a,bool))),fun(fun(X_a,fun(X_a,fun(fun(product_prod(X_a,X_a),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_a),bool),fun(X_a,bool)))),combb(fun(X_a,fun(fun(product_prod(X_a,X_a),bool),bool)),fun(fun(product_prod(X_a,X_a),bool),fun(X_a,bool)),X_a),combc(X_a,fun(product_prod(X_a,X_a),bool),bool)),hAPP(fun(X_a,fun(X_a,product_prod(X_a,X_a))),fun(X_a,fun(X_a,fun(fun(product_prod(X_a,X_a),bool),bool))),hAPP(fun(fun(X_a,product_prod(X_a,X_a)),fun(X_a,fun(fun(product_prod(X_a,X_a),bool),bool))),fun(fun(X_a,fun(X_a,product_prod(X_a,X_a))),fun(X_a,fun(X_a,fun(fun(product_prod(X_a,X_a),bool),bool)))),combb(fun(X_a,product_prod(X_a,X_a)),fun(X_a,fun(fun(product_prod(X_a,X_a),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool)),fun(fun(X_a,product_prod(X_a,X_a)),fun(X_a,fun(fun(product_prod(X_a,X_a),bool),bool))),combb(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),X_a),member(product_prod(X_a,X_a)))),product_Pair(X_a,X_a)))),R_2)),X_2),Xa)) <-> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),X_2),Xa)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2))))) # label(fact_227_listrelp__listrel__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 275 (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_228_rotate1__hd__tl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 276 (all X_a all A1 all A2 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),A1),A2)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2))) <-> A1 = nil(X_a) & A2 = nil(X_a) | (exists X_2 exists Y_2 exists Xs_2 exists Ys (A1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2) & A2 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys) & hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Y_2)),R_2)) & hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_2),Ys)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2))))))) # label(fact_229_listrel_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 277 (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_230_hd_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 278 (all X_a all Xs_1 all Ys_1 all R_2 all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,X_1),Y_1)) -> (hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_2),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_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_1)))))) # label(fact_231_listrelp_OCons) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 279 (all X_a all R_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_2),nil(X_a)),nil(X_a)))) # label(fact_232_listrelp_ONil) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 280 (all X_a all Ys_2 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_2)) = hAPP(list(X_a),X_a,hd(X_a),Ys_2)) & (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_2)) = hAPP(list(X_a),X_a,hd(X_a),Xs)))) # label(fact_233_hd__append) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 281 (all X_a all Ys_2 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_2)) = hAPP(list(X_a),X_a,hd(X_a),Xs))) # label(fact_234_hd__append2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 282 (all X_a all Pa 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),Pa),Xs_1) != nil(X_a) -> -hBOOL(hAPP(X_a,bool,Pa,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),Pa),Xs_1)))))) # label(fact_235_hd__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 283 (all X_a all R_2 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_2),A1),A2)) <-> A1 = nil(X_a) & A2 = nil(X_a) | (exists X_2 exists Y_2 exists Xs_2 exists Ys (A1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2) & A2 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,X_2),Y_2)) & hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_2),Xs_2),Ys)))))) # label(fact_236_listrelp_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 284 (all X_a (cl_HOL_Oequal(X_a) -> equal_equal(X_a) = fequal(X_a))) # label(fact_237_equal) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 285 (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_238_equal__refl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 286 (all X_a (cl_HOL_Oequal(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),equal_equal(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_239_equal__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 287 (all X_a (cl_HOL_Oequal(X_a) -> fequal(X_a) = equal_equal(X_a))) # label(fact_240_eq__equal) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 288 (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_241_last__rev) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 289 (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_242_hd__rev) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 290 (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_243_replicate__append__same) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 291 (all X_a all Pa 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),Pa),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),Pa),Xs_1))),Xs_1)) # label(fact_244_dropWhile__eq__drop) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 292 (all X_a all N_1 all Xs hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),hAPP(list(X_a),list(X_a),butlast(X_a),Xs))) # label(fact_245_butlast__drop) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 293 (all X_a all N_1 all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)) = hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs))) # label(fact_246_drop__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 294 (all X_a all N_1 all Xs hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),hAPP(list(X_a),list(X_a),tl(X_a),Xs))) # label(fact_247_tl__drop) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 295 (all X_a all N_1 all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),hAPP(list(X_a),list(X_a),tl(X_a),Xs)) = hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs))) # label(fact_248_drop__tl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 296 (all X_a (linorder(X_a) -> (all N_1 all Xs (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs))))))) # label(fact_249_sorted__drop) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 297 (all X_a all N_1 hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),nil(X_a)) = nil(X_a)) # label(fact_250_drop__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 298 (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_251_rev__is__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 299 (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_252_rev__swap) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 300 (all X_a all N_1 all X hAPP(list(X_a),list(X_a),rev(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)) # label(fact_253_rev__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 301 (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_254_rev__rev__ident) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 302 (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_255_distinct__drop) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 303 (all X_a all Xs all Ys_2 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_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),rev(X_a),Ys_2)),hAPP(list(X_a),list(X_a),rev(X_a),Xs))) # label(fact_256_rev__append) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 304 (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_257_length__rev) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 305 (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_258_rev__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 306 (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_259_Nil__is__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 307 (all X_a hAPP(list(X_a),list(X_a),rev(X_a),nil(X_a)) = nil(X_a)) # label(fact_260_rev_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 308 (all X_a all N_1 all X all K hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),K),X)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),K),X)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X))) # label(fact_261_append__replicate__commute) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 309 (all X_a all N_1 all X hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)) = N_1) # label(fact_262_length__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 310 (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_263_distinct__rev) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 311 (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_264_rev__singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 312 (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_265_singleton__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 313 (all X_a all N_1 all X all Xs hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)),Xs))) # label(fact_266_replicate__app__Cons__same) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 314 (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_267_rev_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 315 (all X_a all Xs_1 all Y_1 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_1),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_1),nil(X_a))))) # label(fact_268_rev__eq__Cons__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 316 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_1))),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)) = hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_1))),Xs_1)))))) # label(fact_269_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 317 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_1))),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_1))),Xs_1)))))) # label(fact_270_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 318 (all X_a all N all X_1 all Xs_1 hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)) = hAPP(nat,list(X_a),hAPP(fun(nat,list(X_a)),fun(nat,list(X_a)),hAPP(list(X_a),fun(fun(nat,list(X_a)),fun(nat,list(X_a))),nat_case(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),hAPP(list(X_a),fun(nat,list(X_a)),hAPP(fun(nat,fun(list(X_a),list(X_a))),fun(list(X_a),fun(nat,list(X_a))),combc(nat,list(X_a),list(X_a)),drop(X_a)),Xs_1)),N)) # label(fact_271_drop__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 319 (all X_a all Xs_1 hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),hAPP(fun(list(X_a),fun(X_a,list(X_a))),fun(list(X_a),fun(list(X_a),list(X_a))),foldl(list(X_a),X_a),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),fun(X_a,list(X_a))),combc(X_a,list(X_a),list(X_a)),cons(X_a))),nil(X_a)),Xs_1)) # label(fact_272_rev__foldl__cons) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 320 (all X_a all X_1 all N all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs_1)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_273_in__set__dropD) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 321 (all X_a all Xs_1 hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)) = hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)) # label(fact_274_set__rev) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 322 (all X_a all Xs_1 hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),rotate1(X_a),Xs_1)) = hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)) # label(fact_275_set__rotate1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 323 (all X_a all X_1 all Pa all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(X_a,bool,Pa,X_1)))) # label(fact_276_set__takeWhileD) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 324 (all X_a all Pa 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),Pa),Xs_1) = Xs_1 <-> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,Pa,X_2)))))) # label(fact_277_takeWhile__eq__all__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 325 (all X_b all X_a all F all Aa all Xs_1 all Ys_1 hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),Aa),hAPP(list(X_b),list(X_b),hAPP(list(X_b),fun(list(X_b),list(X_b)),append(X_b),Xs_1),Ys_1)) = hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),Aa),Xs_1)),Ys_1)) # label(fact_278_foldl__append) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 326 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs_1)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_279_in__set__butlastD) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 327 (all X_a all Y_1 all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)))) -> ti(X_a,Y_1) = ti(X_a,X_1) | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_280_set__ConsD) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 328 (all X_b all X_a all F all Aa hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),Aa),nil(X_b)) = ti(X_a,Aa)) # label(fact_281_foldl__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 329 (all X_b all X_a all F all Aa all X_1 all Xs_1 hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),Aa),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X_1),Xs_1)) = hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),F,Aa),X_1)),Xs_1)) # label(fact_282_foldl__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 330 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X_1),Xs_1) = Xs_1)) # label(fact_283_in__set__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 331 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))) <-> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)))) # label(fact_284_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 332 (all X_a (linorder(X_a) -> (all Ys_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) -> (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Ys_1)) -> (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Ys_1)) -> (hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1) = hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys_1) -> Xs_1 = Ys_1)))))))) # label(fact_285_sorted__distinct__set__unique) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 333 (all X_a all Ys_1 all Pa all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (-hBOOL(hAPP(X_a,bool,Pa,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),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(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1)))) # label(fact_286_takeWhile__append1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 334 (all X_a all As (As != nil(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(list(X_a),X_a,last(X_a),As)),hAPP(list(X_a),fun(X_a,bool),set(X_a),As))))) # label(fact_287_last__in__set) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 335 (all X_a all Pa 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),Pa),Xs_1) = nil(X_a) <-> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,Pa,X_2)))))) # label(fact_288_dropWhile__eq__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 336 (all X_a all Ys_1 all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs_1)))) | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Ys_1)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),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))))))) # label(fact_289_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 337 (all X_a all Xs_1 (Xs_1 != nil(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(list(X_a),X_a,hd(X_a),Xs_1)),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_290_hd__in__set) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 338 (all X_a all Ys_1 all Pa all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (-hBOOL(hAPP(X_a,bool,Pa,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),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),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),Xs_1)),Ys_1)))) # label(fact_291_dropWhile__append1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 339 (all X_a all X_1 all Xs_1 ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X_1),Xs_1) = Xs_1) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X_1),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)))) # label(fact_292_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 340 (all X_a all X_1 all Xs_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X_1),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))) # label(fact_293_not__in__set__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 341 (all X_a all Pa all Xs_1 all Yes all No (hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(fun(X_a,bool),fun(list(X_a),product_prod(list(X_a),list(X_a))),partition(X_a),Pa),Xs_1) = hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Yes),No) -> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Yes))) -> hBOOL(hAPP(X_a,bool,Pa,X_2)))) & (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),No))) -> -hBOOL(hAPP(X_a,bool,Pa,X_2)))))) # label(fact_294_partition__P) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 342 (all X_a all Zs all Ys_1 all R_2 all Xs_1 ((all X_2 all Y_2 all Z_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Y_2)),R_2)) -> (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),Y_2),Z_1)),R_2)) -> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Z_1)),R_2)))))) -> (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))) -> (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Ys_1),Zs)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Zs)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))))))) # label(fact_295_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 343 (all X_a all Ys_1 all Pa all Xs_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,Pa,X_2)))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),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(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),Ys_1))) # label(fact_296_dropWhile__append2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 344 (all X_a all Ys_1 all Pa all Xs_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,Pa,X_2)))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),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),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Ys_1)))) # label(fact_297_takeWhile__append2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 345 (all X_a all Pa all Xs_1 ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(X_a,bool,Pa,X_2)))) -> -(all Ys all X_2 ((exists Zs_2 Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs_2))) -> -hBOOL(hAPP(X_a,bool,Pa,X_2)))))) # label(fact_298_split__list__propE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 346 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) <-> (exists Ys exists Zs_2 Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs_2))))) # label(fact_299_in__set__conv__decomp) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 347 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) <-> (exists Ys exists Zs_2 (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs_2)) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Zs_2))))))) # label(fact_300_in__set__conv__decomp__last) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 348 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) <-> (exists Ys exists Zs_2 (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs_2)) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys))))))) # label(fact_301_in__set__conv__decomp__first) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 349 (all X_a all X_b all S_2 all Xs_1 all F ((all X_2 all Y_2 all S_3 hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,S_3),X_2)),Y_2) = hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,S_3),Y_2)),X_2)) -> hAPP(list(X_a),X_b,hAPP(X_b,fun(list(X_a),X_b),hAPP(fun(X_b,fun(X_a,X_b)),fun(X_b,fun(list(X_a),X_b)),foldl(X_b,X_a),F),S_2),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)) = hAPP(list(X_a),X_b,hAPP(X_b,fun(list(X_a),X_b),hAPP(fun(X_b,fun(X_a,X_b)),fun(X_b,fun(list(X_a),X_b)),foldl(X_b,X_a),F),S_2),Xs_1))) # label(fact_302_foldl__rev) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 350 (all X_a all Q_1 all Pa all L all K_1 (L = K_1 -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),L))) -> (hBOOL(hAPP(X_a,bool,Pa,X_2)) <-> hBOOL(hAPP(X_a,bool,Q_1,X_2))))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),L) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Q_1),K_1)))) # label(fact_303_dropWhile__cong) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 351 (all X_a all Q_1 all Pa all L all K_1 (L = K_1 -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),L))) -> (hBOOL(hAPP(X_a,bool,Pa,X_2)) <-> hBOOL(hAPP(X_a,bool,Q_1,X_2))))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),L) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Q_1),K_1)))) # label(fact_304_takeWhile__cong) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 352 (all X_b all X_a all F all G all L all K_1 all Aa all Ba (ti(X_a,Aa) = ti(X_a,Ba) -> (L = K_1 -> ((all A_4 all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(list(X_b),fun(X_b,bool),set(X_b),L))) -> hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),F,A_4),X_2) = hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),G,A_4),X_2))) -> hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),Aa),L) = hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),G),Ba),K_1))))) # label(fact_305_foldl__cong) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 353 (all X_b all X_a all F all Xs_1 all Pa all S_2 (hBOOL(hAPP(X_a,bool,Pa,S_2)) -> ((all S_3 all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(list(X_b),fun(X_b,bool),set(X_b),Xs_1))) -> (hBOOL(hAPP(X_a,bool,Pa,S_3)) -> hBOOL(hAPP(X_a,bool,Pa,hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),F,S_3),X_2)))))) -> hBOOL(hAPP(X_a,bool,Pa,hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),S_2),Xs_1)))))) # label(fact_306_foldl__weak__invariant) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 354 (all X_a all Pa all Xs_1 ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(X_a,bool,Pa,X_2)))) -> -(all Ys all X_2 ((exists Zs_2 Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs_2))) -> (hBOOL(hAPP(X_a,bool,Pa,X_2)) -> -(all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys))) -> -hBOOL(hAPP(X_a,bool,Pa,Xa))))))))) # label(fact_307_split__list__first__propE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 355 (all X_a all Pa all Xs_1 ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(X_a,bool,Pa,X_2)))) <-> (exists Ys exists X_2 exists Zs_2 (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs_2)) & hBOOL(hAPP(X_a,bool,Pa,X_2)) & (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Zs_2))) -> -hBOOL(hAPP(X_a,bool,Pa,Xa)))))))) # label(fact_308_split__list__last__prop__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 356 (all X_a all Pa all Xs_1 ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(X_a,bool,Pa,X_2)))) <-> (exists Ys exists X_2 ((exists Zs_2 Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs_2))) & hBOOL(hAPP(X_a,bool,Pa,X_2)) & (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys))) -> -hBOOL(hAPP(X_a,bool,Pa,Xa)))))))) # label(fact_309_split__list__first__prop__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 357 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (exists Ys exists Zs_2 Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs_2))))) # label(fact_310_split__list) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 358 (all X_a all Pa all Xs_1 ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(X_a,bool,Pa,X_2)))) -> -(all Ys all X_2 all Zs_2 (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs_2)) -> (hBOOL(hAPP(X_a,bool,Pa,X_2)) -> -(all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Zs_2))) -> -hBOOL(hAPP(X_a,bool,Pa,Xa))))))))) # label(fact_311_split__list__last__propE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 359 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (exists Ys exists Zs_2 (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs_2)) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys))))))) # label(fact_312_split__list__first) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 360 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (exists Ys exists Zs_2 (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs_2)) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Zs_2))))))) # label(fact_313_split__list__last) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 361 (all X_a all X_b all S_2 all Xs_1 all X_1 all F ((all X_2 all Y_2 all S_3 hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,S_3),X_2)),Y_2) = hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,S_3),Y_2)),X_2)) -> hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,hAPP(list(X_a),X_b,hAPP(X_b,fun(list(X_a),X_b),hAPP(fun(X_b,fun(X_a,X_b)),fun(X_b,fun(list(X_a),X_b)),foldl(X_b,X_a),F),S_2),Xs_1)),X_1) = hAPP(list(X_a),X_b,hAPP(X_b,fun(list(X_a),X_b),hAPP(fun(X_b,fun(X_a,X_b)),fun(X_b,fun(list(X_a),X_b)),foldl(X_b,X_a),F),hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,S_2),X_1)),Xs_1))) # label(fact_314_foldl__fun__comm) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 362 (all X_b all X_a all F all Pa all Xs_1 all Q_1 all X_1 (hBOOL(hAPP(X_a,bool,Q_1,X_1)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(list(X_b),fun(X_b,bool),set(X_b),Xs_1))) -> hBOOL(hAPP(X_b,bool,Pa,X_2)))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) & hBOOL(hAPP(X_a,bool,Q_1,Y_2)) -> hBOOL(hAPP(X_a,bool,Q_1,hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),F,Y_2),X_2))))) -> hBOOL(hAPP(X_a,bool,Q_1,hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),X_1),Xs_1))))))) # label(fact_315_foldl__invariant) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 363 (all X_a all N all X_1 all Xs_1 hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)) = hAPP(nat,list(X_a),hAPP(fun(nat,list(X_a)),fun(nat,list(X_a)),hAPP(list(X_a),fun(fun(nat,list(X_a)),fun(nat,list(X_a))),nat_case(list(X_a)),nil(X_a)),hAPP(fun(nat,list(X_a)),fun(nat,list(X_a)),hAPP(fun(list(X_a),list(X_a)),fun(fun(nat,list(X_a)),fun(nat,list(X_a))),combb(list(X_a),list(X_a),nat),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1)),hAPP(list(X_a),fun(nat,list(X_a)),hAPP(fun(nat,fun(list(X_a),list(X_a))),fun(list(X_a),fun(nat,list(X_a))),combc(nat,list(X_a),list(X_a)),take(X_a)),Xs_1))),N)) # label(fact_316_take__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 364 (all X_a all X_1 all N all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs_1)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_317_in__set__takeD) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 365 (all X_a all N_1 hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),nil(X_a)) = nil(X_a)) # label(fact_318_take__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 366 (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_319_distinct__take) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 367 (all X_a (linorder(X_a) -> (all N_1 all Xs (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs))))))) # label(fact_320_sorted__take) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 368 (all X_a all N_1 all Xs hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs)) = Xs) # label(fact_321_append__take__drop__id) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 369 (all X_a all Pa 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),Pa),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),Pa),Xs_1))),Xs_1)) # label(fact_322_takeWhile__eq__take) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 370 (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_323_append__eq__conv__conj) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 371 (all X_a all N_1 all Xs (Xs != nil(X_a) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N_1)),Xs) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(list(X_a),X_a,hd(X_a),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),hAPP(list(X_a),list(X_a),tl(X_a),Xs))))) # label(fact_324_take__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 372 (all X_a all Xs all Ys_2 ((all I hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I),Xs) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I),Ys_2)) -> Xs = Ys_2)) # label(fact_325_take__equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 373 (all X_a all Xs_1_1 all Xs_2_1 all Ys_1_1 all Ys_2_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1_1),Xs_2_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1_1),Ys_2_1) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1_1)),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1_1))) -> Xs_1_1 = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1_1)),Ys_1_1) & Xs_2_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1_1)),Ys_1_1)),Ys_2_1)) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1_1)),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1_1))) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1_1)),Xs_1_1) = Ys_1_1 & hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1_1)),Xs_1_1)),Xs_2_1) = Ys_2_1))) # label(fact_326_append__eq__append__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 374 (all X_a (preorder(X_a) -> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),X))))) # label(fact_327_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 375 (all X_a all X_b (ord(X_b) -> (all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) <-> (all X_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2)))))))) # label(fact_328_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 376 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_329_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 377 (all X_a (order(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) = ti(X_a,Y_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)))))) # label(fact_330_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 378 (all X_a (preorder(X_a) -> (all X all Y (X = Y -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_331_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 379 (all X_a all X_b (ord(X_b) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))))) # label(fact_332_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 380 (all X_a (order(X_a) -> (all Y_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_333_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 381 (all X_a (ord(X_a) -> (all C_1 all A_2 all B_1 (A_2 = B_1 -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C_1))))))) # label(fact_334_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 382 (all X_a (order(X_a) -> (all C_1 all A_2 all B_1 (ti(X_a,A_2) = ti(X_a,B_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2))))))) # label(fact_335_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 383 (all X_a (ord(X_a) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) -> (B_1 = C_1 -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C_1))))))) # label(fact_336_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 384 (all X_a (order(X_a) -> (all C_1 all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2)) -> (ti(X_a,B_1) = ti(X_a,C_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2))))))) # label(fact_337_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 385 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> ti(X_a,X) = ti(X_a,Y)))))) # label(fact_338_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 386 (all X_a (preorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z))))))) # label(fact_339_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 387 (all X_a (order(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> ti(X_a,X) = ti(X_a,Y)))))) # label(fact_340_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 388 (all X_a (order(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X))))))) # label(fact_341_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 389 (all X_a all X_b (ord(X_b) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))))) # label(fact_342_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 390 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_343_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 391 (all X_a (top(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),top_top(X_a)),A_2)) -> ti(X_a,A_2) = top_top(X_a))))) # label(fact_344_top__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 392 (all X_a (top(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),top_top(X_a)),Aa)) <-> ti(X_a,Aa) = top_top(X_a))))) # label(fact_345_top__unique) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 393 (all X_a (top(X_a) -> (all A_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),top_top(X_a)))))) # label(fact_346_top__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 394 (all X_a all X all Xs all Ys_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_2))) -> Xs != hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Ys_2))) # label(fact_347_impossible__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 395 (all X_a all N_1 all X all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs))) # label(fact_348_take__Suc__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 396 (all X_a all N_1 all X all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,N_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs)) # label(fact_349_drop__Suc__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 397 (all X_a all N_1 all X hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(nat,nat,suc,N_1)),X) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X))) # label(fact_350_replicate__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 398 (all X_a (linorder(X_a) -> (all Zs_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Zs_1))) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Zs_1))))))))) # label(fact_351_sorted__many) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 399 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Zs (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Zs)))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Zs))))))) # label(fact_352_sorted__many__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 400 (all X_a all Xs all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),N_1)) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs) = Xs)) # label(fact_353_take__all) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 401 (all X_a all Pa all Xs_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))) # label(fact_354_length__takeWhile__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 402 (all X_a all N_1 all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),hAPP(list(X_a),list(X_a),tl(X_a),Xs)) = hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N_1)),Xs))) # label(fact_355_take__tl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 403 (all X_a all Pa all Xs_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),Xs_1))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))) # label(fact_356_length__dropWhile__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 404 (all X_a all N_1 all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,N_1)),Xs) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),hAPP(list(X_a),list(X_a),tl(X_a),Xs))) # label(fact_357_drop__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 405 (all X_a (linorder(X_a) -> (all X_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))) <-> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) & (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),X_2)))))))) # label(fact_358_sorted__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 406 (all X_a (linorder(X_a) -> (all Xs_1 all Ys_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1))) <-> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) & hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Ys_1)) & (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Xa)))))))))) # label(fact_359_sorted__append) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 407 (all X_a all N all Xs_1 (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs_1) = nil(X_a) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)),N)))) # label(fact_360_drop__eq__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 408 (all X_a all Xs all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),N_1)) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs) = nil(X_a))) # label(fact_361_drop__all) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 409 (all X_a (linorder(X_a) -> (all Aa (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Aa)) <-> Aa = nil(X_a) | (exists Xs_2 exists X_2 (Aa = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2) & (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_2))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Xa)))) & hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_2)))))))) # label(fact_362_sorted_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 410 (all X_a (linorder(X_a) -> (all X_1 all Xs_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),X_2)))) -> (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)))))))) # label(fact_363_sorted_OCons) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 411 (all X_a all N all Xs_1 (hAPP(nat,nat,suc,N) = hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) <-> (exists Y_2 exists Ys (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) & hAPP(list(X_a),nat,size_size(list(X_a)),Ys) = N)))) # label(fact_364_Suc__length__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 412 (all X_a all A_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),top_top(fun(X_a,bool))))) # label(fact_365_subset__UNIV) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 413 (all X_a all X_b all R_1 all S_1 (hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),R_1)),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),S_1))) <-> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(product_prod(X_a,X_b),bool),bool),ord_less_eq(fun(product_prod(X_a,X_b),bool)),R_1),S_1)))) # label(fact_366_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 414 (all X_b all X_a all B all A_3 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),A_1)) -> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(fun(X_a,X_b),bool),fun(fun(fun(X_a,X_b),bool),bool),ord_less_eq(fun(fun(X_a,X_b),bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_3),B))))) # label(fact_367_Pi__anti__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 415 (all X_a all R_2 all S_2 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(fun(product_prod(X_a,X_a),bool),fun(fun(product_prod(X_a,X_a),bool),bool),ord_less_eq(fun(product_prod(X_a,X_a),bool)),R_2),S_2)) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(fun(product_prod(list(X_a),list(X_a)),bool),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),ord_less_eq(fun(product_prod(list(X_a),list(X_a)),bool)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),S_2))))) # label(fact_368_listrel1__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 416 (all X_a all R_2 all S_2 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(fun(product_prod(X_a,X_a),bool),fun(fun(product_prod(X_a,X_a),bool),bool),ord_less_eq(fun(product_prod(X_a,X_a),bool)),R_2),S_2)) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(fun(product_prod(list(X_a),list(X_a)),bool),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),ord_less_eq(fun(product_prod(list(X_a),list(X_a)),bool)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),S_2))))) # label(fact_369_listrel__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 417 (all X_a all Xs_1 all X_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))))) # label(fact_370_set__subset__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 418 (all X_a all N all Xs_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs_1))),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)))) # label(fact_371_set__take__subset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 419 (all X_a all N all Xs_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs_1))),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)))) # label(fact_372_set__drop__subset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 420 (all X_a all Xs_1 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),M),Xs_1))),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs_1)))))) # label(fact_373_set__take__subset__set__take) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 421 (all X_a all Xs_1 all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),M),Xs_1))),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs_1)))))) # label(fact_374_set__drop__subset__set__drop) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 422 (all X_a all Xs_1 all N (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(nat,nat,suc,N) <-> (exists Y_2 exists Ys (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) & hAPP(list(X_a),nat,size_size(list(X_a)),Ys) = N)))) # label(fact_375_length__Suc__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 423 (all X_a all Ca all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B))))) # label(fact_376_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 424 (all X_a all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1)) -> ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)))) # label(fact_377_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 425 (all X_a all R_1 all S_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),R_1),S_1)))) # label(fact_378_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 426 (all X_a all Q_1 all Pa all X_1 (hBOOL(hAPP(X_a,bool,Pa,X_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),Pa),Q_1)) -> hBOOL(hAPP(X_a,bool,Q_1,X_1))))) # label(fact_379_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 427 (all X_a all X_1 all Pa all Q_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),Pa),Q_1)) -> (hBOOL(hAPP(X_a,bool,Pa,X_1)) -> hBOOL(hAPP(X_a,bool,Q_1,X_1))))) # label(fact_380_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 428 (all X_a all X_b all X_1 all Y_1 all Pa all Q_1 (hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),Pa),Q_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_1),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_1),Y_1))))) # label(fact_381_predicate2D) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 429 (all X_b all X_a all Q_1 all Pa all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_1),Y_1)) -> (hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),Pa),Q_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_1),Y_1))))) # label(fact_382_rev__predicate2D) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 430 (all X_a all A_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),A_1))) # label(fact_383_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 431 (all X_a all A_1 all B (ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1)))) # label(fact_384_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 432 (all X_a all A_1 all B (ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)))) # label(fact_385_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 433 (all X_a all A_1 all B (ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1)))) # label(fact_386_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 434 (all X_a all X_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B))))) # label(fact_387_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 435 (all X_a all B all X_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B))))) # label(fact_388_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 436 (all X_a all X_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B))))) # label(fact_389_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 437 (all X_a all C all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),C)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C))))) # label(fact_390_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 438 (all X_a all A_1 all B (ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))))) # label(fact_391_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 439 (all X_b all X_a all Q_1 all Pa ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_2),Y_2)))) -> hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),Pa),Q_1)))) # label(fact_392_predicate2I) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 440 (all X_b all X_a all B all C all A_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(X_a,fun(X_b,bool),B,X_2)),hAPP(X_a,fun(X_b,bool),C,X_2))))) -> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(fun(X_a,X_b),bool),fun(fun(fun(X_a,X_b),bool),bool),ord_less_eq(fun(fun(X_a,X_b),bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),C))))) # label(fact_393_Pi__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 441 (all X_a all B all A_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)))) # label(fact_394_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 442 (all X_a all N_1 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs))),nil(X_a))) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N_1)),Xs))) # label(fact_395_take__hd__drop) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 443 (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_396_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 444 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) != ti(X_a,Y_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)))))) # label(fact_397_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 445 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) | ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_398_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 446 (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_399_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 447 (all X_a (linorder(X_a) -> (all Y_1 all X_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_400_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 448 (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_401_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 449 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ti(X_a,X) != ti(X_a,Y))))) # label(fact_402_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 450 (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_403_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 451 (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_404_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 452 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ti(X_a,X) != ti(X_a,Y))))) # label(fact_405_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 453 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ti(X_a,Y) != ti(X_a,X))))) # label(fact_406_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 454 (all X_a (preorder(X_a) -> (all Pa all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) -> hBOOL(Pa)))))) # label(fact_407_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 455 (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_408_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 456 (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_409_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 457 (all X_a (ord(X_a) -> (all C_1 all A_2 all B_1 (A_2 = B_1 -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C_1))))))) # label(fact_410_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 458 (all X_a (order(X_a) -> (all C_1 all A_2 all B_1 (ti(X_a,A_2) = ti(X_a,B_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_2))))))) # label(fact_411_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 459 (all X_a (ord(X_a) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> (B_1 = C_1 -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C_1))))))) # label(fact_412_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 460 (all X_a (order(X_a) -> (all C_1 all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) -> (ti(X_a,B_1) = ti(X_a,C_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_2))))))) # label(fact_413_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 461 (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_414_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 462 (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_415_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 463 (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_416_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 464 (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_417_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 465 (all X_a (top(X_a) -> (all Aa (ti(X_a,Aa) != top_top(X_a) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),top_top(X_a))))))) # label(fact_418_less__top) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 466 (all X_a (top(X_a) -> (all A_2 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),top_top(X_a)),A_2))))) # label(fact_419_not__top__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 467 (all X_a (order(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))))))) # label(fact_420_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 468 (all X_a (preorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))))))) # label(fact_421_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 469 (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_eq(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))))))) # label(fact_422_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 470 (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_eq(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))))))) # label(fact_423_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 471 (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_eq(X_a),B_1),A_2)) -> (ti(X_a,A_2) != ti(X_a,B_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))))))) # label(fact_424_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 472 (all X_a (order(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) -> (ti(X_a,A_2) != ti(X_a,B_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))))))) # label(fact_425_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 473 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) | ti(X_a,X) = ti(X_a,Y))))) # label(fact_426_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 474 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_427_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 475 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_428_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 476 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_429_leD) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 477 (all X_a (order(X_a) -> (all A_2 all B_1 (ti(X_a,A_2) != ti(X_a,B_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))))))) # label(fact_430_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 478 (all X_a (order(X_a) -> (all A_2 all B_1 (ti(X_a,A_2) != ti(X_a,B_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_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_431_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 479 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_432_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 480 (all X_a (linorder(X_a) -> (all Y all X (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_433_not__leE) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 481 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_434_leI) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 482 (all X_a (order(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) | ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_435_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 483 (all X_a (preorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)))))) # label(fact_436_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 484 (all X_a (order(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & ti(X_a,X_1) != ti(X_a,Y_1))))) # label(fact_437_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 485 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_438_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 486 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)))))) # label(fact_439_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 487 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)))))) # label(fact_440_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 488 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)))) # label(fact_441_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 489 (all X_a all N_1 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs))) # label(fact_442_take__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 490 (all X_a all N_1 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs)) = hAPP(list(X_a),X_a,last(X_a),Xs))) # label(fact_443_last__drop) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 491 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,N_1)))) # label(fact_444_lessI) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 492 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_1))))) # label(fact_445_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 493 (all X_a all C all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B),C)) -> 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))))) # label(fact_446_subset__psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 494 (all X_a all C all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),C)) -> 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))))) # label(fact_447_psubset__subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 495 (all X_a all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)))) # label(fact_448_psubset__imp__subset) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 496 (all X_a all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) | ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B))) # label(fact_449_subset__iff__psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 497 (all X_a all X_b (ord(X_b) -> (all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G)) <-> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) & -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),G),F)))))) # label(fact_450_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 498 (all X_a all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) & ti(fun(X_a,bool),A_1) != ti(fun(X_a,bool),B))) # label(fact_451_psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 499 (all N_1 N_1 != hAPP(nat,nat,suc,N_1)) # label(fact_452_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 500 (all N_1 hAPP(nat,nat,suc,N_1) != N_1) # label(fact_453_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 501 (all Nat all Nat_1 (hAPP(nat,nat,suc,Nat) = hAPP(nat,nat,suc,Nat_1) <-> Nat = Nat_1)) # label(fact_454_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 502 (all X all Y (hAPP(nat,nat,suc,X) = hAPP(nat,nat,suc,Y) -> X = Y)) # label(fact_455_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 503 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))) # label(fact_456_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 504 (all M all N (M != N <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)))) # label(fact_457_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 505 (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_458_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 506 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))) # label(fact_459_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 507 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1)) -> M_1 != N_1)) # label(fact_460_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 508 (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_461_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 509 (all Pa 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),Pa,N),M))) -> ((M = N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N),M))) -> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N),M))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N),M)))))) # label(fact_462_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 510 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_1))) # label(fact_463_le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 511 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)))) # label(fact_464_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 512 (all M_1 all N_1 (M_1 = N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))) # label(fact_465_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 513 (all K all I_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),K))))) # label(fact_466_le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 514 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)) -> M_1 = N_1))) # label(fact_467_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 515 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)))) # label(fact_468_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 516 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)))) # label(fact_469_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 517 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> M_1 = N_1))) # label(fact_470_less__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 518 (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_471_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 519 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> (hAPP(nat,nat,suc,M_1) != N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),N_1))))) # label(fact_472_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 520 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1))))) # label(fact_473_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 521 (all N_1 all M_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M_1))) -> M_1 = N_1))) # label(fact_474_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 522 (all N all M (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M))) <-> N = M))) # label(fact_475_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 523 (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_476_Suc__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 524 (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_477_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 525 (all M all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M))))) # label(fact_478_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 526 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),N_1))) # label(fact_479_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 527 (all M all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),M)))) # label(fact_480_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 528 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) | M = hAPP(nat,nat,suc,N))) # label(fact_481_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 529 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),hAPP(nat,nat,suc,M))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)))) # label(fact_482_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 530 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,suc,N_1))))) # label(fact_483_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 531 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,suc,N_1))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> M_1 = hAPP(nat,nat,suc,N_1)))) # label(fact_484_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 532 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))) # label(fact_485_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 533 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) | M_1 = N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))) # label(fact_486_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 534 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> (M_1 != N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))))) # label(fact_487_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 535 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))) # label(fact_488_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 536 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) | M = N)) # label(fact_489_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 537 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) & M != N)) # label(fact_490_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 538 (all X_a all F1 all F2 all Nat hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),F1),F2),hAPP(nat,nat,suc,Nat)) = hAPP(nat,X_a,F2,Nat)) # label(fact_491_nat__case__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 539 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)))) # label(fact_492_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 540 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M))) <-> N = M))) # label(fact_493_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 541 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N_1)))) # label(fact_494_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 542 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1))))) # label(fact_495_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 543 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_496_Suc__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 544 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_497_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 545 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),M)))) # label(fact_498_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 546 (all T_2 all T_1 (enum(T_1) & enum(T_2) -> enum(product_prod(T_2,T_1)))) # label(arity_prod___Enum_Oenum) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 547 (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].
% 1.59/1.82 548 (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].
% 1.59/1.82 549 (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].
% 1.59/1.82 550 (all T_2 all T_1 (top(T_1) -> top(fun(T_2,T_1)))) # label(arity_fun___Orderings_Otop) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 551 (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].
% 1.59/1.82 552 (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].
% 1.59/1.82 553 (all T_1 cl_HOL_Oequal(list(T_1))) # label(arity_List_Olist___HOL_Oequal) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 554 (all T_2 all T_1 cl_HOL_Oequal(product_prod(T_2,T_1))) # label(arity_prod___HOL_Oequal) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 555 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 556 (all X_a all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y) = ti(X_a,X)) # label(help_If_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 557 (all X_a all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X),Y) = ti(X_a,Y)) # label(help_If_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 558 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_If_3_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 559 (all P (-hBOOL(hAPP(bool,bool,fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 560 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 561 (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].
% 1.59/1.82 562 (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].
% 1.59/1.86 563 (all X_a all P hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P)) # label(help_COMBI_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.86 564 (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].
% 1.59/1.86 565 (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].
% 1.59/1.86 566 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fTrue_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.86 567 (all Q all P (-hBOOL(P) | -hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.86 568 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.86 569 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.86 570 (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].
% 1.59/1.86 571 (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].
% 1.59/1.86 572 -(all I (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I))) <-> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),c)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I)),c),b))))) # label(conj_0) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.59/1.86
% 1.59/1.86 ============================== end of process non-clausal formulas ===
% 1.59/1.86
% 1.59/1.86 ============================== PROCESS INITIAL CLAUSES ===============
% 1.59/1.86
% 1.59/1.86 ============================== PREDICATE ELIMINATION =================
% 1.59/1.86 573 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom). [assumption].
% 1.59/1.86 574 -linorder(A) | linorder_sorted(A) = ti(fun(list(A),bool),linorder_sorted(A)) # label(tsy_c_List_Olinorder__class_Osorted_res) # label(axiom). [clausify(23)].
% 1.59/1.86 575 -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_94_sorted__single) # label(axiom). [clausify(142)].
% 1.59/1.86 576 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),nil(A))) # label(fact_99_sorted_ONil) # label(axiom). [clausify(147)].
% 1.59/1.86 577 -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_101_sorted__butlast) # label(axiom). [clausify(149)].
% 1.59/1.86 578 -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_117_sorted__takeWhile) # label(axiom). [clausify(165)].
% 1.59/1.86 579 -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_187_sorted__dropWhile) # label(axiom). [clausify(234)].
% 1.59/1.86 580 -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_221_sorted__tl) # label(axiom). [clausify(268)].
% 1.59/1.86 581 -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_249_sorted__drop) # label(axiom). [clausify(296)].
% 1.59/1.86 582 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | -hBOOL(hAPP(list(A),bool,distinct(A),B)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | -hBOOL(hAPP(list(A),bool,distinct(A),C)) | hAPP(list(A),fun(A,bool),set(A),C) != hAPP(list(A),fun(A,bool),set(A),B) | C = B # label(fact_285_sorted__distinct__set__unique) # label(axiom). [clausify(332)].
% 1.59/1.86 583 -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_320_sorted__take) # label(axiom). [clausify(367)].
% 1.59/1.86 584 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_329_linorder__linear) # label(axiom). [clausify(376)].
% 1.59/1.86 585 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_343_linorder__le__cases) # label(axiom). [clausify(390)].
% 1.59/1.86 586 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D)))) # label(fact_351_sorted__many) # label(axiom). [clausify(398)].
% 1.59/1.86 587 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_352_sorted__many__eq) # label(axiom). [clausify(399)].
% 1.59/1.86 588 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D)))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D))) # label(fact_352_sorted__many__eq) # label(axiom). [clausify(399)].
% 1.59/1.86 589 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D))) # label(fact_352_sorted__many__eq) # label(axiom). [clausify(399)].
% 1.59/1.86 590 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) # label(fact_358_sorted__Cons) # label(axiom). [clausify(405)].
% 1.59/1.86 591 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),hAPP(list(A),fun(A,bool),set(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_358_sorted__Cons) # label(axiom). [clausify(405)].
% 1.59/1.86 592 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f195(A,B,C)),hAPP(list(A),fun(A,bool),set(A),C))) # label(fact_358_sorted__Cons) # label(axiom). [clausify(405)].
% 1.59/1.86 593 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f195(A,B,C))) # label(fact_358_sorted__Cons) # label(axiom). [clausify(405)].
% 1.59/1.86 594 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) # label(fact_359_sorted__append) # label(axiom). [clausify(406)].
% 1.59/1.86 595 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) # label(fact_359_sorted__append) # label(axiom). [clausify(406)].
% 1.59/1.86 596 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),hAPP(list(A),fun(A,bool),set(A),B))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),E),hAPP(list(A),fun(A,bool),set(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) # label(fact_359_sorted__append) # label(axiom). [clausify(406)].
% 1.59/1.86 597 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f196(A,B,C)),hAPP(list(A),fun(A,bool),set(A),B))) # label(fact_359_sorted__append) # label(axiom). [clausify(406)].
% 1.59/1.86 598 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f197(A,B,C)),hAPP(list(A),fun(A,bool),set(A),C))) # label(fact_359_sorted__append) # label(axiom). [clausify(406)].
% 1.59/1.86 599 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f196(A,B,C)),f197(A,B,C))) # label(fact_359_sorted__append) # label(axiom). [clausify(406)].
% 1.59/1.86 600 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | nil(A) = B | hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),f199(A,B)),f198(A,B)) = B # label(fact_362_sorted_Osimps) # label(axiom). [clausify(409)].
% 1.59/1.86 601 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | nil(A) = B | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),hAPP(list(A),fun(A,bool),set(A),f198(A,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f199(A,B)),C)) # label(fact_362_sorted_Osimps) # label(axiom). [clausify(409)].
% 1.59/1.86 602 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | nil(A) = B | hBOOL(hAPP(list(A),bool,linorder_sorted(A),f198(A,B))) # label(fact_362_sorted_Osimps) # label(axiom). [clausify(409)].
% 1.59/1.86 603 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | nil(A) != B # label(fact_362_sorted_Osimps) # label(axiom). [clausify(409)].
% 1.59/1.86 604 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D) != B | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f200(A,B,D,C)),hAPP(list(A),fun(A,bool),set(A),D))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),D)) # label(fact_362_sorted_Osimps) # label(axiom). [clausify(409)].
% 1.59/1.86 605 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D) != B | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),f200(A,B,D,C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),D)) # label(fact_362_sorted_Osimps) # label(axiom). [clausify(409)].
% 1.59/1.86 606 -linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f201(A,B,C)),hAPP(list(A),fun(A,bool),set(A),C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C))) # label(fact_363_sorted_OCons) # label(axiom). [clausify(410)].
% 1.59/1.86 607 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f201(A,B,C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C))) # label(fact_363_sorted_OCons) # label(axiom). [clausify(410)].
% 1.59/1.86 608 -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_397_linorder__neq__iff) # label(axiom). [clausify(444)].
% 1.59/1.86 609 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_397_linorder__neq__iff) # label(axiom). [clausify(444)].
% 1.59/1.86 610 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_397_linorder__neq__iff) # label(axiom). [clausify(444)].
% 1.59/1.86 611 -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_398_not__less__iff__gr__or__eq) # label(axiom). [clausify(445)].
% 1.59/1.86 612 -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_398_not__less__iff__gr__or__eq) # label(axiom). [clausify(445)].
% 1.59/1.86 613 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_398_not__less__iff__gr__or__eq) # label(axiom). [clausify(445)].
% 1.59/1.86 614 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_399_linorder__less__linear) # label(axiom). [clausify(446)].
% 1.59/1.86 615 -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_400_linorder__antisym__conv3) # label(axiom). [clausify(447)].
% 1.59/1.86 616 -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_400_linorder__antisym__conv3) # label(axiom). [clausify(447)].
% 1.59/1.86 617 -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_401_linorder__neqE) # label(axiom). [clausify(448)].
% 1.59/1.86 618 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_417_linorder__cases) # label(axiom). [clausify(464)].
% 1.59/1.86 619 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) # label(fact_427_linorder__antisym__conv2) # label(axiom). [clausify(474)].
% 1.59/1.86 620 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_427_linorder__antisym__conv2) # label(axiom). [clausify(474)].
% 1.59/1.86 621 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_429_leD) # label(axiom). [clausify(476)].
% 1.59/1.86 622 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = ti(A,B) # label(fact_432_linorder__antisym__conv1) # label(axiom). [clausify(479)].
% 1.59/1.86 623 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_432_linorder__antisym__conv1) # label(axiom). [clausify(479)].
% 1.59/1.86 624 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_433_not__leE) # label(axiom). [clausify(480)].
% 1.59/1.86 625 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_434_leI) # label(axiom). [clausify(481)].
% 1.59/1.86 626 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_438_linorder__le__less__linear) # label(axiom). [clausify(485)].
% 1.59/1.86 627 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_439_linorder__not__le) # label(axiom). [clausify(486)].
% 1.59/1.86 628 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_439_linorder__not__le) # label(axiom). [clausify(486)].
% 1.59/1.86 629 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_440_linorder__not__less) # label(axiom). [clausify(487)].
% 1.59/1.86 630 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_440_linorder__not__less) # label(axiom). [clausify(487)].
% 1.59/1.86 Derived: linorder_sorted(nat) = ti(fun(list(nat),bool),linorder_sorted(nat)). [resolve(573,a,574,a)].
% 1.59/1.86 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(573,a,575,a)].
% 1.59/1.86 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),nil(nat))). [resolve(573,a,576,a)].
% 1.59/1.86 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(573,a,577,a)].
% 1.59/1.86 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(573,a,578,a)].
% 1.59/1.86 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(573,a,579,a)].
% 1.59/1.86 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(573,a,580,a)].
% 1.59/1.86 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(573,a,581,a)].
% 1.59/1.86 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | -hBOOL(hAPP(list(nat),bool,distinct(nat),A)) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | -hBOOL(hAPP(list(nat),bool,distinct(nat),B)) | hAPP(list(nat),fun(nat,bool),set(nat),B) != hAPP(list(nat),fun(nat,bool),set(nat),A) | B = A. [resolve(573,a,582,a)].
% 1.59/1.86 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(573,a,583,a)].
% 1.59/1.86 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(573,a,584,a)].
% 1.59/1.86 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),B),C))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),B),C)))). [resolve(573,a,586,a)].
% 1.59/1.86 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),B),C)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(573,a,587,a)].
% 1.59/1.86 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),B),C)))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),B),C))). [resolve(573,a,588,a)].
% 1.59/1.86 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),B))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)). [resolve(573,a,590,a)].
% 1.59/1.86 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),B))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),C),hAPP(list(nat),fun(nat,bool),set(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(573,a,591,a)].
% 1.59/1.86 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f195(nat,A,B)),hAPP(list(nat),fun(nat,bool),set(nat),B))). [resolve(573,a,592,a)].
% 1.59/1.86 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f195(nat,A,B))). [resolve(573,a,593,a)].
% 1.59/1.86 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),A),B))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)). [resolve(573,a,594,a)].
% 1.59/1.86 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),A),B))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)). [resolve(573,a,595,a)].
% 1.59/1.86 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),A),B))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),C),hAPP(list(nat),fun(nat,bool),set(nat),A))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),D),hAPP(list(nat),fun(nat,bool),set(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)). [resolve(573,a,596,a)].
% 1.59/1.86 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),A),B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f196(nat,A,B)),hAPP(list(nat),fun(nat,bool),set(nat),A))). [resolve(573,a,597,a)].
% 1.59/1.87 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),A),B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f197(nat,A,B)),hAPP(list(nat),fun(nat,bool),set(nat),B))). [resolve(573,a,598,a)].
% 1.59/1.87 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),A),B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f196(nat,A,B)),f197(nat,A,B))). [resolve(573,a,599,a)].
% 1.59/1.87 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | nil(nat) = A | hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),f199(nat,A)),f198(nat,A)) = A. [resolve(573,a,600,a)].
% 1.59/1.87 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | nil(nat) = A | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),hAPP(list(nat),fun(nat,bool),set(nat),f198(nat,A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f199(nat,A)),B)). [resolve(573,a,601,a)].
% 1.59/1.87 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | nil(nat) = A | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),f198(nat,A))). [resolve(573,a,602,a)].
% 1.59/1.87 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | nil(nat) != A. [resolve(573,a,603,a)].
% 1.59/1.87 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),B),C) != A | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f200(nat,A,C,B)),hAPP(list(nat),fun(nat,bool),set(nat),C))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),C)). [resolve(573,a,604,a)].
% 1.59/1.87 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),B),C) != A | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f200(nat,A,C,B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),C)). [resolve(573,a,605,a)].
% 1.59/1.87 Derived: hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f201(nat,A,B)),hAPP(list(nat),fun(nat,bool),set(nat),B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),B))). [resolve(573,a,606,a)].
% 1.59/1.87 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f201(nat,A,B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),B))). [resolve(573,a,607,a)].
% 1.59/1.87 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(573,a,608,a)].
% 1.59/1.87 Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(573,a,609,a)].
% 1.59/1.87 Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(573,a,610,a)].
% 1.59/1.87 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(573,a,612,a)].
% 1.59/1.87 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) = ti(nat,A). [resolve(573,a,619,a)].
% 1.59/1.87 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(573,a,621,a)].
% 1.59/1.87 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,B) != ti(nat,A). [resolve(573,a,623,a)].
% 3.76/4.08 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(573,a,624,a)].
% 3.76/4.08
% 3.76/4.08 ============================== end predicate elimination =============
% 3.76/4.08
% 3.76/4.08 Auto_denials: (non-Horn, no changes).
% 3.76/4.08
% 3.76/4.08 Term ordering decisions:
% 3.76/4.08 Function symbol KB weights: bool=1. arrow_490897120le_alt=1. nat=1. arrow_660593299e_indi=1. suc=1. arrow_2064824852le_Lin=1. arrow_1111136790e_Prof=1. arrow_1322701812_below=1. arrow_14103264_above=1. f=1. b=1. a=1. arrow_2037941124le_IIA=1. p=1. arrow_218898985ctator=1. c=1. fNot=1. fconj=1. arrow_1278947948_mkbot=1. arrow_1427655034_mktop=1. arrow_831799591nimity=1. fTrue=1. fFalse=1. p_1=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. fun=1. product_prod=1. ti=1. product_Pair=1. pi=1. foldl=1. combk=1. list_case=1. list_rec=1. maps=1. in_rel=1. f6=1. f16=1. f17=1. f18=1. f19=1. f20=1. f21=1. f22=1. f23=1. f24=1. f83=1. f91=1. f92=1. f123=1. f124=1. f125=1. f126=1. f127=1. f198=1. f199=1. list=1. member=1. cons=1. append=1. nil=1. ord_less_eq=1. ord_less=1. set=1. size_size=1. linorder_sorted=1. listrel1=1. rev=1. distinct=1. drop=1. lexord=1. takeWhile=1. take=1. listrel=1. dropWhile=1. butlast=1. last=1. top_top=1. listrelp=1. tl=1. hd=1. replicate=1. lex=1. rotate1=1. equal_equal=1. fequal=1. null=1. insert=1. splice=1. partition=1. collect=1. if=1. nat_case=1. combi=1. lexn=1. order_215145569der_on=1. undefined=1. f8=1. f9=1. f10=1. f11=1. f13=1. f14=1. f15=1. f84=1. combb=1. product_prod_case=1. combc=1. product_curry=1. combs=1. produc1605651328_split=1. product_prod_rec=1. f1=1. f2=1. f3=1. f31=1. f32=1. f33=1. f34=1. f71=1. f72=1. f73=1. f75=1. f76=1. f77=1. f78=1. f79=1. f80=1. f89=1. f90=1. f140=1. f141=1. f147=1. f148=1. f149=1. f150=1. f151=1. f152=1. f153=1. f154=1. f155=1. f165=1. f166=1. f167=1. f168=1. f169=1. f170=1. f171=1. f173=1. f174=1. f175=1. f176=1. f178=1. f179=1. f180=1. f181=1. f182=1. f183=1. f184=1. f185=1. f186=1. f193=1. f195=1. f196=1. f197=1. f201=1. f202=1. f203=1. f204=1. f205=1. f209=1. hAPP=1. f12=1. f29=1. f30=1. f35=1. f36=1. f37=1. f74=1. f81=1. f82=1. f93=1. f94=1. f95=1. f96=1. f111=1. f112=1. f113=1. f114=1. f132=1. f133=1. f134=1. f135=1. f136=1. f137=1. f138=1. f139=1. f145=1. f146=1. f194=1. f200=1. f206=1. f207=1. f7=1. f25=1. f26=1. f27=1. f38=1. f39=1. f40=1. f67=1. f68=1. f69=1. f70=1. f85=1. f86=1. f87=1. f88=1. f97=1. f98=1. f99=1. f100=1. f101=1. f102=1. f103=1. f104=1. f105=1. f106=1. f128=1. f129=1. f130=1. f131=1. f142=1. f143=1. f144=1. f156=1. f157=1. f158=1. f159=1. f160=1. f177=1. f208=1. f4=1. f5=1. f28=1. f58=1. f59=1. f60=1. f61=1. f62=1. f63=1. f64=1. f65=1. f66=1. f109=1. f110=1. f115=1. f116=1. f117=1. f118=1. f119=1. f120=1. f121=1. f122=1. f163=1. f164=1. f172=1. f187=1. f188=1. f189=1. f47=1. f48=1. f49=1. f50=1. f51=1. f52=1. f53=1. f54=1. f55=1. f56=1. f57=1. f107=1. f108=1. f190=1. f191=1. f192=1. f41=1. f42=1. f43=1. f44=1. f45=1. f46=1. f161=1. f162=1.
% 3.76/4.08
% 3.76/4.08 ============================== end of process initial clauses ========
% 3.76/4.08
% 3.76/4.08 ============================== CLAUSES FOR SEARCH ====================
% 3.76/4.08
% 3.76/4.08 ============================== end of clauses for search =============
% 3.76/4.08
% 3.76/4.08 ============================== SEARCH ================================
% 3.76/4.08
% 3.76/4.08 % Starting search at 0.76 seconds.
% 3.76/4.08
% 3.76/4.08 Low Water (keep): wt=199.000, iters=3622
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% 3.76/4.08 Low Water (keep): wt=188.000, iters=3467
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% 3.76/4.08 Low Water (keep): wt=186.000, iters=3429
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% 3.76/4.08 Low Water (keep): wt=182.000, iters=3424
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% 3.76/4.08 Low Water (keep): wt=178.000, iters=3354
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% 3.76/4.08 Low Water (keep): wt=173.000, iters=3336
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% 3.76/4.08 Low Water (keep): wt=172.000, iters=3363
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% 3.76/4.08 Low Water (keep): wt=171.000, iters=3353
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% 3.76/4.08 Low Water (keep): wt=143.000, iters=3434
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% 3.76/4.08 Low Water (keep): wt=142.000, iters=3380
% 104.86/105.15
% 104.86/105.15 Low Water (keep): wt=140.000, iters=3349
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% 104.86/105.15 Low Water (keep): wt=138.000, iters=3440
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% 104.86/105.15 Low Water (keep): wt=128.000, iters=3345
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% 104.86/105.15 Low Water (keep): wt=122.000, iters=3361
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% 104.86/105.15 Low Water (keep): wt=120.000, iters=3401
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% 104.86/105.15 Low Water (keep): wt=118.000, iters=3414
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% 104.86/105.15 Low Water (keep): wt=115.000, iters=3348
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% 104.86/105.15 Low Water (keep): wt=114.000, iters=3350
% 104.86/105.15
% 104.86/105.15 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 118 (0.00 of 2.99 sec).
% 104.86/105.15
% 104.86/105.15 Low Water (keep): wt=112.000, iters=3427
% 104.86/105.15
% 104.86/105.15 Low Water (keep): wt=109.000, iters=3334
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% 104.86/105.15 Low Water (keep): wt=104.000, iters=3472
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% 104.86/105.15 Low Water (keep): wt=103.000, iters=3521
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% 104.86/105.15 Low Water (keep): wt=100.000, iters=3480
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% 104.86/105.15 Low Water (keep): wt=99.000, iters=3447
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% 104.86/105.15 Low Water (keep): wt=97.000, iters=3363
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% 104.86/105.15 Low Water (keep): wt=86.000, iters=3333
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% 104.86/105.15 Low Water (keep): wt=85.000, iters=3536
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% 104.86/105.15 Low Water (keep): wt=82.000, iters=3336
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% 104.86/105.15 Low Water (keep): wt=81.000, iters=3385
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% 104.86/105.15 Low Water (keep): wt=78.000, iters=3490
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% 104.86/105.15 Low Water (keep): wt=76.000, iters=3369
% 104.86/105.15
% 104.86/105.15 Low Water (keep): wt=75.000, iters=3396
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% 104.86/105.15 Low Water (keep): wt=69.000, iters=3334
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% 104.86/105.15 Low Water (keep): wt=56.000, iters=3543
% 104.86/105.15
% 104.86/105.15 Low Water (displace): id=4385, wt=200.000
% 104.86/105.15
% 104.86/105.15 Low Water (displace): id=12703, wt=14.000
% 104.86/105.15
% 104.86/105.15 Low Water (displace): id=12715, wt=12.000
% 104.86/105.15
% 104.86/105.15 Low Water (keep): wt=48.000, iters=3727
% 104.86/105.15
% 104.86/105.15 Low Water (keep): wt=43.000, iters=3407
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% 104.86/105.15 Low Water (keep): wt=31.000, iters=3429
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% 104.86/105.15
% 104.86/105.15 Low Water (keep): wt=25.000, iters=3378
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% 104.86/105.15 Low Water (keep): wt=24.000, iters=3334
% 104.86/105.15
% 104.86/105.15 Low Water (keep): wt=23.000, iters=3369
% 104.86/105.15
% 104.86/105.15 Low Water (keep): wt=22.000, iters=3335
% 104.86/105.15
% 104.86/105.15 Low Water (keep): wt=21.000, iters=3502
% 104.86/105.15
% 104.86/105.15 Low Water (keep): wt=20.000, iters=3333
% 104.86/105.15
% 104.86/105.15 Low Water (keep): wt=18.000, iters=3333
% 104.86/105.15
% 104.86/105.15 ============================== STATISTICS ============================
% 104.86/105.15
% 104.86/105.15 Given=10401. Generated=1605057. Kept=331472. proofs=0.
% 104.86/105.15 Usable=10295. Sos=9983. Demods=815. Limbo=13, Disabled=312183. Hints=0.
% 104.86/105.15 Kept_by_rule=0, Deleted_by_rule=134668.
% 104.86/105.15 Forward_subsumed=93076. Back_subsumed=51.
% 104.86/105.15 Sos_limit_deleted=1045841. Sos_displaced=310389. Sos_removed=0.
% 104.86/105.15 New_demodulators=999 (0 lex), Back_demodulated=732. Back_unit_deleted=9.
% 104.86/105.15 Demod_attempts=79569407. Demod_rewrites=221810.
% 104.86/105.15 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
% 104.86/105.15 Nonunit_fsub_feature_tests=3024240. Nonunit_bsub_feature_tests=11879.
% 104.86/105.15 Megabytes=419.43.
% 104.86/105.15 User_CPU=102.52, System_CPU=1.01, Wall_clock=104.
% 104.86/105.15
% 104.86/105.15 Megs malloced by palloc(): 400.
% 104.86/105.15 type (bytes each) gets frees in use bytes
% 104.86/105.15 chunk ( 104) 51568 51568 0 0.0 K
% 104.86/105.15 string_buf ( 8) 46036 46036 0 0.0 K
% 104.86/105.15 token ( 20) 118757 118757 0 0.0 K
% 104.86/105.15 pterm ( 16) 82423 82423 0 0.0 K
% 104.86/105.15 hashtab ( 8) 572 572 0 0.0 K
% 104.86/105.15 hashnode ( 8) 2243 2243 0 0.0 K
% 104.86/105.15 term ( 20) 115397235 106292369 9104866 177829.4 K
% 104.86/105.16 term arg arrays: 43258.2 K
% 104.86/105.16 attribute ( 12) 5208 204 5004 58.6 K
% 104.86/105.16 ilist ( 8) 808087772 806680391 1407381 10995.2 K
% 104.86/105.16 plist ( 8) 8459526 8095236 364290 2846.0 K
% 104.86/105.16 i2list ( 12) 7138237 7138237 0 0.0 K
% 104.86/105.16 just ( 12) 1861665 1518109 343556 4026.0 K
% 104.86/105.16 parajust ( 16) 339786 294024 45762 715.0 K
% 104.86/105.16 instancejust ( 8) 0 0 0 0.0 K
% 104.86/105.16 ivyjust ( 24) 0 0 0 0.0 K
% 104.86/105.16 formula ( 28) 25629 16813 8816 241.1 K
% 104.86/105.16 formula arg arrays: 30.0 K
% 104.86/105.16 topform ( 52) 1606649 1273585 333064 16913.4 K
% 104.86/105.16 clist_pos ( 20) 988420 655131 333289 6509.6 K
% 104.86/105.16 clist ( 16) 8 1 7 0.1 K
% 104.86/105.16 context ( 808) 8670177 8670175 2 1.6 K
% 104.86/105.16 trail ( 12) 21325226 21325222 4 0.0 K
% 104.86/105.16 ac_match_pos (70044) 0 0 0 0.0 K
% 104.86/105.16 ac_match_free_vars_pos (20020)
% 104.86/105.16 0 0 0 0.0 K
% 104.86/105.16 btm_state ( 60) 0 0 0 0.0 K
% 104.86/105.16 btu_state ( 60) 0 0 0 0.0 K
% 104.86/105.16 ac_position (285432) 0 0 0 0.0 K
% 104.86/105.16 fpa_trie ( 20) 2273423 1860774 412649 8059.6 K
% 104.86/105.16 fpa_state ( 28) 21699065 21699065 0 0.0 K
% 104.86/105.16 fpa_index ( 12) 10 0 10 0.1 K
% 104.86/105.16 fpa_chunk ( 20) 3393547 3215275 178272 3481.9 K
% 104.86/105.16 fpa_list ( 16) 1952713 0 1952713 30511.1 K
% 104.86/105.16 fpa_list chunks: 14247.9 K
% 104.86/105.16 discrim ( 12) 3345695 3203820 141875 1662.6 K
% 104.86/105.16 discrim_pos ( 16) 274887 274887 0 0.0 K
% 104.86/105.16 flat2 ( 32) 46110639 46110639 0 0.0 K
% 104.86/105.16 flat ( 48) 0 0 0 0.0 K
% 104.86/105.16 flatterm ( 32) 118830194 118830194 0 0.0 K
% 104.86/105.16 mindex ( 28) 13 0 13 0.4 K
% 104.86/105.16 mindex_pos ( 56) 4395723 4395723 0 0.0 K
% 104.86/105.16 lindex ( 12) 5 0 5 0.1 K
% 104.86/105.16 clash ( 40) 0 0 0 0.0 K
% 104.86/105.16 di_tree ( 12) 28991215 21793969 7197246 84342.7 K
% 104.86/105.16 avl_node ( 20) 661747 641781 19966 390.0 K
% 104.86/105.16
% 104.86/105.16 Memory report, 20 @ 20 = 400 megs (400.00 megs used).
% 104.86/105.16 List 1, length 7, 0.0 K
% 104.86/105.16 List 2, length 1215, 9.5 K
% 104.86/105.16 List 3, length 28288, 331.5 K
% 104.86/105.16 List 4, length 16, 0.2 K
% 104.86/105.16 List 5, length 337, 6.6 K
% 104.86/105.16 List 6, length 259, 6.1 K
% 104.86/105.16 List 7, length 119, 3.3 K
% 104.86/105.16 List 8, length 436, 13.6 K
% 104.86/105.16 List 10, length 4, 0.2 K
% 104.86/105.16 List 11, length 12, 0.5 K
% 104.86/105.16 List 12, length 21, 1.0 K
% 104.86/105.16 List 14, length 2, 0.1 K
% 104.86/105.16 List 15, length 2, 0.1 K
% 104.86/105.16 List 16, length 2198, 137.4 K
% 104.86/105.16 List 26, length 885, 89.9 K
% 104.86/105.16 List 32, length 42, 5.2 K
% 104.86/105.16 List 64, length 40, 10.0 K
% 104.86/105.16 List 128, length 2, 1.0 K
% 104.86/105.16 List 202, length 2, 1.6 K
% 104.86/105.16 List 256, length 189, 189.0 K
% 104.86/105.16
% 104.86/105.16 ============================== SELECTOR REPORT =======================
% 104.86/105.16 Sos_deleted=1045841, Sos_displaced=310389, Sos_size=9983
% 104.86/105.16 SELECTOR PART PRIORITY ORDER SIZE SELECTED
% 104.86/105.16 I 2147483647 high age 0 913
% 104.86/105.16 H 1 high weight 0 0
% 104.86/105.16 A 1 low age 9983 1055
% 104.86/105.16 F 4 low weight 1081 4217
% 104.86/105.16 T 4 low weight 8902 4216
% 104.86/105.16 ============================== end of selector report ================
% 104.86/105.16
% 104.86/105.16 ============================== end of statistics =====================
% 104.86/105.16
% 104.86/105.16 Exiting with failure.
% 104.86/105.16
% 104.86/105.16 Process 15777 exit (max_megs) Sat Jul 2 06:19:07 2022
% 104.86/105.16 Prover9 interrupted
%------------------------------------------------------------------------------