TSTP Solution File: SCT170+7 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT170+7 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 119.78s 119.98s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT170+7 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 2 09:28:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.98/2.43 ============================== Prover9 ===============================
% 1.98/2.43 Prover9 (32) version 2009-11A, November 2009.
% 1.98/2.43 Process 18461 was started by sandbox on n006.cluster.edu,
% 1.98/2.43 Sat Jul 2 09:28:54 2022
% 1.98/2.43 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18308_n006.cluster.edu".
% 1.98/2.43 ============================== end of head ===========================
% 1.98/2.43
% 1.98/2.43 ============================== INPUT =================================
% 1.98/2.43
% 1.98/2.43 % Reading from file /tmp/Prover9_18308_n006.cluster.edu
% 1.98/2.43
% 1.98/2.43 set(prolog_style_variables).
% 1.98/2.43 set(auto2).
% 1.98/2.43 % set(auto2) -> set(auto).
% 1.98/2.43 % set(auto) -> set(auto_inference).
% 1.98/2.43 % set(auto) -> set(auto_setup).
% 1.98/2.43 % set(auto_setup) -> set(predicate_elim).
% 1.98/2.43 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.98/2.43 % set(auto) -> set(auto_limits).
% 1.98/2.43 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.98/2.43 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.98/2.43 % set(auto) -> set(auto_denials).
% 1.98/2.43 % set(auto) -> set(auto_process).
% 1.98/2.43 % set(auto2) -> assign(new_constants, 1).
% 1.98/2.43 % set(auto2) -> assign(fold_denial_max, 3).
% 1.98/2.43 % set(auto2) -> assign(max_weight, "200.000").
% 1.98/2.43 % set(auto2) -> assign(max_hours, 1).
% 1.98/2.43 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.98/2.43 % set(auto2) -> assign(max_seconds, 0).
% 1.98/2.43 % set(auto2) -> assign(max_minutes, 5).
% 1.98/2.43 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.98/2.43 % set(auto2) -> set(sort_initial_sos).
% 1.98/2.43 % set(auto2) -> assign(sos_limit, -1).
% 1.98/2.43 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.98/2.43 % set(auto2) -> assign(max_megs, 400).
% 1.98/2.43 % set(auto2) -> assign(stats, some).
% 1.98/2.43 % set(auto2) -> clear(echo_input).
% 1.98/2.43 % set(auto2) -> set(quiet).
% 1.98/2.43 % set(auto2) -> clear(print_initial_clauses).
% 1.98/2.43 % set(auto2) -> clear(print_given).
% 1.98/2.43 assign(lrs_ticks,-1).
% 1.98/2.43 assign(sos_limit,10000).
% 1.98/2.43 assign(order,kbo).
% 1.98/2.43 set(lex_order_vars).
% 1.98/2.43 clear(print_given).
% 1.98/2.43
% 1.98/2.43 % formulas(sos). % not echoed (1165 formulas)
% 1.98/2.43
% 1.98/2.43 ============================== end of input ==========================
% 1.98/2.43
% 1.98/2.43 % From the command line: assign(max_seconds, 300).
% 1.98/2.43
% 1.98/2.43 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.98/2.43
% 1.98/2.43 % Formulas that are not ordinary clauses:
% 1.98/2.43 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].
% 1.98/2.43 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].
% 1.98/2.43 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].
% 1.98/2.43 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].
% 1.98/2.43 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].
% 1.98/2.43 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].
% 1.98/2.43 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].
% 1.98/2.43 8 (all X_a (minus(X_a) -> ti(fun(X_a,fun(X_a,X_a)),minus_minus(X_a)) = minus_minus(X_a))) # label(tsy_c_Groups_Ominus__class_Ominus_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 9 (all X_a (one(X_a) -> ti(X_a,one_one(X_a)) = one_one(X_a))) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 10 (all X_a (monoid_add(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 11 (all X_a (ab_semigroup_add(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 12 (all X_a (cancel_semigroup_add(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_2_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 13 (all X_a (zero(X_a) -> ti(X_a,zero_zero(X_a)) = zero_zero(X_a))) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 14 (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].
% 1.98/2.43 15 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 16 (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].
% 1.98/2.43 17 (all X_a ti(fun(list(X_a),fun(list(X_a),list(X_a))),append(X_a)) = append(X_a)) # label(tsy_c_List_Oappend_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 18 (all X_a ti(fun(list(X_a),list(X_a)),butlast(X_a)) = butlast(X_a)) # label(tsy_c_List_Obutlast_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 19 (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].
% 1.98/2.43 20 (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].
% 1.98/2.43 21 (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].
% 1.98/2.43 22 (all X_a ti(fun(list(X_a),X_a),hd(X_a)) = hd(X_a)) # label(tsy_c_List_Ohd_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 23 (all X_a ti(fun(X_a,fun(list(X_a),list(X_a))),insert(X_a)) = insert(X_a)) # label(tsy_c_List_Oinsert_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 24 (all X_a ti(fun(list(X_a),X_a),last(X_a)) = last(X_a)) # label(tsy_c_List_Olast_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 25 (all X_a ti(fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool)),lenlex(X_a)) = lenlex(X_a)) # label(tsy_c_List_Olenlex_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 26 (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].
% 1.98/2.43 27 (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].
% 1.98/2.43 28 (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].
% 1.98/2.43 29 (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].
% 1.98/2.43 30 (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].
% 1.98/2.43 31 (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].
% 1.98/2.43 32 (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].
% 1.98/2.43 33 (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].
% 1.98/2.43 34 (all X_a ti(fun(fun(X_a,nat),fun(list(X_a),nat)),list_size(X_a)) = list_size(X_a)) # label(tsy_c_List_Olist_Olist__size_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 35 (all X_a all X_b ti(fun(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool))),list_all2(X_a,X_b)) = list_all2(X_a,X_b)) # label(tsy_c_List_Olist__all2_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 36 (all X_a ti(fun(list(X_a),fun(nat,fun(X_a,list(X_a)))),list_update(X_a)) = list_update(X_a)) # label(tsy_c_List_Olist__update_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 37 (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].
% 1.98/2.43 38 (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].
% 1.98/2.43 39 (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].
% 1.98/2.43 40 (all X_a ti(fun(list(fun(X_a,bool)),fun(list(X_a),bool)),listset(X_a)) = listset(X_a)) # label(tsy_c_List_Olistset_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 41 (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].
% 1.98/2.43 42 (all X_a ti(fun(list(X_a),fun(nat,X_a)),nth(X_a)) = nth(X_a)) # label(tsy_c_List_Onth_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 43 (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].
% 1.98/2.43 44 (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].
% 1.98/2.43 45 (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].
% 1.98/2.43 46 (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].
% 1.98/2.43 47 (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].
% 1.98/2.43 48 (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].
% 1.98/2.43 49 (all X_a ti(fun(fun(X_a,bool),fun(fun(list(X_a),bool),fun(list(X_a),bool))),set_Cons(X_a)) = set_Cons(X_a)) # label(tsy_c_List_Oset__Cons_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 50 (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].
% 1.98/2.43 51 (all X_a ti(fun(list(X_a),fun(fun(nat,bool),list(X_a))),sublist(X_a)) = sublist(X_a)) # label(tsy_c_List_Osublist_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 52 (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].
% 1.98/2.43 53 (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].
% 1.98/2.43 54 (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].
% 1.98/2.43 55 (all X_a all X_b ti(fun(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b)))),zip(X_a,X_b)) = zip(X_a,X_b)) # label(tsy_c_List_Ozip_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 56 (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].
% 1.98/2.43 57 (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_1_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 58 (all X_a (ord(X_a) -> ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a))),min(X_a)) = min(X_a))) # label(tsy_c_Orderings_Oord_Omin_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 59 (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].
% 1.98/2.43 60 (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].
% 1.98/2.43 61 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,X_a)),ord_min(X_a)) = ord_min(X_a))) # label(tsy_c_Orderings_Oord__class_Omin_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 62 (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].
% 1.98/2.43 63 (all X_a ti(fun(fun(X_a,fun(X_a,bool)),bool),reflp(X_a)) = reflp(X_a)) # label(tsy_c_Predicate_Oreflp_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 64 (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].
% 1.98/2.43 65 (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].
% 1.98/2.43 66 (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].
% 1.98/2.43 67 (all X_a all X_c all X_b all X_d ti(fun(fun(X_a,X_c),fun(fun(X_b,X_d),fun(product_prod(X_a,X_b),product_prod(X_c,X_d)))),product_map_pair(X_a,X_c,X_b,X_d)) = product_map_pair(X_a,X_c,X_b,X_d)) # label(tsy_c_Product__Type_Omap__pair_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 68 (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].
% 1.98/2.43 69 (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].
% 1.98/2.43 70 (all X_a ti(fun(fun(X_a,bool),fun(fun(product_prod(X_a,X_a),bool),bool)),refl_on(X_a)) = refl_on(X_a)) # label(tsy_c_Relation_Orefl__on_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 71 (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].
% 1.98/2.43 72 (all X_a ti(fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool)),transitive_rtrancl(X_a)) = transitive_rtrancl(X_a)) # label(tsy_c_Transitive__Closure_Ortrancl_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 73 (all X_a all X_b ti(fun(fun(product_prod(X_a,X_a),bool),fun(fun(product_prod(X_b,X_b),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool))),lex_prod(X_a,X_b)) = lex_prod(X_a,X_b)) # label(tsy_c_Wellfounded_Olex__prod_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 74 (all X_a ti(fun(fun(X_a,nat),fun(product_prod(X_a,X_a),bool)),measure(X_a)) = measure(X_a)) # label(tsy_c_Wellfounded_Omeasure_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 75 (all X_a ti(fun(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool))),mlex_prod(X_a)) = mlex_prod(X_a)) # label(tsy_c_Wellfounded_Omlex__prod_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 76 (all X_a ti(fun(fun(X_a,bool),bool),fEx(X_a)) = fEx(X_a)) # label(tsy_c_fEx_res) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 77 (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].
% 1.98/2.43 78 (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].
% 1.98/2.43 79 (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].
% 1.98/2.43 80 (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].
% 1.98/2.43 81 (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].
% 1.98/2.43 82 (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].
% 1.98/2.43 83 (all I (hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I))) <-> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p_1,I))))) # label(fact_5_iff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 84 -(all C_2 -hBOOL(hAPP(list(arrow_2142409994le_alt),bool,distinct(arrow_2142409994le_alt),hAPP(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt)),cons(arrow_2142409994le_alt),a),hAPP(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt)),cons(arrow_2142409994le_alt),b),hAPP(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt)),cons(arrow_2142409994le_alt),C_2),nil(arrow_2142409994le_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].
% 1.98/2.43 85 (all X_1 all Y_1 all L_3 all Z_2 (hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_1),Y_1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,L_3),Z_2))) <-> ti(arrow_2142409994le_alt,Y_1) != ti(arrow_2142409994le_alt,Z_2) & (ti(arrow_2142409994le_alt,X_1) = ti(arrow_2142409994le_alt,Z_2) -> ti(arrow_2142409994le_alt,X_1) != ti(arrow_2142409994le_alt,Y_1)) & (ti(arrow_2142409994le_alt,X_1) != ti(arrow_2142409994le_alt,Z_2) -> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_1),Y_1)),L_3))))) # label(fact_10_in__mkbot) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 86 (all X_1 all Y_1 all L_3 all Z_2 (hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_1),Y_1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,L_3),Z_2))) <-> ti(arrow_2142409994le_alt,X_1) != ti(arrow_2142409994le_alt,Z_2) & (ti(arrow_2142409994le_alt,Y_1) = ti(arrow_2142409994le_alt,Z_2) -> ti(arrow_2142409994le_alt,X_1) != ti(arrow_2142409994le_alt,Y_1)) & (ti(arrow_2142409994le_alt,Y_1) != ti(arrow_2142409994le_alt,Z_2) -> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_1),Y_1)),L_3))))) # label(fact_11_in__mktop) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 87 (all X_1 all Y_1 all L_3 all Aa all Ba (ti(arrow_2142409994le_alt,Aa) != ti(arrow_2142409994le_alt,Ba) -> (hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin)) -> (hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_1),Y_1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,L_3),Aa),Ba))) <-> ti(arrow_2142409994le_alt,X_1) != ti(arrow_2142409994le_alt,Y_1) & (ti(arrow_2142409994le_alt,Y_1) = ti(arrow_2142409994le_alt,Aa) -> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_1),Ba)),L_3))) & (ti(arrow_2142409994le_alt,Y_1) != ti(arrow_2142409994le_alt,Aa) -> (ti(arrow_2142409994le_alt,X_1) = ti(arrow_2142409994le_alt,Aa) -> ti(arrow_2142409994le_alt,Y_1) = ti(arrow_2142409994le_alt,Ba) | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Ba),Y_1)),L_3))) & (ti(arrow_2142409994le_alt,X_1) != ti(arrow_2142409994le_alt,Aa) -> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_1),Y_1)),L_3)))))))) # label(fact_12_in__below) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 88 (all X_a all X_b all Pa ((all X1 hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,X1))) <-> (all A_5 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_5),B_2)))))) # label(fact_13_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 89 (all X_b all X_a all Aa all Ba all A_3 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_3),B_3) <-> ti(X_a,Aa) = ti(X_a,A_3) & ti(X_b,Ba) = ti(X_b,B_3))) # label(fact_14_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 90 (all X_b all X_a all A_1 all B 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_1),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),A_6),B_4) -> -(ti(X_a,A_1) = ti(X_a,A_6) -> ti(X_b,B) != ti(X_b,B_4)))) # label(fact_15_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 91 (all X_b all X_a all R_2 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_2),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_2)))) # label(fact_16_in__rel__def) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 92 (all L_3 all X_1 all Y_1 (ti(arrow_2142409994le_alt,X_1) != ti(arrow_2142409994le_alt,Y_1) -> (hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin)) -> hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,L_3),X_1),Y_1)),arrow_1568854078le_Lin))))) # label(fact_17_below__Lin) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 93 (all P_a all Pa all A_3 all B_3 all Aa all Ba (ti(arrow_2142409994le_alt,Aa) != ti(arrow_2142409994le_alt,Ba) -> (ti(arrow_2142409994le_alt,A_3) != ti(arrow_2142409994le_alt,B_3) -> (ti(arrow_2142409994le_alt,Aa) != ti(arrow_2142409994le_alt,B_3) -> (ti(arrow_2142409994le_alt,Ba) != ti(arrow_2142409994le_alt,A_3) -> (hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),Pa),arrow_301600364e_Prof)) -> (hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),P_a),arrow_301600364e_Prof)) -> ((all I (hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Pa,I))) <-> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_3),B_3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),P_a,I))))) -> (hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,Pa))) -> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_3),B_3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,P_a)))))))))))) # label(fact_19__C1_C) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 94 (all P_a all Pa all A_3 all B_3 all Aa all Ba (ti(arrow_2142409994le_alt,Aa) != ti(arrow_2142409994le_alt,Ba) -> (ti(arrow_2142409994le_alt,A_3) != ti(arrow_2142409994le_alt,B_3) -> (ti(arrow_2142409994le_alt,Aa) != ti(arrow_2142409994le_alt,B_3) -> (ti(arrow_2142409994le_alt,Ba) != ti(arrow_2142409994le_alt,A_3) -> (hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),Pa),arrow_301600364e_Prof)) -> (hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),P_a),arrow_301600364e_Prof)) -> ((all I (hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Pa,I))) <-> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_3),B_3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),P_a,I))))) -> (hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,Pa))) <-> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_3),B_3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,P_a)))))))))))) # label(fact_20__C2_C) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 95 (all L_3 (hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin)) -> hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),combk(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),arrow_1998540521e_indi),L_3)),arrow_301600364e_Prof)))) # label(fact_22_const__Lin__Prof) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 96 (all X_1 all L_3 (hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin)) -> hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,L_3),X_1)),arrow_1568854078le_Lin)))) # label(fact_23_mkbot__Lin) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 97 (all X_1 all L_3 (hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin)) -> hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,L_3),X_1)),arrow_1568854078le_Lin)))) # label(fact_24_mktop__Lin) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 98 (all Aa all Ba all L_3 (hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin)) -> (hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),L_3)) -> -hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Ba),Aa)),L_3))))) # label(fact_25_Lin__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 99 (all X_1 all Y_1 all L_3 (hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin)) -> (ti(arrow_2142409994le_alt,X_1) != ti(arrow_2142409994le_alt,Y_1) -> (-hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_1),Y_1)),L_3)) <-> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Y_1),X_1)),L_3)))))) # label(fact_26_notin__Lin__iff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 100 (all A_1 all B (ti(arrow_2142409994le_alt,A_1) != ti(arrow_2142409994le_alt,B) -> (exists C_2 hBOOL(hAPP(list(arrow_2142409994le_alt),bool,distinct(arrow_2142409994le_alt),hAPP(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt)),cons(arrow_2142409994le_alt),A_1),hAPP(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt)),cons(arrow_2142409994le_alt),B),hAPP(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt)),cons(arrow_2142409994le_alt),C_2),nil(arrow_2142409994le_alt))))))))) # label(fact_27_third__alt) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 101 (all Fa_1 (hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,Fa_1)) <-> (all X_2 (hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X_2),arrow_301600364e_Prof)) -> (all Xa (hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),Xa),arrow_301600364e_Prof)) -> (all A_5 all B_2 ((all I (hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X_2,I))) <-> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Xa,I))))) -> (hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa_1,X_2))) <-> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa_1,Xa)))))))))))) # label(fact_28_IIA__def) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 102 (all Fa_1 (hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,Fa_1)) <-> (all X_2 (hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X_2),arrow_301600364e_Prof)) -> (all A_5 all B_2 ((all I hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X_2,I)))) -> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa_1,X_2))))))))) # label(fact_29_unanimity__def) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 103 (all Aa all Ba (ti(arrow_2142409994le_alt,Aa) != ti(arrow_2142409994le_alt,Ba) -> (exists X_2 (hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X_2),arrow_1568854078le_Lin)) & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),X_2)))))) # label(fact_30_complete__Lin) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 104 (all X_1 all Y_1 all L_3 all Aa all Ba (ti(arrow_2142409994le_alt,Aa) != ti(arrow_2142409994le_alt,Ba) -> (hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin)) -> (hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_1),Y_1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,L_3),Aa),Ba))) <-> ti(arrow_2142409994le_alt,X_1) != ti(arrow_2142409994le_alt,Y_1) & (ti(arrow_2142409994le_alt,X_1) = ti(arrow_2142409994le_alt,Ba) -> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Y_1)),L_3))) & (ti(arrow_2142409994le_alt,X_1) != ti(arrow_2142409994le_alt,Ba) -> (ti(arrow_2142409994le_alt,Y_1) = ti(arrow_2142409994le_alt,Ba) -> ti(arrow_2142409994le_alt,X_1) = ti(arrow_2142409994le_alt,Aa) | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_1),Aa)),L_3))) & (ti(arrow_2142409994le_alt,Y_1) != ti(arrow_2142409994le_alt,Ba) -> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_1),Y_1)),L_3)))))))) # label(fact_31_in__above) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 105 (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].
% 1.98/2.43 106 (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].
% 1.98/2.43 107 (all X_a all A_6 all List_4 nil(X_a) != hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_6),List_4)) # label(fact_34_list_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 108 (all X_a all A_6 all List_4 hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_6),List_4) != nil(X_a)) # label(fact_35_list_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 109 (exists A_5 exists B_2 exists C_2 hBOOL(hAPP(list(arrow_2142409994le_alt),bool,distinct(arrow_2142409994le_alt),hAPP(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt)),cons(arrow_2142409994le_alt),A_5),hAPP(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt)),cons(arrow_2142409994le_alt),B_2),hAPP(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(list(arrow_2142409994le_alt),list(arrow_2142409994le_alt)),cons(arrow_2142409994le_alt),C_2),nil(arrow_2142409994le_alt))))))) # label(fact_36_alt3) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 110 (exists L_4 hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_4),arrow_1568854078le_Lin))) # label(fact_37_linear__alt) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 111 (all Fa_1 all I_1 (hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,Fa_1),I_1)) <-> (all X_2 (hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X_2),arrow_301600364e_Prof)) -> hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa_1,X_2) = hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X_2,I_1))))) # label(fact_38_dictator__def) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 112 (all X_a all Aa all List all A_3 all List_3 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Aa),List) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_3),List_3) <-> ti(X_a,Aa) = ti(X_a,A_3) & List = List_3)) # label(fact_39_list_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 113 (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_40_not__Cons__self2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 114 (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_41_not__Cons__self) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 115 (all L_3 all X_1 all Y_1 (ti(arrow_2142409994le_alt,X_1) != ti(arrow_2142409994le_alt,Y_1) -> (hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin)) -> hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,L_3),X_1),Y_1)),arrow_1568854078le_Lin))))) # label(fact_42_above__Lin) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.43 116 (all I_1 all Fa_1 (hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),Fa_1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) -> ((all X_2 (hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X_2),arrow_301600364e_Prof)) -> (all A_5 all B_2 (ti(arrow_2142409994le_alt,A_5) != ti(arrow_2142409994le_alt,B_2) -> (hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X_2,I_1))) -> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa_1,X_2)))))))) -> hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,Fa_1),I_1))))) # label(fact_43_dictatorI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 117 (all X_a all X_b all X_1 all F all A_2 all B_1 (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_2),B_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_1,X_1))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2))))) # label(fact_44_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 118 (all X_a all Y (Y != nil(X_a) -> -(all A_5 all List_2 Y != hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_5),List_2)))) # label(fact_45_list_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 119 (all X_a all Xs_1 (Xs_1 != nil(X_a) <-> (exists Y_2 exists Ys_2 Xs_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_2)))) # label(fact_46_neq__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 120 (all X_a all A_2 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_2),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),combk(fun(X_a,bool),X_a),A_2))))) # label(fact_47_funcset__id) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 121 (all X_a all X_b all X_1 all F all A_2 all B_1 (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_2),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B_1)))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> 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_1))))) # label(fact_48_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 122 (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].
% 1.98/2.44 123 (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].
% 1.98/2.44 124 (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].
% 1.98/2.44 125 (all X_a all X_b all Pa ((exists X1 hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,X1))) <-> (exists A_5 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_5),B_2)))))) # label(fact_52_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 126 (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_5 all B_2 all C_2 all D_3 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_5),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_3),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_53_prod__induct6) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 127 (all X_a all X all Xs all Y all Ys_1 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Ys_1)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),Xs),Ys_1)))) # label(fact_54_splice_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 128 (all X_a all Ys_1 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),nil(X_a)),Ys_1) = Ys_1) # label(fact_55_splice_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 129 (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_56_splice__Nil2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 130 (all X_a all X_b all X_1 all F all A_2 all B_1 (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_2),B_1))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> 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_1,X_1)))))) # label(fact_57_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 131 (all X_a all X_b all X_c all X_d all X_e all X_f all Y -(all A_5 all B_2 all C_2 all D_3 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_5),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_3),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_58_prod__cases6) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 132 (all X_a all X_b all X_c all X_d all X_e all Y -(all A_5 all B_2 all C_2 all D_3 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_5),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_3),E)))))) # label(fact_59_prod__cases5) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 133 (all X_a all X_b all X_c all X_d all X_e all X_1 all Pa ((all A_5 all B_2 all C_2 all D_3 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_5),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_3),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_60_prod__induct5) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 134 (all X_b all X_a all F all B_1 all A_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),A_2)) -> 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_1,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_2),B_1))))) # label(fact_61_Pi__I) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 135 (all X_a all X_b all X_c all X_d all Y -(all A_5 all B_2 all C_2 all D_3 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_5),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_3))))) # label(fact_62_prod__cases4) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 136 (all X_a all X_b all X_c all X_d all X_1 all Pa ((all A_5 all B_2 all C_2 all D_3 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_5),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_3)))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,Pa,X_1)))) # label(fact_63_prod__induct4) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 137 (all X_a all X_b all X_c all Y -(all A_5 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_5),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_64_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 138 (all X_a all X_b all X_c all X_1 all Pa ((all A_5 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_5),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_65_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 139 (all X_b all X_a all F all B_1 all A_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),A_2)) -> 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_1)))) -> 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_2),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B_1)))))) # label(fact_66_funcsetI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 140 (all X_b all X_a all F all B_1 all A_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),A_2)) -> 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_1,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_2),B_1))))) # label(fact_67_Pi__I_H) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 141 (all X_b all X_a all B_1 all F all G all A_2 ((all W (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),W),A_2)) -> 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_2),B_1))) <-> 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_2),B_1)))))) # label(fact_68_Pi__cong) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 142 (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_69_PairE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 143 (all X_a all X_b all Y -(all A_5 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_5),B_2))) # label(fact_70_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 144 (all X_a all X_b all S_2 all R_2 ((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_2)) <-> 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_2)))) <-> ti(fun(product_prod(X_a,X_b),bool),R_2) = ti(fun(product_prod(X_a,X_b),bool),S_2))) # label(fact_71_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 145 (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].
% 1.98/2.44 146 (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].
% 1.98/2.44 147 (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_74_list__nonempty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 148 (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].
% 1.98/2.44 149 (all X_a all X_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) <-> hBOOL(hAPP(X_a,bool,A_2,X_1)))) # label(fact_76_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 150 (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].
% 1.98/2.44 151 (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_78_list_Orecs_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 152 (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_79_list_Orecs_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 153 (all X_b all X_c all X_a all X_2 all Xa all Xb_1 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_1) = 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_1))) # label(fact_80_curry__def) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 154 (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_81_curryI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 155 (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_82_curryE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 156 (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_83_curryD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 157 (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_84_distinct__insert) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 158 (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_85_curry__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 159 (all X_b hBOOL(hAPP(list(X_b),bool,null(X_b),nil(X_b)))) # label(fact_86_null__rec_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 160 (all X_a all Xs_1 (hBOOL(hAPP(list(X_a),bool,null(X_a),Xs_1)) <-> Xs_1 = nil(X_a))) # label(fact_87_List_Onull__def) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 161 (all X_a all Xs_1 (Xs_1 = nil(X_a) <-> hBOOL(hAPP(list(X_a),bool,null(X_a),Xs_1)))) # label(fact_88_eq__Nil__null) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 162 (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_89_null__rec_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 163 (all X_a all Aa all X_1 all Ba all Y_1 all R_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)),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_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),Aa),Ba)),R_1)) | 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_1))))) # label(fact_91_lexord__cons__cons) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 164 (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_92_maps__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 165 (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_93_sorted__single) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 166 (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_94_distinct__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 167 (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_95_last_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 168 (all X_a all X_1 hBOOL(hAPP(X_a,bool,top_top(fun(X_a,bool)),X_1))) # label(fact_96_top1I) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 169 (all X_a (linorder(X_a) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),nil(X_a))))) # label(fact_97_sorted_ONil) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 170 (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_98_sorted__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 171 (all X_a all X_b all A_2 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_2),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_99_Pi__UNIV) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 172 (all X_a hAPP(list(X_a),list(X_a),butlast(X_a),nil(X_a)) = nil(X_a)) # label(fact_100_butlast_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 173 (all X_a all X_1 all R_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),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_1)))) # label(fact_101_lexord__Nil__right) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 174 (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_102_butlast_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 175 (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_103_last__ConsL) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 176 (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_104_last__ConsR) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 177 (all X_a all Y_1 all R_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)),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_1))) <-> (exists A_5 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_5),X_2)))) # label(fact_105_lexord__Nil__left) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 178 (all X_a all X_1 all Y_1 all R_1 ((all A_5 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_5),B_2)),R_1)) | ti(X_a,A_5) = 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_5)),R_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),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_1))) | 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_1))))) # label(fact_106_lexord__linear) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 179 (all X_a all Xs_1 all R_1 ((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_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),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_1))))) # label(fact_107_lexord__irreflexive) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 180 (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_108_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 181 (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_109_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 182 (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_110_top__apply) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 183 (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_111_takeWhile__not__last) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 184 (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_112_equal__Nil__null) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 185 (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_113_partition_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 186 (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_114_append__butlast__last__id) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 187 (all X_a all Xs_1 all L_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(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),L_1))) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1))) # label(fact_115_takeWhile__tail) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 188 (all X_a all Ys_1 all Us_2 all Xs all Xs1 all Zs_2 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Xs1) = Zs_2 -> (Ys_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs1),Us_2) -> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs_2),Us_2)))) # label(fact_116_append__eq__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 189 (all X_a all Ys all Xs_1 all Zs_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs_1),Xs_1) <-> Ys = Zs_1)) # label(fact_117_append__same__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 190 (all X_a all Xs_1 all Ys all Zs_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Zs_1) <-> Ys = Zs_1)) # label(fact_118_same__append__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 191 (all X_a all Xs_1 all Ys all Zs_1 all Ts (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs_1),Ts) <-> (exists Us (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs_1),Us) & hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us),Ys) = Ts | hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Us) = Zs_1 & Ys = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us),Ts))))) # label(fact_119_append__eq__append__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 192 (all X_a all Xs all Ys_1 all Zs_2 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)),Zs_2) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs_2))) # label(fact_120_append__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 193 (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_121_equal__list__def) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 194 (all X_a all X all Xs all Ys_1 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),Ys_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1))) # label(fact_122_append__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 195 (all X_a all Xs all Zs_2 all X all Xs1 all Ys_1 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs1) = Ys_1 -> (Xs = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs1),Zs_2) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs_2)))) # label(fact_123_Cons__eq__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 196 (all X_a all Ys_1 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),nil(X_a)),Ys_1) = Ys_1) # label(fact_124_append__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 197 (all X_a all Xs_1 all Ys (nil(X_a) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys) <-> Xs_1 = nil(X_a) & Ys = nil(X_a))) # label(fact_125_Nil__is__append__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 198 (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_126_append__Nil2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 199 (all X_a all Xs_1 all Ys (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys) <-> Ys = nil(X_a))) # label(fact_127_self__append__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 200 (all X_a all Ys all Xs_1 (Ys = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys) <-> Xs_1 = nil(X_a))) # label(fact_128_self__append__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 201 (all X_a all Xs_1 all Ys (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys) = nil(X_a) <-> Xs_1 = nil(X_a) & Ys = nil(X_a))) # label(fact_129_append__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 202 (all X_a all Xs_1 all Ys (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys) = Xs_1 <-> Ys = nil(X_a))) # label(fact_130_append__self__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 203 (all X_a all Xs_1 all Ys (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys) = Ys <-> Xs_1 = nil(X_a))) # label(fact_131_append__self__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 204 (all X_a all Xs all Ys_1 (Xs = Ys_1 -> Xs = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),nil(X_a)),Ys_1))) # label(fact_132_eq__Nil__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 205 (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_133_takeWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 206 (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_134_distinct__takeWhile) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 207 (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_135_sorted__takeWhile) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 208 (all X_a all Ys all Zs_1 all X_1 all Xs_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),Zs_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1) <-> Ys = nil(X_a) & Zs_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1) | (exists Ys_3 (Ys = 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_1) = Xs_1)))) # label(fact_136_append__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 209 (all X_a all X_1 all Xs_1 all Ys all Zs_1 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),Zs_1) <-> Ys = nil(X_a) & hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1) = Zs_1 | (exists Ys_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 & 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_1))))) # label(fact_137_Cons__eq__append__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 210 (all X_a all Xs_1 all X_1 all Ys all Y_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),nil(X_a))) <-> Xs_1 = Ys & ti(X_a,X_1) = ti(X_a,Y_1))) # label(fact_138_append1__eq__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 211 (all X_a all Xs all Ys_1 ((Ys_1 = nil(X_a) -> hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),list(X_a),butlast(X_a),Xs)) & (Ys_1 != nil(X_a) -> hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),butlast(X_a),Ys_1))))) # label(fact_139_butlast__append) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 212 (all X_a all Xs all Ys_1 (Ys_1 = nil(X_a) -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),X_a,last(X_a),Xs))) # label(fact_140_last__appendL) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 213 (all X_a all Xs all Ys_1 (Ys_1 != nil(X_a) -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),X_a,last(X_a),Ys_1))) # label(fact_141_last__appendR) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 214 (all X_a all Xs all Ys_1 ((Ys_1 = nil(X_a) -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),X_a,last(X_a),Xs)) & (Ys_1 != nil(X_a) -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),X_a,last(X_a),Ys_1)))) # label(fact_142_last__append) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 215 (all X_a all X_1 all U all V all R_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)),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_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)),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_1))))) # label(fact_143_lexord__append__leftI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 216 (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_144_takeWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 217 (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_145_maps__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 218 (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_146_butlast__snoc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 219 (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_147_last__snoc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 220 (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_148_UNIV__def) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 221 (all X_a all U all X_1 all Y_1 all Aa all Ba all R_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),Aa),Ba)),R_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)),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_1))))) # label(fact_149_lexord__append__left__rightI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 222 (all X_a all Xs_1 all X_1 all Ys (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))) = Ys <-> Ys != nil(X_a) & hAPP(list(X_a),list(X_a),butlast(X_a),Ys) = Xs_1 & hAPP(list(X_a),X_a,last(X_a),Ys) = ti(X_a,X_1))) # label(fact_150_snoc__eq__iff__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 223 (all X_a all X_1 all R_1 all Y_1 ((exists B_2 exists Z 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)) -> 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_1))))) # label(fact_151_lexord__append__rightI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 224 (all X_a all X_1 all U all V all R_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)),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_1))) -> ((all A_5 -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_5),A_5)),R_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)),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_1)))))) # label(fact_152_lexord__append__leftD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 225 (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_153_rev__induct) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 226 (all X_a all Xs (Xs != nil(X_a) -> -(all Ys_2 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_2),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_154_rev__cases) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 227 (all X_a all Xs_1 all X_1 all Ys all Y_1 all R_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)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)))),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),nil(X_a))))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_1))) & ti(X_a,X_1) = ti(X_a,Y_1) | Xs_1 = 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_1),Y_1)),R_1)))) # label(fact_155_snoc__listrel1__snoc__iff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.44 228 (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_156_rotate1__def) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 229 (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_157_rotate__simps) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 230 (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_158_UNIV__witness) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 231 (all X_a all A_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),A_2))) -> top_top(fun(X_a,bool)) = ti(fun(X_a,bool),A_2))) # label(fact_159_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 232 (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_160_rotate1__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 233 (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_161_distinct1__rotate) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 234 (all X_a all X_1 all Xs_1 all Ys all R_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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_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)),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))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_1))))) # label(fact_162_listrel1I2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 235 (all X_a all Xs_1 all R_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),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_1)))) # label(fact_163_not__listrel1__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 236 (all X_a all Xs_1 all R_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)),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_1)))) # label(fact_164_not__Nil__listrel1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 237 (all X_a all Us_1 all Vs_1 all Xs_1 all Ys all R_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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_1))) & Us_1 = Vs_1 | Xs_1 = Ys & 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_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)),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),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_1))))) # label(fact_165_append__listrel1I) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 238 (all X_a all X_1 all Xs_1 all Y_1 all Ys all R_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)),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))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_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_1)) & Xs_1 = Ys | 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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_1))))) # label(fact_166_Cons__listrel1__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 239 (all X_a all Xs_1 all X_1 all Y_1 all R_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_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)),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_1))))) # label(fact_167_listrel1I1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 240 (all X_a all Ys all Xs_1 all Us_1 all Vs_1 all X_1 all Y_1 all R_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_1)) -> (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 = 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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_1))))))) # label(fact_168_listrel1I) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 241 (all X_a all Xs_1 all Ys all R_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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_1))) -> -(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_1)) -> (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 != 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_169_listrel1E) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 242 (all X_a all X_1 all Xs_1 all Ys all R_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)),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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_1))) -> ((all Y_2 (Ys = 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_1)))) -> -(all Zs (Ys = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs) -> -hBOOL(hAPP(fun(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),listrel1(X_a),R_1)))))))) # label(fact_170_Cons__listrel1E1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 243 (all X_a all Xs_1 all Y_1 all Ys all R_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),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_1))) -> ((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) -> -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_1)))) -> -(all Zs (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) -> -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),Ys)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_1)))))))) # label(fact_171_Cons__listrel1E2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 244 (all X_a all Pa all Xs_1 all Y_1 all Ys (hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),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) <-> 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)) & -hBOOL(hAPP(X_a,bool,Pa,Y_1)))) # label(fact_173_dropWhile__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 245 (all X_a all Xs_1 all R_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),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_1)))) # label(fact_174_Nil2__notin__lex) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 246 (all X_a all Ys all R_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)),nil(X_a)),Ys)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lex(X_a),R_1)))) # label(fact_175_Nil__notin__lex) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 247 (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_176_partition_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 248 (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_177_split__twice) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 249 (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_178_split__weak__cong) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 250 (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_179_prod_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 251 (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_180_split__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 252 (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_181_dropWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 253 (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_182_dropWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 254 (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_183_distinct__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 255 (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_184_sorted__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 256 (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_185_split__eta) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 257 (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_186_split__curry) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 258 (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_187_curry__split) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 259 (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_188_internal__split__def) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 260 (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_189_takeWhile__dropWhile__id) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 261 (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_190_cond__split__eta) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 262 (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_191_splitE2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 263 (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_192_split__cong) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 264 (all X_a all X_1 all Xs_1 all Y_1 all Ys all R_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)),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))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lex(X_a),R_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_1)) & hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(list(X_a),nat,size_size(list(X_a)),Ys) | 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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lex(X_a),R_1))))) # label(fact_193_Cons__in__lex) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 265 (all X_a all Ws_1 (-hBOOL(hAPP(list(X_a),bool,distinct(X_a),Ws_1)) -> (exists Xs_2 exists Ys_2 exists Zs exists Y_2 Ws_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_2),hAPP(list(X_a),list(X_a),hAPP(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_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))),Zs))))))) # label(fact_194_not__distinct__decomp) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 266 (all X_a all Xs_1 all Ys all X_1 all Y_1 all R_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_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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_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)),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))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_1)))))) # label(fact_195_listrel_OCons) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 267 (all X_a all Xs_1 all Ys hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys)) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),list(X_a)),hAPP(list(X_a),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),list(X_a))),list_case(list(X_a),X_a),hAPP(list(X_a),list(X_a),tl(X_a),Ys)),hAPP(fun(list(X_a),list(X_a)),fun(X_a,fun(list(X_a),list(X_a))),combk(fun(list(X_a),list(X_a)),X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),hAPP(fun(list(X_a),fun(list(X_a),list(X_a))),fun(list(X_a),fun(list(X_a),list(X_a))),combc(list(X_a),list(X_a),list(X_a)),append(X_a)),Ys))),Xs_1)) # label(fact_196_tl__append) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 268 (all X_a (cl_HOL_Oequal(X_a) -> equal_equal(X_a) = fequal(X_a))) # label(fact_197_equal) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 269 (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_198_splitI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 270 (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_199_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 271 (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_200_mem__splitI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 272 (all X_a all Xs_1 all R_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),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_1))) -> Xs_1 = nil(X_a))) # label(fact_201_listrel__Nil2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 273 (all X_a all Xs_1 all R_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)),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_1))) -> Xs_1 = nil(X_a))) # label(fact_202_listrel__Nil1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 274 (all X_a all Xs all Ys_1 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs) != hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1) -> Xs != Ys_1)) # label(fact_203_neq__if__length__neq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 275 (all X_a all Xs_1 all Ys all R_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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_1))) -> hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(list(X_a),nat,size_size(list(X_a)),Ys))) # label(fact_204_listrel__eq__len) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 276 (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_205_splitD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 277 (all X_c all X_a all X_b all R_2 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_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),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_2,Aa),Ba),Ca)))) # label(fact_206_splitD_H) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 278 (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_207_length__rotate1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 279 (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_208_tl_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 280 (all X_a hAPP(list(X_a),list(X_a),tl(X_a),nil(X_a)) = nil(X_a)) # label(fact_209_tl_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 281 (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_210_distinct__tl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 282 (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_211_sorted__tl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 283 (all X_a all Xs_1 all Ys all R_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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_1))) -> hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(list(X_a),nat,size_size(list(X_a)),Ys))) # label(fact_212_listrel1__eq__len) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 284 (all X_a all R_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)),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_1)))) # label(fact_213_listrel_ONil) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 285 (all X_a all Ys_1 all Xs (Xs != nil(X_a) -> hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),tl(X_a),Xs)),Ys_1))) # label(fact_214_tl__append2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 286 (all X_a all X_1 all Y_1 all R_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),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_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),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_1))) & 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_215_lexord__lex) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 287 (all X_a (cl_HOL_Oequal(X_a) -> fequal(X_a) = equal_equal(X_a))) # label(fact_216_eq__equal) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 288 (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_217_equal__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 289 (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_218_equal__refl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 290 (all X_a all Xs_1 all Y_1 all Ys all R_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),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_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_1))) -> -(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_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_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_1)))))))) # label(fact_219_listrel__Cons2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 291 (all X_a all Y_1 all Ys all Xs_1 all R_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)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys)),Xs_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_1))) -> -(all Y_2 all Ys_2 (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_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_1),Y_2)),R_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)),Ys),Ys_2)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_1)))))))) # label(fact_220_listrel__Cons1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 292 (all X_a all X_b all Pa all Xs_1 all Ys (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(list(X_b),nat,size_size(list(X_b)),Ys) -> (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),Pa,nil(X_a)),nil(X_b))) -> ((all X_2 all Xs_2 all Y_2 all Ys_2 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_2) = hAPP(list(X_b),nat,size_size(list(X_b)),Ys_2) -> (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),Pa,Xs_2),Ys_2)) -> 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_2)))))) -> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),Pa,Xs_1),Ys)))))) # label(fact_221_list__induct2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 293 (all X_a all X_b all Ca all P_1 ((all A_5 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_5),B_2) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Ca,A_5),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_222_splitI2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 294 (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_223_splitE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 295 (all X_c all X_a all X_b all Z_2 all Ca all P_1 ((all A_5 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_5),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_5),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_224_mem__splitI2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 296 (all X_c all X_b all X_a all Ca all X_1 all P_1 ((all A_5 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_5),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_5),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_225_splitI2_H) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 297 (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_226_mem__splitE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 298 (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_227_split__part) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 299 (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_228_splitE_H) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 300 (all X_a all R_1 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_1)),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_1))))) # label(fact_229_listrelp__listrel__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 301 (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_230_rotate1__hd__tl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 302 (all X_a all A1 all A2 all R_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)),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_1))) <-> A1 = nil(X_a) & A2 = nil(X_a) | (exists X_2 exists Y_2 exists Xs_2 exists Ys_2 (A1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2) & A2 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_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_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_2),Ys_2)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_1))))))) # label(fact_231_listrel_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 303 (all X_a all Xs_1 all Ys all R_1 all N_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)),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_1),N_2))) -> hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = N_2 & hAPP(list(X_a),nat,size_size(list(X_a)),Ys) = N_2)) # label(fact_232_lexn__length) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 304 (all X_a all N exists Xs_2 hAPP(list(X_a),nat,size_size(list(X_a)),Xs_2) = N) # label(fact_233_Ex__list__of__length) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 305 (all X_a all I_2 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_2),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_2),X))) # label(fact_234_replicate__append__same) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 306 (all X_a all N all X hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)) = N) # label(fact_235_length__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 307 (all X_a all N all X all K hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),K),X)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),K),X)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X))) # label(fact_236_append__replicate__commute) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 308 (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_237_hd_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 309 (all X_a all N all X all Xs hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)),Xs))) # label(fact_238_replicate__app__Cons__same) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.45 310 (all X_a all Xs_1 all Ys all R_1 all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,X_1),Y_1)) -> (hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),Xs_1),Ys)) -> hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys)))))) # label(fact_239_listrelp_OCons) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 311 (all X_a all R_1 hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),nil(X_a)),nil(X_a)))) # label(fact_240_listrelp_ONil) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 312 (all X_a all Ys_1 all Xs ((Xs = nil(X_a) -> hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),X_a,hd(X_a),Ys_1)) & (Xs != nil(X_a) -> hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),X_a,hd(X_a),Xs)))) # label(fact_241_hd__append) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 313 (all X_a all Ys_1 all Xs (Xs != nil(X_a) -> hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),X_a,hd(X_a),Xs))) # label(fact_242_hd__append2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 314 (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_243_hd__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 315 (all X_a all R_1 all A1 all A2 (hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),A1),A2)) <-> A1 = nil(X_a) & A2 = nil(X_a) | (exists X_2 exists Y_2 exists Xs_2 exists Ys_2 (A1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2) & A2 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_2) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,X_2),Y_2)) & hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),Xs_2),Ys_2)))))) # label(fact_244_listrelp_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 316 (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_245_last__rev) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 317 (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_246_hd__rev) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 318 (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_247_dropWhile__eq__drop) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 319 (all X_a all Xs all X all Ys_1 all Y hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Ys_1))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),Y) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Ys_1))) # label(fact_248_list__update__length) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 320 (all X_b all X_d all X_a all X_c all F all G hAPP(fun(X_b,X_d),fun(product_prod(X_a,X_b),product_prod(X_c,X_d)),hAPP(fun(X_a,X_c),fun(fun(X_b,X_d),fun(product_prod(X_a,X_b),product_prod(X_c,X_d))),product_map_pair(X_a,X_c,X_b,X_d),F),G) = hAPP(fun(X_a,fun(X_b,product_prod(X_c,X_d))),fun(product_prod(X_a,X_b),product_prod(X_c,X_d)),product_prod_case(X_a,X_b,product_prod(X_c,X_d)),hAPP(fun(X_b,X_d),fun(X_a,fun(X_b,product_prod(X_c,X_d))),hAPP(fun(X_a,fun(fun(X_b,X_d),fun(X_b,product_prod(X_c,X_d)))),fun(fun(X_b,X_d),fun(X_a,fun(X_b,product_prod(X_c,X_d)))),combc(X_a,fun(X_b,X_d),fun(X_b,product_prod(X_c,X_d))),hAPP(fun(X_a,fun(X_d,product_prod(X_c,X_d))),fun(X_a,fun(fun(X_b,X_d),fun(X_b,product_prod(X_c,X_d)))),hAPP(fun(fun(X_d,product_prod(X_c,X_d)),fun(fun(X_b,X_d),fun(X_b,product_prod(X_c,X_d)))),fun(fun(X_a,fun(X_d,product_prod(X_c,X_d))),fun(X_a,fun(fun(X_b,X_d),fun(X_b,product_prod(X_c,X_d))))),combb(fun(X_d,product_prod(X_c,X_d)),fun(fun(X_b,X_d),fun(X_b,product_prod(X_c,X_d))),X_a),combb(X_d,product_prod(X_c,X_d),X_b)),hAPP(fun(X_a,X_c),fun(X_a,fun(X_d,product_prod(X_c,X_d))),hAPP(fun(X_c,fun(X_d,product_prod(X_c,X_d))),fun(fun(X_a,X_c),fun(X_a,fun(X_d,product_prod(X_c,X_d)))),combb(X_c,fun(X_d,product_prod(X_c,X_d)),X_a),product_Pair(X_c,X_d)),F))),G))) # label(fact_249_map__pair__def) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 321 (all X_a all Xs_1 all Ys all R_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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_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)),hAPP(fun(product_prod(list(X_a),list(X_a)),bool),fun(product_prod(list(X_a),list(X_a)),bool),transitive_rtrancl(list(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_1)))))) # label(fact_250_rtrancl__listrel1__if__listrel) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 322 (all X_a all Xs_1 all R_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),Xs_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1))))) # label(fact_251_listrel__rtrancl__refl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 323 (all X_a all X_b all X_2 hAPP(product_prod(X_a,X_b),product_prod(X_a,X_b),hAPP(fun(X_b,X_b),fun(product_prod(X_a,X_b),product_prod(X_a,X_b)),hAPP(fun(X_a,X_a),fun(fun(X_b,X_b),fun(product_prod(X_a,X_b),product_prod(X_a,X_b))),product_map_pair(X_a,X_a,X_b,X_b),combi(X_a)),combi(X_b)),X_2) = ti(product_prod(X_a,X_b),X_2)) # label(fact_252_map__pair__ident) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 324 (all X_a all Xs all X all X_3 all I_2 all I_4 (I_2 != I_4 -> hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_2),X)),I_4),X_3) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_4),X_3)),I_2),X))) # label(fact_253_list__update__swap) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 325 (all X_a all Xs all I_2 all X all Y hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_2),X)),I_2),Y) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_2),Y)) # label(fact_254_list__update__overwrite) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 326 (all X_a all Xs_1 all Ys (hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) = hAPP(list(X_a),list(X_a),rev(X_a),Ys) <-> Xs_1 = Ys)) # label(fact_255_rev__is__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 327 (all X_a all Xs_1 all Ys (hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) = Ys <-> Xs_1 = hAPP(list(X_a),list(X_a),rev(X_a),Ys))) # label(fact_256_rev__swap) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 328 (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_257_rev__rev__ident) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 329 (all X_a all R_1 hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1)) = hAPP(fun(product_prod(list(X_a),list(X_a)),bool),fun(product_prod(list(X_a),list(X_a)),bool),transitive_rtrancl(list(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_1))) # label(fact_258_listrel__rtrancl__eq__rtrancl__listrel1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 330 (all X_a all N hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),nil(X_a)) = nil(X_a)) # label(fact_259_drop__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 331 (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].
% 1.98/2.46 332 (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_261_Nil__is__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 333 (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_262_rev__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 334 (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_263_length__rev) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 335 (all X_a all Xs all Ys_1 hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Ys_1)),hAPP(list(X_a),list(X_a),rev(X_a),Xs))) # label(fact_264_rev__append) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 336 (all X_a all I_2 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_2),Xs))))) # label(fact_265_distinct__drop) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 337 (all X_a (linorder(X_a) -> (all N all Xs (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))))))) # label(fact_266_sorted__drop) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 338 (all X_a all Xs_1 all K_1 all X_1 (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs_1),K_1),X_1) = nil(X_a) <-> Xs_1 = nil(X_a))) # label(fact_267_list__update__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 339 (all X_a all I_2 all V_1 hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),nil(X_a)),I_2),V_1) = nil(X_a)) # label(fact_268_list__update_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 340 (all X_a all I_2 all Y hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),nil(X_a)),I_2),Y) = nil(X_a)) # label(fact_269_list__update__code_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 341 (all X_a all Xs all I_2 all X hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_2),X)) = hAPP(list(X_a),nat,size_size(list(X_a)),Xs)) # label(fact_270_length__list__update) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 342 (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_271_distinct__rev) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 343 (all X_a all N all X hAPP(list(X_a),list(X_a),rev(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)) # label(fact_272_rev__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 344 (all X_a all N all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)) = hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))) # label(fact_273_drop__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 345 (all X_a all N all Xs hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),butlast(X_a),Xs))) # label(fact_274_butlast__drop) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 346 (all X_a all N all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),tl(X_a),Xs)) = hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))) # label(fact_275_drop__tl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 347 (all X_a all N all Xs hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),tl(X_a),Xs))) # label(fact_276_tl__drop) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 348 (all X_c all X_d all X_a all X_b all F all G all Aa all Ba hAPP(product_prod(X_c,X_d),product_prod(X_a,X_b),hAPP(fun(X_d,X_b),fun(product_prod(X_c,X_d),product_prod(X_a,X_b)),hAPP(fun(X_c,X_a),fun(fun(X_d,X_b),fun(product_prod(X_c,X_d),product_prod(X_a,X_b))),product_map_pair(X_c,X_a,X_d,X_b),F),G),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),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),hAPP(X_c,X_a,F,Aa)),hAPP(X_d,X_b,G,Ba))) # label(fact_277_map__pair__simp) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 349 (all X_a all Xs_1 all Ys all X_1 all Y_1 all R_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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_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)),hAPP(fun(product_prod(list(X_a),list(X_a)),bool),fun(product_prod(list(X_a),list(X_a)),bool),transitive_rtrancl(list(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_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)),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))),hAPP(fun(product_prod(list(X_a),list(X_a)),bool),fun(product_prod(list(X_a),list(X_a)),bool),transitive_rtrancl(list(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_1))))))) # label(fact_278_rtrancl__listrel1__ConsI2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 350 (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_279_rev__singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 351 (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_280_singleton__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 352 (all X_a all Zs_1 all Xs_1 all Ys all R_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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_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)),Ys),Zs_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_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),Zs_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1))))))) # label(fact_281_listrel__rtrancl__trans) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 353 (all X_a all X_1 all Xs_1 all Ys all R_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)),hAPP(fun(product_prod(list(X_a),list(X_a)),bool),fun(product_prod(list(X_a),list(X_a)),bool),transitive_rtrancl(list(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_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)),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))),hAPP(fun(product_prod(list(X_a),list(X_a)),bool),fun(product_prod(list(X_a),list(X_a)),bool),transitive_rtrancl(list(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_1)))))) # label(fact_282_rtrancl__listrel1__ConsI1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 354 (all X_a all X_1 all Y_1 all R_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),Y_1)),hAPP(fun(product_prod(list(X_a),list(X_a)),bool),fun(product_prod(list(X_a),list(X_a)),bool),transitive_rtrancl(list(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_1)))) -> 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_283_rtrancl__listrel1__eq__len) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 355 (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_284_rev_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 356 (all X_a all Xs_1 all Y_1 all Ys (hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys) <-> Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Ys)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),nil(X_a))))) # label(fact_285_rev__eq__Cons__iff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 357 (all X_a all Xs_1 all Ys all R_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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1)))))) # label(fact_286_listrel__reflcl__if__listrel1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 358 (all X_a all Aa all R_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),Aa),Aa)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1)))) # label(fact_287_rtrancl_Ortrancl__refl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 359 (all X_a all P_1 all R_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)),P_1),R_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)),P_1),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1))))) # label(fact_288_r__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 360 (all X_a all Ca all Aa all Ba all R_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),Aa),Ba)),R_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),Ba),Ca)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_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),Aa),Ca)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1)))))) # label(fact_289_converse__rtrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 361 (all X_a all Ca all Aa all Ba all R_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),Aa),Ba)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_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),Ba),Ca)),R_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),Aa),Ca)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1)))))) # label(fact_290_rtrancl_Ortrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 362 (all X_a all Ca all Aa all Ba all R_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),Aa),Ba)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_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),Ba),Ca)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_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),Aa),Ca)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1)))))) # label(fact_291_rtrancl__trans) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 363 (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_292_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 364 (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_293_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 365 (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_294_set__ConsD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 366 (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_295_set__rev) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 367 (all X_a all X_1 all N_2 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_2),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_296_in__set__dropD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 368 (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_297_takeWhile__eq__all__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 369 (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_298_set__takeWhileD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 370 (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_299_in__set__butlastD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 371 (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_300_set__rotate1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 372 (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_301_in__set__insert) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 373 (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_302_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 374 (all X_a (linorder(X_a) -> (all Ys all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) -> (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Ys)) -> (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Ys)) -> (hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1) = hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys) -> Xs_1 = Ys)))))))) # label(fact_303_sorted__distinct__set__unique) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 375 (all X_a all Ys 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)) = 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_304_takeWhile__append1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 376 (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_305_last__in__set) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 377 (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_306_dropWhile__eq__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 378 (all X_a all Ys all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs_1)))) | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Ys)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys))))))) # label(fact_307_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 379 (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_308_hd__in__set) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 380 (all X_a all Ys 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)) = 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)))) # label(fact_309_dropWhile__append1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 381 (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_310_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 382 (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_311_not__in__set__insert) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 383 (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_312_partition__P) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 384 (all X_a all R_1 hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1)) = hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1)) # label(fact_313_rtrancl__idemp) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 385 (all X_a all Zs_1 all Ys all R_1 all Xs_1 ((all X_2 all Y_2 all Z (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_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),Y_2),Z)),R_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),Z)),R_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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_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)),Ys),Zs_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_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),Zs_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_1))))))) # label(fact_314_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 386 (all X_a all Ys 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)) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),Ys))) # label(fact_315_dropWhile__append2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 387 (all X_a all Ys 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)) = 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)))) # label(fact_316_takeWhile__append2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 388 (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_2 all X_2 ((exists Zs Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs))) -> -hBOOL(hAPP(X_a,bool,Pa,X_2)))))) # label(fact_317_split__list__propE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 389 (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_2 exists Zs (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs)) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys_2))))))) # label(fact_318_in__set__conv__decomp__first) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 390 (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_2 exists Zs (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs)) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Zs))))))) # label(fact_319_in__set__conv__decomp__last) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 391 (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_2 exists Zs Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs))))) # label(fact_320_in__set__conv__decomp) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 392 (all X_a all Q_1 all Pa all L_1 all K_1 (L_1 = 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_1))) -> (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_1) = 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_321_dropWhile__cong) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 393 (all X_a all Q_1 all Pa all L_1 all K_1 (L_1 = 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_1))) -> (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_1) = 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_322_takeWhile__cong) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 394 (all X_a all Pa all Aa all Ba all R_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),Aa),Ba)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1))) -> (hBOOL(hAPP(X_a,bool,Pa,Aa)) -> ((all Y_2 all Z (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),Y_2)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_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),Y_2),Z)),R_1)) -> (hBOOL(hAPP(X_a,bool,Pa,Y_2)) -> hBOOL(hAPP(X_a,bool,Pa,Z)))))) -> hBOOL(hAPP(X_a,bool,Pa,Ba)))))) # label(fact_323_rtrancl__induct) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 395 (all X_a all Pa all Aa all Ba all R_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),Aa),Ba)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1))) -> (hBOOL(hAPP(X_a,bool,Pa,Ba)) -> ((all Y_2 all Z (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)),R_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),Z),Ba)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1))) -> (hBOOL(hAPP(X_a,bool,Pa,Z)) -> hBOOL(hAPP(X_a,bool,Pa,Y_2)))))) -> hBOOL(hAPP(X_a,bool,Pa,Aa)))))) # label(fact_324_converse__rtrancl__induct) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 396 (all X_a all X_1 all Z_2 all R_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),Z_2)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1))) -> (ti(X_a,X_1) != ti(X_a,Z_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_1),Y_2)),R_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),Y_2),Z_2)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1)))))))) # label(fact_325_converse__rtranclE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 397 (all X_a all Aa all Ba all R_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),Aa),Ba)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1))) -> (ti(X_a,Aa) != ti(X_a,Ba) -> -(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),Aa),Y_2)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_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),Y_2),Ba)),R_1))))))) # label(fact_326_rtranclE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 398 (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_2 all X_2 ((exists Zs Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs))) -> (hBOOL(hAPP(X_a,bool,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_2))) -> -hBOOL(hAPP(X_a,bool,Pa,Xa))))))))) # label(fact_327_split__list__first__propE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 399 (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_2 all X_2 all Zs (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs)) -> (hBOOL(hAPP(X_a,bool,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))) -> -hBOOL(hAPP(X_a,bool,Pa,Xa))))))))) # label(fact_328_split__list__last__propE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 400 (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_2 exists Zs (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs)) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys_2))))))) # label(fact_329_split__list__first) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 401 (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_2 exists Zs (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs)) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Zs))))))) # label(fact_330_split__list__last) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 402 (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_2 exists Zs Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs))))) # label(fact_331_split__list) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 403 (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_2 exists X_2 exists Zs (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs)) & hBOOL(hAPP(X_a,bool,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))) -> -hBOOL(hAPP(X_a,bool,Pa,Xa)))))))) # label(fact_332_split__list__last__prop__iff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 404 (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_2 exists X_2 ((exists Zs Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs))) & hBOOL(hAPP(X_a,bool,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_2))) -> -hBOOL(hAPP(X_a,bool,Pa,Xa)))))))) # label(fact_333_split__list__first__prop__iff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 405 (all X_a all X_1 all Xs_1 all I_1 all V hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),I_1),V) = hAPP(nat,list(X_a),hAPP(fun(nat,list(X_a)),fun(nat,list(X_a)),hAPP(list(X_a),fun(fun(nat,list(X_a)),fun(nat,list(X_a))),nat_case(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),V),Xs_1)),hAPP(fun(nat,list(X_a)),fun(nat,list(X_a)),hAPP(fun(list(X_a),list(X_a)),fun(fun(nat,list(X_a)),fun(nat,list(X_a))),combb(list(X_a),list(X_a),nat),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1)),hAPP(X_a,fun(nat,list(X_a)),hAPP(fun(nat,fun(X_a,list(X_a))),fun(X_a,fun(nat,list(X_a))),combc(nat,X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs_1)),V))),I_1)) # label(fact_334_list__update_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 406 (all X_a all N_2 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_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(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_2)) # label(fact_335_drop__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 407 (all X_a all X_b all Xa_1 all Xb all Za all Zb all R_1 (hBOOL(hAPP(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool,hAPP(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),fun(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool),member(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),hAPP(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),hAPP(product_prod(X_a,X_b),fun(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),product_Pair(product_prod(X_a,X_b),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),Xa_1),Xb)),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),Za),Zb))),hAPP(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),transitive_rtrancl(product_prod(X_a,X_b)),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),Xa_1),Xb) != 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),Za),Zb) -> -(all A_5 all B_2 (hBOOL(hAPP(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool,hAPP(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),fun(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool),member(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),hAPP(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),hAPP(product_prod(X_a,X_b),fun(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),product_Pair(product_prod(X_a,X_b),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),Xa_1),Xb)),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_2))),R_1)) -> -hBOOL(hAPP(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool,hAPP(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),fun(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool),member(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),hAPP(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),hAPP(product_prod(X_a,X_b),fun(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),product_Pair(product_prod(X_a,X_b),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),A_5),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),Za),Zb))),hAPP(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),transitive_rtrancl(product_prod(X_a,X_b)),R_1)))))))) # label(fact_336_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.46 408 (all X_a all X_b all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool,hAPP(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),fun(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool),member(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),hAPP(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),hAPP(product_prod(X_a,X_b),fun(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),product_Pair(product_prod(X_a,X_b),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),Ax),Ay)),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),Bx),By))),hAPP(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),transitive_rtrancl(product_prod(X_a,X_b)),R_1))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,Bx),By)) -> ((all A_5 all B_2 all Aa_1 all Ba_1 (hBOOL(hAPP(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool,hAPP(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),fun(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool),member(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),hAPP(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),hAPP(product_prod(X_a,X_b),fun(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),product_Pair(product_prod(X_a,X_b),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),A_5),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),Aa_1),Ba_1))),R_1)) -> (hBOOL(hAPP(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool,hAPP(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),fun(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool),member(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),hAPP(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),hAPP(product_prod(X_a,X_b),fun(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),product_Pair(product_prod(X_a,X_b),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),Aa_1),Ba_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),Bx),By))),hAPP(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),transitive_rtrancl(product_prod(X_a,X_b)),R_1))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,Aa_1),Ba_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,A_5),B_2)))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,Ax),Ay)))))) # label(fact_337_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 409 (all X_a all X_b all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool,hAPP(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),fun(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool),member(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),hAPP(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),hAPP(product_prod(X_a,X_b),fun(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),product_Pair(product_prod(X_a,X_b),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),Ax),Ay)),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),Bx),By))),hAPP(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),transitive_rtrancl(product_prod(X_a,X_b)),R_1))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,Ax),Ay)) -> ((all A_5 all B_2 all Aa_1 all Ba_1 (hBOOL(hAPP(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool,hAPP(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),fun(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool),member(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),hAPP(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),hAPP(product_prod(X_a,X_b),fun(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),product_Pair(product_prod(X_a,X_b),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),Ax),Ay)),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_2))),hAPP(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),transitive_rtrancl(product_prod(X_a,X_b)),R_1))) -> (hBOOL(hAPP(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool,hAPP(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),fun(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool),member(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),hAPP(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),hAPP(product_prod(X_a,X_b),fun(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),product_Pair(product_prod(X_a,X_b),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),A_5),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),Aa_1),Ba_1))),R_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,A_5),B_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,Aa_1),Ba_1)))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,Bx),By)))))) # label(fact_338_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 410 (all X_a all N_2 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_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(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_2)) # label(fact_339_take__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 411 (all X_a all A1 all A2 all R_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),A1),A2)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1))) <-> (exists A_5 (ti(X_a,A1) = ti(X_a,A_5) & ti(X_a,A2) = ti(X_a,A_5))) | (exists A_5 exists B_2 exists C_2 (ti(X_a,A1) = ti(X_a,A_5) & ti(X_a,A2) = ti(X_a,C_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_5),B_2)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_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),B_2),C_2)),R_1)))))) # label(fact_340_rtrancl_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 412 (all X_a all R_1 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_1)),hAPP(fun(product_prod(list(X_a),list(X_a)),bool),fun(product_prod(list(X_a),list(X_a)),bool),transitive_rtrancl(list(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_1))))) # label(fact_341_listrel__subset__rtrancl__listrel1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 413 (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_2 exists X_2 ((exists Zs Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs))) & hBOOL(hAPP(X_a,bool,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_2))) -> -hBOOL(hAPP(X_a,bool,Pa,Xa)))))))) # label(fact_342_split__list__first__prop) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 414 (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_2 exists X_2 exists Zs (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs)) & hBOOL(hAPP(X_a,bool,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))) -> -hBOOL(hAPP(X_a,bool,Pa,Xa)))))))) # label(fact_343_split__list__last__prop) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 415 (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_344_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 416 (all X_a all A_2 all B_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_2),B_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)),B_1),A_2)) -> ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_1)))) # label(fact_345_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 417 (all X_a all Ca all A_2 all B_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_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B_1))))) # label(fact_346_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 418 (all X_a all N_2 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_2),Xs_1))),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)))) # label(fact_347_set__take__subset) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 419 (all X_a all R_1 all S (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_1),S)) -> 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_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),S))))) # label(fact_348_listrel__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 420 (all X_a all R_1 all S (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_1),S)) -> 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_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),S))))) # label(fact_349_listrel1__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 421 (all X_b all X_a all B_1 all A_4 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_4),A_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_2),B_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_4),B_1))))) # label(fact_350_Pi__anti__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 422 (all X_a all R_2 all S_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S_2))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),R_2),S_2)))) # label(fact_351_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 423 (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_352_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 424 (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_353_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 425 (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_354_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 426 (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_355_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 427 (all X_a all A_2 all B_1 (ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_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_2),B_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)),B_1),A_2))))) # label(fact_356_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 428 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),X))))))) # label(fact_357_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 429 (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_358_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 430 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z_1))))))) # label(fact_359_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 431 (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_360_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 432 (all X_a (order(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1))))))) # label(fact_361_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 433 (all X_a (ord(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_362_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 434 (all X_a all C_1 all A_2 all B_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_2),B_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)),B_1),C_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_2),C_1))))) # label(fact_363_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 435 (all X_a all X_1 all A_2 all B_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_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_1))))) # label(fact_364_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 436 (all X_a all B_1 all X_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_1))))) # label(fact_365_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 437 (all X_a (order(X_a) -> (all C all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1))))))) # label(fact_366_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 438 (all X_a (ord(X_a) -> (all C all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_367_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 439 (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_368_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 440 (all X_a all X_1 all A_2 all B_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_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_1))))) # label(fact_369_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 441 (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_370_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 442 (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_371_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 443 (all X_a all A_2 all B_1 (ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_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)),B_1),A_2)))) # label(fact_372_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 444 (all X_a all A_2 all B_1 (ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_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_2),B_1)))) # label(fact_373_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 445 (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_374_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 446 (all X_a all A_2 all B_1 (ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_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_2),B_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)),B_1),A_2)))) # label(fact_375_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 447 (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_376_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 448 (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_377_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 449 (all X_a all A_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),A_2))) # label(fact_378_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 450 (all X_a all N hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),nil(X_a)) = nil(X_a)) # label(fact_379_take__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 451 (all X_a all X_1 all N_2 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_2),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_380_in__set__takeD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 452 (all X_a all I_2 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_2),Xs))))) # label(fact_381_distinct__take) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 453 (all X_a (top(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),top_top(X_a)))))) # label(fact_382_top__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 454 (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_383_top__unique) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 455 (all X_a (top(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),top_top(X_a)),A_1)) -> ti(X_a,A_1) = top_top(X_a))))) # label(fact_384_top__le) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 456 (all X_a all A_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),top_top(fun(X_a,bool))))) # label(fact_385_subset__UNIV) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 457 (all X_a (linorder(X_a) -> (all N all Xs (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs))))))) # label(fact_386_sorted__take) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 458 (all X_a all R_1 all S (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_1),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),S))) -> 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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),S))))) # label(fact_387_rtrancl__subset__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 459 (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(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)),S_2),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_2))) -> hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),S_2) = hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_2)))) # label(fact_388_rtrancl__subset) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 460 (all X_a all R_1 all S (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_1),S)) -> 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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),S))))) # label(fact_389_rtrancl__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 461 (all X_a all N all Xs hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs)) = Xs) # label(fact_390_append__take__drop__id) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 462 (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_391_takeWhile__eq__take) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 463 (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_392_set__subset__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 464 (all X_a (linorder(X_a) -> (all Zs_2 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Zs_2))) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Zs_2))))))))) # label(fact_393_sorted__many) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 465 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Zs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Zs_1)))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Zs_1))))))) # label(fact_394_sorted__many__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 466 (all X_a all N_2 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_2),Xs_1))),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)))) # label(fact_395_set__drop__subset) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 467 (all X_a all I_1 all X_1 all Xs_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs_1),I_1),X_1))),A_2))))) # label(fact_396_set__update__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 468 (all X_a all Xs_1 all Ys all Zs_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys) = Zs_1 <-> Xs_1 = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)),Zs_1) & Ys = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)),Zs_1))) # label(fact_397_append__eq__conv__conj) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 469 (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_398_sorted__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 470 (all X_a (linorder(X_a) -> (all Xs_1 all Ys (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys))) <-> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) & hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Ys)) & (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Xa)))))))))) # label(fact_399_sorted__append) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 471 (all X_a all R_1 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),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1))),hAPP(fun(product_prod(list(X_a),list(X_a)),bool),fun(product_prod(list(X_a),list(X_a)),bool),transitive_rtrancl(list(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_1))))) # label(fact_400_listrel1__rtrancl__subset__rtrancl__listrel1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 472 (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_401_sorted_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 473 (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_402_sorted_OCons) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 474 (all X_a all B_1 all A_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),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B_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_2),B_1)))) # label(fact_403_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 475 (all X_b all X_a all B_1 all C_1 all A_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),A_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(X_a,fun(X_b,bool),B_1,X_2)),hAPP(X_a,fun(X_b,bool),C_1,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_2),B_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_2),C_1))))) # label(fact_404_Pi__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 476 (all X_a all X_b (ord(X_b) -> (all F all G ((all X_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2)))) -> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)))))) # label(fact_405_le__funI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 477 (all X_a all R_1 all R_3 (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_1),R_3)) -> (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(fun(X_a,bool),fun(fun(product_prod(X_a,X_a),bool),bool),refl_on(X_a),top_top(fun(X_a,bool))),R_3)) -> 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_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_3)))))) # label(fact_406_listrel1__subset__listrel) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 478 (all X_a all X all Xs all Ys_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1))) -> Xs != hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Ys_1))) # label(fact_407_impossible__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 479 (all X_a all Xs all N (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)) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs) = Xs)) # label(fact_408_take__all) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 480 (all X_a all X all Xs all I_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)),I_2)) -> hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_2),X) = Xs)) # label(fact_409_list__update__beyond) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 481 (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_410_length__takeWhile__le) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 482 (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_411_length__dropWhile__le) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 483 (all X_a all X_b all R_2 all S_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))),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_2)),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_2))) <-> 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_2),S_2)))) # label(fact_412_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 484 (all X_a all R_1 hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(fun(X_a,bool),fun(fun(product_prod(X_a,X_a),bool),bool),refl_on(X_a),top_top(fun(X_a,bool))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1)))) # label(fact_413_refl__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 485 (all X_a all Xs_1 all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(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_2),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_2),Xs_1)))))) # label(fact_414_set__take__subset__set__take) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 486 (all X_a all Xs_1 all N_2 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),M_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(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_2),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_2),Xs_1)))))) # label(fact_415_set__drop__subset__set__drop) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 487 (all X_a all Xs all N (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)) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs) = nil(X_a))) # label(fact_416_drop__all) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 488 (all X_a all N_2 all Xs_1 (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_2),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_2)))) # label(fact_417_drop__eq__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 489 (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_418_append__eq__append__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 490 (all X_a all R_1 (hBOOL(hAPP(fun(X_a,fun(X_a,bool)),bool,reflp(X_a),R_1)) <-> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(fun(X_a,bool),fun(fun(product_prod(X_a,X_a),bool),bool),refl_on(X_a),top_top(fun(X_a,bool))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),collect(product_prod(X_a,X_a)),hAPP(fun(X_a,fun(X_a,bool)),fun(product_prod(X_a,X_a),bool),product_prod_case(X_a,X_a,bool),R_1)))))) # label(fact_419_reflp__def) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 491 (all X_a all Aa all A_2 all R_1 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(fun(X_a,bool),fun(fun(product_prod(X_a,X_a),bool),bool),refl_on(X_a),A_2),R_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),A_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),Aa)),R_1))))) # label(fact_420_refl__onD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 492 (all X_a all X_1 all Y_1 all A_2 all R_1 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(fun(X_a,bool),fun(fun(product_prod(X_a,X_a),bool),bool),refl_on(X_a),A_2),R_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_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2))))) # label(fact_421_refl__onD1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 493 (all X_a all X_1 all Y_1 all A_2 all R_1 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(fun(X_a,bool),fun(fun(product_prod(X_a,X_a),bool),bool),refl_on(X_a),A_2),R_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_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_2))))) # label(fact_422_refl__onD2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 494 (all X_a all N all Xs (Xs != nil(X_a) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N)),Xs) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(list(X_a),X_a,hd(X_a),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),tl(X_a),Xs))))) # label(fact_423_take__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 495 (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_424_rev__predicate2D) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 496 (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_425_predicate2D) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 497 (all X_a all X_1 all R_1 (hBOOL(hAPP(fun(X_a,fun(X_a,bool)),bool,reflp(X_a),R_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,X_1),X_1)))) # label(fact_426_reflpE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 498 (all X_a all N all X all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs))) # label(fact_427_take__Suc__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 499 (all X_a all N all X all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,N)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs)) # label(fact_428_drop__Suc__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 500 (all X_a all X all Xs all I_2 all Y hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),hAPP(nat,nat,suc,I_2)),Y) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_2),Y))) # label(fact_429_list__update__code_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 501 (all X_a all N all X hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(nat,nat,suc,N)),X) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X))) # label(fact_430_replicate__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 502 (all X_a all N all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),tl(X_a),Xs)) = hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N)),Xs))) # label(fact_431_take__tl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 503 (all X_a all N all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,N)),Xs) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),tl(X_a),Xs))) # label(fact_432_drop__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 504 (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_433_predicate2I) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 505 (all X_a all N_2 all Xs_1 (hAPP(nat,nat,suc,N_2) = hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) <-> (exists Y_2 exists Ys_2 (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_2) & hAPP(list(X_a),nat,size_size(list(X_a)),Ys_2) = N_2)))) # label(fact_434_Suc__length__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 506 (all X_a all Xs_1 all N_2 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(nat,nat,suc,N_2) <-> (exists Y_2 exists Ys_2 (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_2) & hAPP(list(X_a),nat,size_size(list(X_a)),Ys_2) = N_2)))) # label(fact_435_length__Suc__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 507 (all X_a all N all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))),nil(X_a))) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N)),Xs))) # label(fact_436_take__hd__drop) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 508 (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_437_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 509 (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_438_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.47 510 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> 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].
% 1.98/2.47 511 (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_440_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 512 (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_441_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 513 (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_442_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 514 (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_443_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 515 (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_444_leI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 516 (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_445_not__leE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 517 (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_446_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 518 (all X_a (order(X_a) -> (all A_1 all B (ti(X_a,A_1) != ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_447_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 519 (all X_a (order(X_a) -> (all A_1 all B (ti(X_a,A_1) != ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_448_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 520 (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_449_leD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 521 (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_450_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 522 (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_451_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 523 (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_452_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 524 (all X_a (order(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (ti(X_a,A_1) != ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_453_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 525 (all X_a (order(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (ti(X_a,A_1) != ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_454_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 526 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))))))) # label(fact_455_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 527 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))))))) # label(fact_456_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 528 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))))))) # label(fact_457_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 529 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))))))) # label(fact_458_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 530 (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_459_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 531 (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_460_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 532 (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_461_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 533 (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_462_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 534 (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_463_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 535 (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_464_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 536 (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_465_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 537 (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_466_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 538 (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_467_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 539 (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_468_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 540 (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_469_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 541 (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_470_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 542 (all X_a (preorder(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)))))) # label(fact_471_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 543 (all X_a (order(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_472_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 544 (all X_a (ord(X_a) -> (all C all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))))))) # label(fact_473_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 545 (all X_a (order(X_a) -> (all C all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1))))))) # label(fact_474_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 546 (all X_a (ord(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))))))) # label(fact_475_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 547 (all X_a (order(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1))))))) # label(fact_476_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 548 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))))))) # label(fact_477_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 549 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))))))) # label(fact_478_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 550 (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_479_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 551 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(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_480_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 552 (all X_a (top(X_a) -> (all A_1 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),top_top(X_a)),A_1))))) # label(fact_481_not__top__less) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 553 (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_482_less__top) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 554 (all X_a all X_1 all N_2 all Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs_1),N_2),X_1)))))) # label(fact_483_set__update__memI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 555 (all X_a all Ys_1 all X all I_2 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)),I_2),X) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_2),X)),Ys_1))) # label(fact_484_list__update__append1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 556 (all X_a all N all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs))) # label(fact_485_take__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 557 (all X_a all N all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs)) = hAPP(list(X_a),X_a,last(X_a),Xs))) # label(fact_486_last__drop) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 558 (all X_a all A_1 all I_2 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_2),A_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_2),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_1),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,I_2)),Xs))))) # label(fact_487_upd__conv__take__nth__drop) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 559 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,N)))) # label(fact_488_lessI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 560 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))))) # label(fact_489_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 561 (all X_a all R_1 hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lenlex(X_a),R_1) = hAPP(fun(product_prod(list(X_a),list(X_a)),bool),fun(product_prod(list(X_a),list(X_a)),bool),collect(product_prod(list(X_a),list(X_a))),hAPP(fun(list(X_a),fun(list(X_a),bool)),fun(product_prod(list(X_a),list(X_a)),bool),product_prod_case(list(X_a),list(X_a),bool),hAPP(fun(list(X_a),fun(list(X_a),bool)),fun(list(X_a),fun(list(X_a),bool)),hAPP(fun(list(X_a),fun(fun(list(X_a),bool),fun(list(X_a),bool))),fun(fun(list(X_a),fun(list(X_a),bool)),fun(list(X_a),fun(list(X_a),bool))),combs(list(X_a),fun(list(X_a),bool),fun(list(X_a),bool)),hAPP(fun(list(X_a),fun(list(X_a),fun(bool,bool))),fun(list(X_a),fun(fun(list(X_a),bool),fun(list(X_a),bool))),hAPP(fun(fun(list(X_a),fun(bool,bool)),fun(fun(list(X_a),bool),fun(list(X_a),bool))),fun(fun(list(X_a),fun(list(X_a),fun(bool,bool))),fun(list(X_a),fun(fun(list(X_a),bool),fun(list(X_a),bool)))),combb(fun(list(X_a),fun(bool,bool)),fun(fun(list(X_a),bool),fun(list(X_a),bool)),list(X_a)),combs(list(X_a),bool,bool)),hAPP(fun(list(X_a),fun(list(X_a),bool)),fun(list(X_a),fun(list(X_a),fun(bool,bool))),hAPP(fun(fun(list(X_a),bool),fun(list(X_a),fun(bool,bool))),fun(fun(list(X_a),fun(list(X_a),bool)),fun(list(X_a),fun(list(X_a),fun(bool,bool)))),combb(fun(list(X_a),bool),fun(list(X_a),fun(bool,bool)),list(X_a)),hAPP(fun(bool,fun(bool,bool)),fun(fun(list(X_a),bool),fun(list(X_a),fun(bool,bool))),combb(bool,fun(bool,bool),list(X_a)),fdisj)),hAPP(fun(list(X_a),nat),fun(list(X_a),fun(list(X_a),bool)),hAPP(fun(list(X_a),fun(fun(list(X_a),nat),fun(list(X_a),bool))),fun(fun(list(X_a),nat),fun(list(X_a),fun(list(X_a),bool))),combc(list(X_a),fun(list(X_a),nat),fun(list(X_a),bool)),hAPP(fun(list(X_a),fun(nat,bool)),fun(list(X_a),fun(fun(list(X_a),nat),fun(list(X_a),bool))),hAPP(fun(fun(nat,bool),fun(fun(list(X_a),nat),fun(list(X_a),bool))),fun(fun(list(X_a),fun(nat,bool)),fun(list(X_a),fun(fun(list(X_a),nat),fun(list(X_a),bool)))),combb(fun(nat,bool),fun(fun(list(X_a),nat),fun(list(X_a),bool)),list(X_a)),combb(nat,bool,list(X_a))),hAPP(fun(list(X_a),nat),fun(list(X_a),fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(list(X_a),nat),fun(list(X_a),fun(nat,bool))),combb(nat,fun(nat,bool),list(X_a)),ord_less(nat)),size_size(list(X_a))))),size_size(list(X_a)))))),hAPP(fun(list(X_a),fun(list(X_a),bool)),fun(list(X_a),fun(list(X_a),bool)),hAPP(fun(list(X_a),fun(fun(list(X_a),bool),fun(list(X_a),bool))),fun(fun(list(X_a),fun(list(X_a),bool)),fun(list(X_a),fun(list(X_a),bool))),combs(list(X_a),fun(list(X_a),bool),fun(list(X_a),bool)),hAPP(fun(list(X_a),fun(list(X_a),fun(bool,bool))),fun(list(X_a),fun(fun(list(X_a),bool),fun(list(X_a),bool))),hAPP(fun(fun(list(X_a),fun(bool,bool)),fun(fun(list(X_a),bool),fun(list(X_a),bool))),fun(fun(list(X_a),fun(list(X_a),fun(bool,bool))),fun(list(X_a),fun(fun(list(X_a),bool),fun(list(X_a),bool)))),combb(fun(list(X_a),fun(bool,bool)),fun(fun(list(X_a),bool),fun(list(X_a),bool)),list(X_a)),combs(list(X_a),bool,bool)),hAPP(fun(list(X_a),fun(list(X_a),bool)),fun(list(X_a),fun(list(X_a),fun(bool,bool))),hAPP(fun(fun(list(X_a),bool),fun(list(X_a),fun(bool,bool))),fun(fun(list(X_a),fun(list(X_a),bool)),fun(list(X_a),fun(list(X_a),fun(bool,bool)))),combb(fun(list(X_a),bool),fun(list(X_a),fun(bool,bool)),list(X_a)),hAPP(fun(bool,fun(bool,bool)),fun(fun(list(X_a),bool),fun(list(X_a),fun(bool,bool))),combb(bool,fun(bool,bool),list(X_a)),fconj)),hAPP(fun(list(X_a),nat),fun(list(X_a),fun(list(X_a),bool)),hAPP(fun(list(X_a),fun(fun(list(X_a),nat),fun(list(X_a),bool))),fun(fun(list(X_a),nat),fun(list(X_a),fun(list(X_a),bool))),combc(list(X_a),fun(list(X_a),nat),fun(list(X_a),bool)),hAPP(fun(list(X_a),fun(nat,bool)),fun(list(X_a),fun(fun(list(X_a),nat),fun(list(X_a),bool))),hAPP(fun(fun(nat,bool),fun(fun(list(X_a),nat),fun(list(X_a),bool))),fun(fun(list(X_a),fun(nat,bool)),fun(list(X_a),fun(fun(list(X_a),nat),fun(list(X_a),bool)))),combb(fun(nat,bool),fun(fun(list(X_a),nat),fun(list(X_a),bool)),list(X_a)),combb(nat,bool,list(X_a))),hAPP(fun(list(X_a),nat),fun(list(X_a),fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(list(X_a),nat),fun(list(X_a),fun(nat,bool))),combb(nat,fun(nat,bool),list(X_a)),fequal(nat)),size_size(list(X_a))))),size_size(list(X_a)))))),hAPP(fun(product_prod(list(X_a),list(X_a)),bool),fun(list(X_a),fun(list(X_a),bool)),hAPP(fun(list(X_a),fun(fun(product_prod(list(X_a),list(X_a)),bool),fun(list(X_a),bool))),fun(fun(product_prod(list(X_a),list(X_a)),bool),fun(list(X_a),fun(list(X_a),bool))),combc(list(X_a),fun(product_prod(list(X_a),list(X_a)),bool),fun(list(X_a),bool)),hAPP(fun(list(X_a),fun(list(X_a),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool))),fun(list(X_a),fun(fun(product_prod(list(X_a),list(X_a)),bool),fun(list(X_a),bool))),hAPP(fun(fun(list(X_a),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool)),fun(fun(product_prod(list(X_a),list(X_a)),bool),fun(list(X_a),bool))),fun(fun(list(X_a),fun(list(X_a),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool))),fun(list(X_a),fun(fun(product_prod(list(X_a),list(X_a)),bool),fun(list(X_a),bool)))),combb(fun(list(X_a),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool)),fun(fun(product_prod(list(X_a),list(X_a)),bool),fun(list(X_a),bool)),list(X_a)),combc(list(X_a),fun(product_prod(list(X_a),list(X_a)),bool),bool)),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(fun(product_prod(list(X_a),list(X_a)),bool),bool))),hAPP(fun(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool))),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(fun(product_prod(list(X_a),list(X_a)),bool),bool)))),combb(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool)),list(X_a)),hAPP(fun(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool)),fun(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool))),combb(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),list(X_a)),member(product_prod(list(X_a),list(X_a))))),product_Pair(list(X_a),list(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_1))))))) # label(fact_490_lenlex__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 562 (all X_2 hAPP(nat,fun(nat,bool),ord_less(nat),X_2) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X_2))) # label(fact_491_less__eq__Suc__le__raw) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 563 (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_492_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 564 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),B_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_2),B_1)) & ti(fun(X_a,bool),A_2) != ti(fun(X_a,bool),B_1))) # label(fact_493_psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 565 (all X_a all A_2 all B_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_2),B_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),B_1)) | ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_1))) # label(fact_494_subset__iff__psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 566 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),B_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_2),B_1)))) # label(fact_495_psubset__imp__subset) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 567 (all X_a all C_1 all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),B_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)),B_1),C_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),C_1))))) # label(fact_496_psubset__subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 568 (all X_a all C_1 all A_2 all B_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_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B_1),C_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),C_1))))) # label(fact_497_subset__psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 569 (all N N != hAPP(nat,nat,suc,N)) # label(fact_498_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 570 (all N hAPP(nat,nat,suc,N) != N) # label(fact_499_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 571 (all Nat_4 all Nat_5 (hAPP(nat,nat,suc,Nat_4) = hAPP(nat,nat,suc,Nat_5) <-> Nat_4 = Nat_5)) # label(fact_500_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 572 (all X all Y (hAPP(nat,nat,suc,X) = hAPP(nat,nat,suc,Y) -> X = Y)) # label(fact_501_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 573 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))) # label(fact_502_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 574 (all M_2 all N_2 (M_2 != N_2 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_2)))) # label(fact_503_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 575 (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_504_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 576 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))) # label(fact_505_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 577 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> M != N)) # label(fact_506_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 578 (all S_1 all T_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S_1),T_3)) -> S_1 != T_3)) # label(fact_507_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 579 (all Pa all M_2 all N_2 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N_2),M_2))) -> ((M_2 = N_2 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N_2),M_2))) -> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N_2),M_2))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N_2),M_2)))))) # label(fact_508_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 580 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N))) # label(fact_509_le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 581 (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),N),M)))) # label(fact_510_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 582 (all M all N (M = N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_511_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 583 (all K all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),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_2),K))))) # label(fact_512_le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 584 (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),N),M)) -> M = N))) # label(fact_513_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 585 (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_514_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 586 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_515_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 587 (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_516_less__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 588 (all K all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),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_2)),K))))) # label(fact_517_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 589 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> (hAPP(nat,nat,suc,M) != N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N))))) # label(fact_518_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 590 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))))) # label(fact_519_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 591 (all N all M (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M))) -> M = N))) # label(fact_520_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 592 (all N_2 all M_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_2))) <-> N_2 = M_2))) # label(fact_521_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 593 (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_2)),hAPP(nat,nat,suc,N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)))) # label(fact_522_Suc__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 594 (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),hAPP(nat,nat,suc,N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)) | M_2 = N_2)) # label(fact_523_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 595 (all M_2 all N_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_2))))) # label(fact_524_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 596 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),N))) # label(fact_525_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 597 (all M_2 all N_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_2)),M_2)))) # label(fact_526_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 598 (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),hAPP(nat,nat,suc,N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) | M_2 = hAPP(nat,nat,suc,N_2))) # label(fact_527_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 599 (all N_2 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_2)),hAPP(nat,nat,suc,M_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),M_2)))) # label(fact_528_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 600 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N))))) # label(fact_529_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 601 (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_530_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 602 (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_eq(nat),M),N)))) # label(fact_531_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 603 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) | M = N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_532_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 604 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> (M != N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))))) # label(fact_533_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 605 (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)))) # label(fact_534_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 606 (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)) | M_2 = N_2)) # label(fact_535_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 607 (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) & M_2 != N_2)) # label(fact_536_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 608 (all X_a all F1 all F2 all Nat_4 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_4)) = hAPP(nat,X_a,F2,Nat_4)) # label(fact_537_nat__case__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 609 (all N_2 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_2)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_2)),M_2)))) # label(fact_538_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 610 (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),hAPP(nat,nat,suc,N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)))) # label(fact_539_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 611 (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_2)),N_2)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)))) # label(fact_540_Suc__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 612 (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),hAPP(nat,nat,suc,N))))) # label(fact_541_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 613 (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),hAPP(nat,nat,suc,M)),N)))) # label(fact_542_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 614 (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_2))) <-> N_2 = M_2))) # label(fact_543_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 615 (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_544_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 616 (all Pa all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,Pa,J_2)) -> ((all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2)) -> (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,I))) -> hBOOL(hAPP(nat,bool,Pa,I))))) -> hBOOL(hAPP(nat,bool,Pa,I_1)))))) # label(fact_545_inc__induct) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 617 (all X_a (order(X_a) -> (all N_2 all N_3 all F ((all N_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,N_1)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_1))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),N_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,N_3)))))))) # label(fact_546_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 618 (all X_a (order(X_a) -> (all N_2 all N_3 all F ((all N_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_1)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_1))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),N_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,N_3)))))))) # label(fact_547_lift__Suc__mono__less) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 619 (all X_a (order(X_a) -> (all N_2 all M_2 all F ((all N_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_1)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_1))))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,M_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_2))))))) # label(fact_548_lift__Suc__mono__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 620 (all X_a all Ca all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B_1))))) # label(fact_549_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 621 (all X_a all C_1 all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B_1),C_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),C_1))))) # label(fact_550_psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 622 (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_2)),N_2)) <-> hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2)),N_2)))) # label(fact_551_less__eq__nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 623 (all X_a all X_b all S all R_1 ((all X_2 all Y_2 (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),Y_2)),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),Y_2)),S)))) -> 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)))) # label(fact_552_subrelI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 624 (all I_1 all J_2 all F ((all I all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I)),hAPP(nat,nat,F,J_1))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,I_1)),hAPP(nat,nat,F,J_2)))))) # label(fact_553_less__mono__imp__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 625 (all N all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),M_3)) -> (exists M_1 M_3 = hAPP(nat,nat,suc,M_1)))) # label(fact_554_Suc__le__D) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 626 (all I_2 all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K)) -> (K != hAPP(nat,nat,suc,I_2) -> -(all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1)) -> K != hAPP(nat,nat,suc,J_1)))))) # label(fact_555_lessE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 627 (all I_2 all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_2)),K)) -> -(all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1)) -> K != hAPP(nat,nat,suc,J_1))))) # label(fact_556_Suc__lessE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 628 (all X_a (dense_linorder(X_a) -> (all Z_1 all Y ((all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z_1)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)))))) # label(fact_557_dense__le) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 629 (all X_a (dense_linorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ((all W (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W),Z_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1))))))) # label(fact_558_dense__le__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 630 (all X_b all X_a (order(X_a) & ord(X_b) -> (all Ca all F all Ba all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Ba)),Aa)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),Ba)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Ca)),Aa)))))))) # label(fact_559_xt6) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 631 (all X_b all X_a (order(X_a) & order(X_b) -> (all Ca all F all Ba all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Ba)),Aa)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),Ba)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Ca)),Aa)))))))) # label(fact_560_xt4) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 632 (all X_a all X_b (order(X_b) & order(X_a) -> (all Ca all Aa all F all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),hAPP(X_b,X_a,F,Ba))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),Ca)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,Ca))))))))) # label(fact_561_order__le__less__subst1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 633 (all X_b all X_a (order(X_a) & order(X_b) -> (all Ca all F all Ba all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),hAPP(X_a,X_b,F,Ba))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),hAPP(X_a,X_b,F,Aa))))))))) # label(fact_562_xt5) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 634 (all X_b all X_a (order(X_a) & order(X_b) -> (all Ca all F all Ba all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Aa)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),hAPP(X_a,X_b,F,Ba))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),hAPP(X_a,X_b,F,Aa))))))))) # label(fact_563_xt7) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 635 (all X_a all X_b (order(X_b) & order(X_a) -> (all F all Ca all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Ba)),Ca)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),Ca)))))))) # label(fact_564_order__less__le__subst2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 636 (all X_a all X_b (order(X_b) & order(X_a) -> (all Ca all Aa all F all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,Ba))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),Ca)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,Ca))))))))) # label(fact_565_order__less__le__subst1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 637 (all X_a all X_b (order(X_b) & order(X_a) -> (all F all Ca all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Ba)),Ca)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),Ca)))))))) # label(fact_566_order__le__less__subst2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 638 (all X_a all I_2 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> Xs = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_2),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_2)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,I_2)),Xs))))) # label(fact_567_id__take__nth__drop) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 639 (all X_a all Xs all I_2 hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_2),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_2)) = Xs) # label(fact_568_list__update__id) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 640 (all X_a all Xs all X all I_2 all J (I_2 != J -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_2),X)),J) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),J))) # label(fact_569_nth__list__update__neq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 641 (all X_a all X all Xs all N hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),hAPP(nat,nat,suc,N)) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),N)) # label(fact_570_nth__Cons__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 642 (all X_a all Xs_1 all Ys (Xs_1 = Ys <-> hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(list(X_a),nat,size_size(list(X_a)),Ys) & (all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys),I))))) # label(fact_571_list__eq__iff__nth__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 643 (all X_a all Xs all I_2 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N)) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs)),I_2) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_2))) # label(fact_572_nth__take) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 644 (all X_a all N all Xs all Y all Ys_1 (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Ys_1) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),N) = ti(X_a,Y))) # label(fact_573_nth__via__drop) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 645 (all X_a all X all I_2 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N)) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)),I_2) = ti(X_a,X))) # label(fact_574_nth__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 646 (all X_a all X_1 all Xs_1 all N_2 hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),N_2) = hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),X_1),hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1)),N_2)) # label(fact_575_nth_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 647 (all X_a all N_2 all Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),N_2)),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_576_nth__mem) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 648 (all X_a 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)))) <-> (all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> hBOOL(hAPP(X_a,bool,Pa,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I))))))) # label(fact_577_all__set__conv__all__nth) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 649 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) <-> (exists I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) & hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I) = ti(X_a,X_1))))) # label(fact_578_in__set__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 650 (all X_a all Xs all X all Ys_1 hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Ys_1))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)) = ti(X_a,X)) # label(fact_579_nth__append__length) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 651 (all X_a all J_2 all I_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> (hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I_1) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),J_2) <-> I_1 = J_2))))) # label(fact_580_nth__eq__iff__index__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 652 (all X_a all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) <-> (all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> (all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> (I != J_1 -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I) != hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),J_1)))))))) # label(fact_581_distinct__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 653 (all X_a all X all J all I_2 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> (I_2 = J -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_2),X)),J) = ti(X_a,X)) & (I_2 != J -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_2),X)),J) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),J)))) # label(fact_582_nth__list__update) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 654 (all X_a all X_1 all I_1 all Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs_1),I_1),X_1) = Xs_1 <-> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I_1) = ti(X_a,X_1)))) # label(fact_583_list__update__same__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 655 (all X_a all X all I_2 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_2),X)),I_2) = ti(X_a,X))) # label(fact_584_nth__list__update__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 656 (all X_a all Pa all Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> -hBOOL(hAPP(X_a,bool,Pa,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1))))))) # label(fact_585_nth__length__takeWhile) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 657 (all X_a all J_2 all Pa all Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),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(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1)),J_2) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),J_2))) # label(fact_586_takeWhile__nth) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 658 (all X_a (linorder(X_a) -> (all I_2 all J all Xs (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_2)),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),J))))))))) # label(fact_587_sorted__nth__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.48 659 (all X_a (linorder(X_a) -> (all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) <-> (all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> (all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I)),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),J_1))))))))))) # label(fact_588_sorted__equals__nth__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 660 (all X_a all I_2 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_2)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,I_2)),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),I_2),Xs))) # label(fact_589_nth__drop_H) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 661 (all X_a all Xs_1 all Ys all R_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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_1))) <-> hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(list(X_a),nat,size_size(list(X_a)),Ys) & (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> hBOOL(hAPP(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),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),N_1)),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys),N_1))),R_1)))))) # label(fact_590_listrel__iff__nth) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 662 (all X_a all N all Xs (Xs != nil(X_a) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs)) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),N)))) # label(fact_591_hd__drop__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 663 (all X_a (linorder(X_a) -> (all I_2 all J all Xs (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),J)),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_2))))))))) # label(fact_592_sorted__rev__nth__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 664 (all X_a all I_2 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,I_2)),Xs) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_2),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_2)),nil(X_a))))) # label(fact_593_take__Suc__conv__app__nth) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 665 (all X_a all Xs_1 all Ys all R_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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_1))) <-> (exists Y_2 exists N_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),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),N_1)),Y_2)),R_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) & Ys = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs_1),N_1),Y_2))))) # label(fact_594_listrel1__iff__update) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 666 (all X_a (linorder(X_a) -> (all Xs ((all I all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I)),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),J_1)))))) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs)))))) # label(fact_595_sorted__nth__monoI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 667 (all X_a all Pa all Xs_1 all N_2 ((all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),N_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> hBOOL(hAPP(X_a,bool,Pa,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I)))))) -> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> -hBOOL(hAPP(X_a,bool,Pa,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),N_2)))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_2),Xs_1)))) # label(fact_596_takeWhile__eq__take__P__nth) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 668 (all X_a all Pa all Xs_1 all J_2 ((all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2)) -> hBOOL(hAPP(X_a,bool,Pa,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),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))))))) # label(fact_597_length__takeWhile__less__P__nth) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 669 (all X_a all Ys_1 all K all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1))) -> ((all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K)) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys_1),I))) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),K),Xs) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),K),Ys_1))))) # label(fact_598_nth__take__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 670 (all X_a all X_1 all Pa all Xs_1 ((all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> hBOOL(hAPP(X_a,bool,Pa,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I))))) -> (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_599_all__nth__imp__all__set) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 671 (all X_a all Pa all N_2 all Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> ((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)))) -> hBOOL(hAPP(X_a,bool,Pa,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),N_2)))))) # label(fact_600_list__ball__nth) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 672 (all X_a all Xs all Ys_1 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs) = hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1) -> ((all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys_1),I))) -> Xs = Ys_1))) # label(fact_601_nth__equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 673 (all X_a all Pa all K_1 ((all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K_1)) -> (exists X1 hBOOL(hAPP(X_a,bool,hAPP(nat,fun(X_a,bool),Pa,I),X1))))) <-> (exists Xs_2 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_2) = K_1 & (all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K_1)) -> hBOOL(hAPP(X_a,bool,hAPP(nat,fun(X_a,bool),Pa,I),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_2),I))))))))) # label(fact_602_Skolem__list__nth) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 674 (all X_a all X_1 all Y_1 all R_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),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_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(list(X_a),nat,size_size(list(X_a)),X_1)),hAPP(list(X_a),nat,size_size(list(X_a)),Y_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)),X_1)),Y_1) = X_1 | (exists I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(list(X_a),nat,size_size(list(X_a)),X_1)),hAPP(list(X_a),nat,size_size(list(X_a)),Y_1)))) & hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I),X_1) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I),Y_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),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),X_1),I)),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Y_1),I))),R_1)))))) # label(fact_603_lexord__take__index__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 675 (all X_a all R_1 ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,X_2),X_2))) -> hBOOL(hAPP(fun(X_a,fun(X_a,bool)),bool,reflp(X_a),R_1)))) # label(fact_604_reflpI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 676 (all X_a all J_2 all Pa all Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),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(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),Xs_1)),J_2) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),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)))))) # label(fact_605_dropWhile__nth) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 677 (all X_a (linorder(X_a) -> (all Z_2 all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),Y_1)))))) # label(fact_606_min__less__iff__conj) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 678 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1)),Z_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),Z_2)))))) # label(fact_607_min__less__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 679 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_608_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 680 (all Y all X all Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_609_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 681 (all I_2 all J all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K)))) # label(fact_610_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 682 (all M all N all K all L (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),L) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))))) # label(fact_611_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 683 (all K all L all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L)))))) # label(fact_612_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 684 (all K all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))))) # label(fact_613_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 685 (all M all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J))))) # label(fact_614_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 686 (all M all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M))))) # label(fact_615_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 687 (all K_1 all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)))) # label(fact_616_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 688 (all J all I_2 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_2)),I_2))) # label(fact_617_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 689 (all I_2 all J -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),I_2))) # label(fact_618_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 690 (all X_a all N all M all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),M),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),Xs)) # label(fact_619_drop__drop) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 691 (all X_a all N all M all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),M),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),N),M)),Xs)) # label(fact_620_take__take) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 692 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1)),Z_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),Z_2)))))) # label(fact_621_min__le__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 693 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_622_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 694 (all Y all X all Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_623_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 695 (all N all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)))) # label(fact_624_le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 696 (all N all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)))) # label(fact_625_le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 697 (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) <-> (exists K_2 N_2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),K_2)))) # label(fact_626_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 698 (all K_1 all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)))) # label(fact_627_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 699 (all M all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M))))) # label(fact_628_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 700 (all M all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J))))) # label(fact_629_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 701 (all K all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))))) # label(fact_630_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 702 (all K all L all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),L)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L)))))) # label(fact_631_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 703 (all M all K all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N)))) # label(fact_632_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 704 (all M all K all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_633_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 705 (all M all K all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),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),K),N))))) # label(fact_634_add__leE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 706 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) # label(fact_635_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 707 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) # label(fact_636_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 708 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N))) # label(fact_637_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 709 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),M),N))) # label(fact_638_min__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 710 (all M_2 all K_1 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K_1) <-> M_2 = N_2)) # label(fact_639_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 711 (all K_1 all M_2 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2) <-> M_2 = N_2)) # label(fact_640_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 712 (all M all N all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K))) # label(fact_641_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 713 (all X all Y all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Z_1))) # label(fact_642_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 714 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)) # label(fact_643_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 715 (all X_a all N all Xs hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),N)) # label(fact_644_length__take) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 716 (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)) <-> (exists K_2 N_2 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),K_2))))) # label(fact_645_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 717 (all I_2 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),I_2))))) # label(fact_646_less__add__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 718 (all I_2 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),M))))) # label(fact_647_less__add__Suc1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 719 (all X_a all Xs all Ys_1 hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1))) # label(fact_648_length__append) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 720 (all X_a all I_2 all K all X hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_2),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),K),X)) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),I_2),K)),X)) # label(fact_649_take__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 721 (all X_a all N all M all X hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),X) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),M),X))) # label(fact_650_replicate__add) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 722 (all X_a all N all M all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),M),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),M),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),Xs))) # label(fact_651_take__drop) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 723 (all X_a all Xs all Ys_1 hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),Xs),Ys_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1))) # label(fact_652_length__splice) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 724 (all X_a all Xs all Ys_1 all N hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),N)) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys_1),N)) # label(fact_653_nth__append__length__plus) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 725 (all X_a all I_2 all J all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),Xs) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_2),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),J),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),I_2),Xs)))) # label(fact_654_take__add) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 726 (all X_a all N all I_2 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),I_2)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs)),I_2) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),I_2)))) # label(fact_655_nth__drop) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 727 (all M_2 all K_1 all F ((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,F,M_1)),hAPP(nat,nat,F,N_1))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,F,M_2)),K_1)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),K_1)))))) # label(fact_656_mono__nat__linear__lb) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 728 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> (exists K_2 N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2))))) # label(fact_657_less__imp__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 729 (all X_a (ordere223160158up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_658_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 730 (all X_a (cancel_semigroup_add(X_a) -> (all B all A_1 all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1) -> ti(X_a,B) = ti(X_a,C))))) # label(fact_659_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 731 (all X_a (cancel146912293up_add(X_a) -> (all A_1 all B all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) -> ti(X_a,B) = ti(X_a,C))))) # label(fact_660_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 732 (all X_a (cancel_semigroup_add(X_a) -> (all A_1 all B all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) -> ti(X_a,B) = ti(X_a,C))))) # label(fact_661_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 733 (all X_a (cancel_semigroup_add(X_a) -> (all Ba all Aa all Ca (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Aa) <-> ti(X_a,Ba) = ti(X_a,Ca))))) # label(fact_662_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 734 (all X_a (cancel_semigroup_add(X_a) -> (all Aa all Ba all Ca (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ca) <-> ti(X_a,Ba) = ti(X_a,Ca))))) # label(fact_663_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 735 (all X_a (ab_semigroup_add(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))) # label(fact_664_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 736 (all X_a (ordere236663937imp_le(X_a) -> (all Aa all Ca all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Ca))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)))))) # label(fact_665_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 737 (all X_a (ordere236663937imp_le(X_a) -> (all Ca all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)))))) # label(fact_666_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 738 (all X_a (ordere779506340up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))))) # label(fact_667_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 739 (all X_a (ordere779506340up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))))))) # label(fact_668_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 740 (all X_a (ordere779506340up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_669_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 741 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_670_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 742 (all X_a (ordere236663937imp_le(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_671_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 743 (all X_a (ordere236663937imp_le(X_a) -> (all Aa all Ca all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Ca))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)))))) # label(fact_672_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 744 (all X_a (ordere236663937imp_le(X_a) -> (all Ca all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)))))) # label(fact_673_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 745 (all X_a (ordere223160158up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))))) # label(fact_674_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 746 (all X_a (ordere223160158up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))))))) # label(fact_675_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 747 (all X_a (ordere223160158up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_676_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 748 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_677_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 749 (all X_a (ordere236663937imp_le(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_678_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 750 (all X_a (ordere236663937imp_le(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z_1))))) # label(fact_679_min__add__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 751 (all X_a (ordere223160158up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_680_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 752 (all X_a (ord(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Least),X) = ti(X_a,Least))))) # label(fact_681_min__leastL) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 753 (all X_a (order(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Least) = ti(X_a,Least))))) # label(fact_682_min__leastR) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 754 (all X_a (ord(X_a) -> ord_min(X_a) = hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),min(X_a),ord_less_eq(X_a)))) # label(fact_683_min__ord__min) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 755 (all X_a all I_1 all K_1 all F all R_1 ((all I 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),hAPP(nat,X_a,F,hAPP(nat,nat,suc,I))),hAPP(nat,X_a,F,I))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_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),hAPP(nat,X_a,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1))),hAPP(nat,X_a,F,I_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),transitive_rtrancl(X_a),R_1))))) # label(fact_684_sequence__trans) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 756 (all X_a (linorder(X_a) -> (all A_1 all B all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_685_min__max_Oless__infI2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 757 (all X_a (linorder(X_a) -> (all B all A_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_686_min__max_Oless__infI1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 758 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1))))) # label(fact_687_min__max_Oinf__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 759 (all X_a (linorder(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),C))))) # label(fact_688_min__max_Oinf_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 760 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z_1))))) # label(fact_689_min__max_Oinf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 761 (all X_a (linorder(X_a) -> (all B all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),C))))) # label(fact_690_min__max_Oinf_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 762 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)))) # label(fact_691_min__max_Oinf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 763 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)))) # label(fact_692_min__max_Oinf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 764 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),X)))) # label(fact_693_min__max_Oinf__commute) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 765 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),A_1)))) # label(fact_694_min__max_Oinf_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 766 (all X_a (linorder(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),A_1) = ti(X_a,A_1)))) # label(fact_695_min__max_Oinf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 767 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),X))))) # label(fact_696_min__max_Oinf__le1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 768 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Y))))) # label(fact_697_min__max_Oinf__le2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 769 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1) = ti(X_a,X_1))))) # label(fact_698_min__max_Ole__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 770 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y_1),Z_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z_2)))))) # label(fact_699_min__max_Ole__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 771 (all X_a (linorder(X_a) -> (all B all A_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_700_min__max_Ole__infI1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 772 (all X_a (linorder(X_a) -> (all A_1 all B all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_701_min__max_Ole__infI2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 773 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y) = ti(X_a,X))))) # label(fact_702_min__max_Oinf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 774 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y) = ti(X_a,Y))))) # label(fact_703_min__max_Oinf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 775 (all X_a (linorder(X_a) -> (all B all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)))))))) # label(fact_704_min__max_Ole__infI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 776 (all X_a (linorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1)))))))) # label(fact_705_min__max_Oinf__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 777 (all X_a (linorder(X_a) -> (all B all D_1 all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),C),D_1)))))))) # label(fact_706_min__max_Oinf__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 778 (all X_a (linorder(X_a) -> (all X all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B))) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B))))))) # label(fact_707_min__max_Ole__infE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 779 (all X_a all X_b all Aa all Ba all A_3 all B_3 all R_1 all S (hBOOL(hAPP(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool,hAPP(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),fun(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool),member(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),hAPP(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),hAPP(product_prod(X_a,X_b),fun(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),product_Pair(product_prod(X_a,X_b),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),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_3),B_3))),hAPP(fun(product_prod(X_b,X_b),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),hAPP(fun(product_prod(X_a,X_a),bool),fun(fun(product_prod(X_b,X_b),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool)),lex_prod(X_a,X_b),R_1),S))) <-> 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),A_3)),R_1)) | ti(X_a,Aa) = ti(X_a,A_3) & hBOOL(hAPP(fun(product_prod(X_b,X_b),bool),bool,hAPP(product_prod(X_b,X_b),fun(fun(product_prod(X_b,X_b),bool),bool),member(product_prod(X_b,X_b)),hAPP(X_b,product_prod(X_b,X_b),hAPP(X_b,fun(X_b,product_prod(X_b,X_b)),product_Pair(X_b,X_b),Ba),B_3)),S)))) # label(fact_708_in__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 780 (all X_a all X_1 all Y_1 all F (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)),hAPP(fun(X_a,nat),fun(product_prod(X_a,X_a),bool),measure(X_a),F))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X_a,nat,F,X_1)),hAPP(X_a,nat,F,Y_1))))) # label(fact_709_in__measure) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 781 (all F ((all I hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,hAPP(nat,nat,suc,I))),hAPP(nat,nat,F,I)))) -> (exists I all K_2 hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_2)) = hAPP(nat,nat,F,I)))) # label(fact_710_weak__decr__stable) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 782 (all X_a all R_2 all F all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X_a,nat,F,X_1)),hAPP(X_a,nat,F,Y_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)) -> 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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),hAPP(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool)),mlex_prod(X_a),F),R_2)))))) # label(fact_711_mlex__leq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 783 (all X_a all R_2 all F all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X_a,nat,F,X_1)),hAPP(X_a,nat,F,Y_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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),hAPP(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool)),mlex_prod(X_a),F),R_2))))) # label(fact_712_mlex__less) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 784 (all X_a all L_1 all L_2 all A_2 hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),L_1),L_2)),A_2) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),L_1),A_2)),hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),L_2),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),hAPP(list(X_a),nat,size_size(list(X_a)),L_1)))),A_2))))) # label(fact_713_sublist__append) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 785 (all X_a all X_1 all Xs_1 all I_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),Xs_1),I_3)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_714_in__set__sublistD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 786 (all X_a all I_3 all X_1 all Xs_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),Xs_1),I_3)))))) # label(fact_715_notin__set__sublistI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 787 (all X_a all A_2 hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),nil(X_a)),A_2) = nil(X_a)) # label(fact_716_sublist__nil) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 788 (all X_a all I_3 all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),Xs_1),I_3))))) # label(fact_717_distinct__sublistI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 789 (all X_a all Xs_1 all I_3 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),Xs_1),I_3))),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)))) # label(fact_718_set__sublist__subset) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 790 (all X_a all X_1 all L_1 all A_2 hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),L_1)),A_2) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),hAPP(bool,fun(list(X_a),fun(list(X_a),list(X_a))),if(list(X_a)),hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),A_2)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))),nil(X_a))),hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),L_1),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),A_2))))) # label(fact_719_sublist__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.49 791 (all X_a all Xs_1 all I_3 hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),Xs_1),I_3)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,fun(nat,bool)),fun(X_a,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(X_a,fun(nat,bool)),fun(X_a,bool)),combb(fun(nat,bool),bool,X_a),fEx(nat)),hAPP(fun(nat,bool),fun(X_a,fun(nat,bool)),hAPP(fun(X_a,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(X_a,fun(nat,bool))),combc(X_a,fun(nat,bool),fun(nat,bool)),hAPP(fun(X_a,fun(nat,fun(bool,bool))),fun(X_a,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(X_a,fun(nat,fun(bool,bool))),fun(X_a,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),X_a),combs(nat,bool,bool)),hAPP(fun(X_a,fun(nat,bool)),fun(X_a,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(X_a,fun(nat,bool)),fun(X_a,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),X_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),hAPP(fun(nat,X_a),fun(X_a,fun(nat,bool)),hAPP(fun(X_a,fun(fun(nat,X_a),fun(nat,bool))),fun(fun(nat,X_a),fun(X_a,fun(nat,bool))),combc(X_a,fun(nat,X_a),fun(nat,bool)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(nat,X_a),fun(nat,bool))),hAPP(fun(fun(X_a,bool),fun(fun(nat,X_a),fun(nat,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(nat,X_a),fun(nat,bool)))),combb(fun(X_a,bool),fun(fun(nat,X_a),fun(nat,bool)),X_a),combb(X_a,bool,nat)),fequal(X_a))),hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1))))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),I_3)))))) # label(fact_720_set__sublist) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 792 (all X_a all N all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs)),N) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),hAPP(nat,nat,suc,N))))) # label(fact_721_rev__nth) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 793 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_722_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 794 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N))) # label(fact_723_le0) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 795 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N)))) # label(fact_724_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 796 (all X_b all X_a (minus(X_a) -> (all A_2 all B_1 all X_1 hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),minus_minus(fun(X_b,X_a)),A_2),B_1),X_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_b,X_a,A_2,X_1)),hAPP(X_b,X_a,B_1,X_1))))) # label(fact_725_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 797 (all X_a all X_b (minus(X_b) -> (all A_2 all B_1 all X_2 hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),minus_minus(fun(X_a,X_b)),A_2),B_1),X_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,A_2,X_2)),hAPP(X_a,X_b,B_1,X_2))))) # label(fact_726_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 798 (all Pa all Aa all Ba (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba))) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba)) -> hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))) & (all D_3 (Aa = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),D_3) -> hBOOL(hAPP(nat,bool,Pa,D_3)))))) # label(fact_727_nat__diff__split) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 799 (all Pa all Aa all Ba (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba))) <-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba)) & -hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))) | (exists D_3 (Aa = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),D_3) & -hBOOL(hAPP(nat,bool,Pa,D_3))))))) # label(fact_728_nat__diff__split__asm) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 800 (all X_a (monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_729_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 801 (all X_a (comm_monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_730_add__0) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 802 (all X_a (linord219039673up_add(X_a) -> (all Aa (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_731_double__zero__sym) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 803 (all X_a (monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_732_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 804 (all X_a (comm_monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_733_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 805 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),B) = ti(X_a,A_1)))) # label(fact_734_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 806 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),B) = ti(X_a,A_1)))) # label(fact_735_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 807 (all X_a (ordered_ab_group_add(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z_1))))) # label(fact_736_min__diff__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 808 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = M -> N = zero_zero(nat))) # label(fact_737_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 809 (all M all I_2 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),I_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),M),N)),I_2)) # label(fact_738_min__diff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 810 (all M all K all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) # label(fact_739_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 811 (all K all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) # label(fact_740_diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 812 (all I_2 all J all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),J)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))) # label(fact_741_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 813 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),N) = M) # label(fact_742_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 814 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),N) = M) # label(fact_743_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 815 (all M_2 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),N_2) = zero_zero(nat) <-> M_2 = zero_zero(nat) & N_2 = zero_zero(nat))) # label(fact_744_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 816 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)) = zero_zero(nat)) # label(fact_745_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 817 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),zero_zero(nat)) = M) # label(fact_746_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 818 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),N),zero_zero(nat)) = zero_zero(nat)) # label(fact_747_min__0R) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 819 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N) = N) # label(fact_748_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 820 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),zero_zero(nat)),N) = zero_zero(nat)) # label(fact_749_min__0L) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 821 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),zero_zero(X_a))))))) # label(fact_750_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 822 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba all Ca all D (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Ca),D) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),D))))))) # label(fact_751_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 823 (all X_a (ab_group_add(X_a) -> (all Aa all Ba all Ca all D (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Ca),D) -> (ti(X_a,Aa) = ti(X_a,Ba) <-> ti(X_a,Ca) = ti(X_a,D)))))) # label(fact_752_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 824 (all X_a (group_add(X_a) -> (all Aa all Ba (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba) = zero_zero(X_a) <-> ti(X_a,Aa) = ti(X_a,Ba))))) # label(fact_753_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 825 (all X_a (ab_group_add(X_a) -> (all Aa all Ba (ti(X_a,Aa) = ti(X_a,Ba) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba) = zero_zero(X_a))))) # label(fact_754_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 826 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_1) = zero_zero(X_a)))) # label(fact_755_diff__self) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 827 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_756_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 828 (all X_a (zero(X_a) -> (all X_1 (zero_zero(X_a) = ti(X_a,X_1) <-> ti(X_a,X_1) = zero_zero(X_a))))) # label(fact_757_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 829 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),zero_zero(X_a))))))) # label(fact_758_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 830 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba all Ca all D (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Ca),D) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),D))))))) # label(fact_759_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 831 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))) = N)) # label(fact_760_Suc__pred) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 832 (all I_2 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,I_2))),N)))) # label(fact_761_diff__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 833 (all N (N != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_762_gr0I) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 834 (all L all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M)))))) # label(fact_763_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 835 (all N all J all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),N)),K)))) # label(fact_764_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 836 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> N != zero_zero(nat))) # label(fact_765_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 837 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),M))))) # label(fact_766_diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 838 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_767_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 839 (all N_2 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),M_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)))) # label(fact_768_zero__less__diff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 840 (all N_2 (N_2 != zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)))) # label(fact_769_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 841 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_770_not__less0) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 842 (all X_a all M_2 all X_1 all N_2 all Y_1 (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),M_2),X_1) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_2),Y_1) <-> M_2 = N_2 & (M_2 != zero_zero(nat) -> ti(X_a,X_1) = ti(X_a,Y_1)))) # label(fact_771_replicate__eq__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 843 (all X_a all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),zero_zero(nat)),Xs) = Xs) # label(fact_772_drop__0) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 844 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N))) # label(fact_773_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 845 (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),zero_zero(nat))) <-> N_2 = zero_zero(nat))) # label(fact_774_le__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 846 (all M all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),M))) # label(fact_775_diff__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 847 (all M_2 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),N_2) = zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)))) # label(fact_776_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 848 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = zero_zero(nat))) # label(fact_777_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 849 (all L 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,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M))))) # label(fact_778_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 850 (all L 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,hAPP(nat,fun(nat,nat),minus_minus(nat),M),L)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),L))))) # label(fact_779_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 851 (all I_2 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),I_2)) = I_2)) # label(fact_780_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 852 (all N_2 all K_1 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_2)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),K_1) <-> M_2 = N_2)))) # label(fact_781_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 853 (all N all K all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)))) # label(fact_782_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 854 (all N_2 all K_1 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)))))) # label(fact_783_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 855 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_784_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 856 (all Nat_3 zero_zero(nat) != hAPP(nat,nat,suc,Nat_3)) # label(fact_785_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 857 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_786_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 858 (all Nat_2 hAPP(nat,nat,suc,Nat_2) != zero_zero(nat)) # label(fact_787_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 859 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) # label(fact_788_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 860 (all M all N all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N)),hAPP(nat,nat,suc,K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),K)) # label(fact_789_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 861 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_790_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 862 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_791_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 863 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = zero_zero(nat) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M) = zero_zero(nat) -> M = N))) # label(fact_792_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 864 (all I_2 all J all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),J)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),K)),J)) # label(fact_793_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 865 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M) = zero_zero(nat)) # label(fact_794_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 866 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat)) = M) # label(fact_795_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 867 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N) = zero_zero(nat)) # label(fact_796_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 868 (all X_a all F1 all F2 hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),F1),F2),zero_zero(nat)) = ti(X_a,F1)) # label(fact_797_nat__case__0) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 869 (all M_2 all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),hAPP(nat,nat,suc,N_2)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),combi(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),N_2))) # label(fact_798_diff__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 870 (all I_2 all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_2)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)),I_2))) # label(fact_799_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 871 (all I_2 all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)),I_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_2)),K))) # label(fact_800_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 872 (all I_2 all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)))) # label(fact_801_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 873 (all K_1 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1) = K_1 <-> J_2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),I_1)))) # label(fact_802_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 874 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N) = M)) # label(fact_803_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 875 (all I_1 all K_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_2))))) # label(fact_804_le__diff__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 876 (all I_2 all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),K))) # label(fact_805_add__diff__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 877 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = M)) # label(fact_806_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 878 (all M all K all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),K))))) # label(fact_807_le__add__diff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 879 (all J_2 all K_1 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)),I_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1))))) # label(fact_808_le__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 880 (all I_2 all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K)),J))) # label(fact_809_diff__diff__right) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 881 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_1),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),C)))))) # label(fact_810_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 882 (all N_2 all K_1 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)))))) # label(fact_811_less__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 883 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)))) # label(fact_812_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 884 (all I_1 all J_2 all K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_2)))) # label(fact_813_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 885 (all M all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = M)) # label(fact_814_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 886 (all M all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),hAPP(nat,nat,suc,M)))) # label(fact_815_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 887 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_816_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 888 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_817_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 889 (all X_a (linord219039673up_add(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))))))) # label(fact_818_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 890 (all X_a (linord219039673up_add(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa)))))) # label(fact_819_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 891 (all X_a all N all Xs hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),N)) # label(fact_820_length__drop) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 892 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_821_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 893 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_822_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 894 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_823_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 895 (all X_a (ordere216010020id_add(X_a) -> (all Y_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y_1)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_1) = zero_zero(X_a) <-> ti(X_a,X_1) = zero_zero(X_a) & ti(X_a,Y_1) = zero_zero(X_a))))))) # label(fact_824_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 896 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_825_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 897 (all X_a (linord219039673up_add(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))))))) # label(fact_826_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 898 (all X_a (linord219039673up_add(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)))))) # label(fact_827_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 899 (all X_a all N all M all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),M),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))) # label(fact_828_drop__take) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 900 (all X_a all I_2 all K all X hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),I_2),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),K),X)) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K),I_2)),X)) # label(fact_829_drop__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 901 (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),hAPP(nat,nat,suc,N_2))) <-> M_2 = zero_zero(nat) | (exists J_1 (M_2 = hAPP(nat,nat,suc,J_1) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),N_2)))))) # label(fact_830_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 902 (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,zero_zero(nat)))) <-> N_2 = zero_zero(nat))) # label(fact_831_less__Suc0) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 903 (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)) <-> (exists M_1 N_2 = hAPP(nat,nat,suc,M_1)))) # label(fact_832_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 904 (all M_2 all N_2 (hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),N_2) <-> M_2 = hAPP(nat,nat,suc,zero_zero(nat)) & N_2 = zero_zero(nat) | M_2 = zero_zero(nat) & N_2 = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_833_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 905 (all M_2 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),N_2) = hAPP(nat,nat,suc,zero_zero(nat)) <-> M_2 = hAPP(nat,nat,suc,zero_zero(nat)) & N_2 = zero_zero(nat) | M_2 = zero_zero(nat) & N_2 = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_834_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 906 (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_2)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)))) # label(fact_835_add__gr__0) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 907 (all X_a hAPP(list(X_a),nat,size_size(list(X_a)),nil(X_a)) = zero_zero(nat)) # label(fact_836_list_Osize_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 908 (all X_a all Xs_1 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = zero_zero(nat) <-> Xs_1 = nil(X_a))) # label(fact_837_length__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 909 (all X_a all X all Xs hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),zero_zero(nat)) = ti(X_a,X)) # label(fact_838_nth__Cons__0) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 910 (all X_a all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),zero_zero(nat)),Xs) = nil(X_a)) # label(fact_839_take__0) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 911 (all X_a all N_2 all Xs_1 (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_2),Xs_1) = nil(X_a) <-> N_2 = zero_zero(nat) | Xs_1 = nil(X_a))) # label(fact_840_take__eq__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 912 (all X_a all X all Xs all Y hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),zero_zero(nat)),Y) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Xs)) # label(fact_841_list__update__code_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 913 (all X_a all X hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),zero_zero(nat)),X) = nil(X_a)) # label(fact_842_replicate__0) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 914 (all X_a all N_2 all X_1 (nil(X_a) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_2),X_1) <-> N_2 = zero_zero(nat))) # label(fact_843_empty__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 915 (all X_a all N_2 all X_1 (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_2),X_1) = nil(X_a) <-> N_2 = zero_zero(nat))) # label(fact_844_replicate__empty) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 916 (all X_a all X_1 all N_2 all Y_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_2),Y_1)))) <-> ti(X_a,X_1) = ti(X_a,Y_1) & N_2 != zero_zero(nat))) # label(fact_845_in__set__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 917 (all X_a all Pa all N_2 all Aa ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_2),Aa)))) & hBOOL(hAPP(X_a,bool,Pa,X_2)))) <-> hBOOL(hAPP(X_a,bool,Pa,Aa)) & N_2 != zero_zero(nat))) # label(fact_846_Bex__set__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 918 (all X_a all Pa all N_2 all Aa ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_2),Aa)))) -> hBOOL(hAPP(X_a,bool,Pa,X_2)))) <-> hBOOL(hAPP(X_a,bool,Pa,Aa)) | N_2 = zero_zero(nat))) # label(fact_847_Ball__set__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 919 (all X_a all X all N (N != zero_zero(nat) -> hAPP(list(X_a),X_a,last(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)) = ti(X_a,X))) # label(fact_848_last__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 920 (all X_a all X all N (N != zero_zero(nat) -> hAPP(list(X_a),X_a,hd(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)) = ti(X_a,X))) # label(fact_849_hd__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 921 (all N_2 all M_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,suc,N_2)),M_2) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),ord_min(nat),N_2))),M_2)) # label(fact_850_min__Suc1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 922 (all M_2 all N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),M_2),hAPP(nat,nat,suc,N_2)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),ord_min(nat)),N_2))),M_2)) # label(fact_851_min__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 923 (all M all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,suc,J)))) # label(fact_852_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 924 (all M all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K))),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,J)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)))) # label(fact_853_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 925 (all X_a all N all Xs all Ys_1 hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))),Ys_1))) # label(fact_854_take__append) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 926 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_855_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 927 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_856_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 928 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_857_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 929 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_858_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 930 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_859_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 931 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_860_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 932 (all X_a all N all Xs all Ys_1 hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))),Ys_1))) # label(fact_861_drop__append) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 933 (all X_a all Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) <-> Xs_1 != nil(X_a))) # label(fact_862_length__greater__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 934 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))))) # label(fact_863_length__pos__if__in__set) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 935 (all X_a all X_1 all A_2 ((hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),A_2)) -> hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))),A_2) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))) & (-hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),A_2)) -> hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))),A_2) = nil(X_a)))) # label(fact_864_sublist__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 936 (all X_a all Xs (Xs != nil(X_a) -> hAPP(list(X_a),X_a,hd(X_a),Xs) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),zero_zero(nat)))) # label(fact_865_hd__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 937 (all X_a all Ys_1 all N all Xs ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)),N) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),N)) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)),N) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))))) # label(fact_866_nth__append) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 938 (all X_a all Ys_1 all X all N all Xs ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)),N),X) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),N),X)),Ys_1)) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)),N),X) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Ys_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))),X))))) # label(fact_867_list__update__append) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 939 (all X_a all I_2 all Xs hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),I_2),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),I_2)),hAPP(list(X_a),list(X_a),rev(X_a),Xs))) # label(fact_868_rev__drop) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 940 (all X_a all I_2 all Xs hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_2),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),I_2)),hAPP(list(X_a),list(X_a),rev(X_a),Xs))) # label(fact_869_rev__take) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 941 (all X_a all A_1 all List_1 hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_1),List_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),List_1)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_870_list_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 942 (all X_a all Xs_1 hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,fun(nat,bool)),fun(X_a,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(X_a,fun(nat,bool)),fun(X_a,bool)),combb(fun(nat,bool),bool,X_a),fEx(nat)),hAPP(fun(nat,bool),fun(X_a,fun(nat,bool)),hAPP(fun(X_a,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(X_a,fun(nat,bool))),combc(X_a,fun(nat,bool),fun(nat,bool)),hAPP(fun(X_a,fun(nat,fun(bool,bool))),fun(X_a,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(X_a,fun(nat,fun(bool,bool))),fun(X_a,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),X_a),combs(nat,bool,bool)),hAPP(fun(X_a,fun(nat,bool)),fun(X_a,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(X_a,fun(nat,bool)),fun(X_a,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),X_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),hAPP(fun(nat,X_a),fun(X_a,fun(nat,bool)),hAPP(fun(X_a,fun(fun(nat,X_a),fun(nat,bool))),fun(fun(nat,X_a),fun(X_a,fun(nat,bool))),combc(X_a,fun(nat,X_a),fun(nat,bool)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(nat,X_a),fun(nat,bool))),hAPP(fun(fun(X_a,bool),fun(fun(nat,X_a),fun(nat,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(nat,X_a),fun(nat,bool)))),combb(fun(X_a,bool),fun(fun(nat,X_a),fun(nat,bool)),X_a),combb(X_a,bool,nat)),fequal(X_a))),hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1))))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))))) # label(fact_871_set__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 943 (all N_2 all Pa (-hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))) -> (hBOOL(hAPP(nat,bool,Pa,N_2)) -> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),N_2)) & (all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K_2)) -> -hBOOL(hAPP(nat,bool,Pa,I)))) & hBOOL(hAPP(nat,bool,Pa,K_2))))))) # label(fact_872_ex__least__nat__le) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 944 (all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) -> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2)) & hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_2) = J)))) # label(fact_873_less__imp__add__positive) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 945 (all X_a all C_1 all A_2 all B_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_2),B_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)),B_1),C_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),C_1),A_2)) = ti(fun(X_a,bool),A_2)))) # label(fact_874_double__diff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 946 (all X_a all D_2 all B_1 all A_2 all C_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_2),C_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)),D_2),B_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,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),C_1),D_2)))))) # label(fact_875_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 947 (all X_a all A_2 all B_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,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1)),A_2))) # label(fact_876_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 948 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (exists M_1 N = hAPP(nat,nat,suc,M_1)))) # label(fact_877_gr0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 949 (all X_a (linordered_idom(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))))))) # label(fact_878_even__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 950 (all X_a all Ca all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1))) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B_1))))) # label(fact_879_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 951 (all X_a all B_1 all Ca all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1)))))) # label(fact_880_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 952 (all X_a all Ca all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B_1)))) # label(fact_881_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 953 (all X_a all Ca all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_2)))) # label(fact_882_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 954 (all X_a all A_2 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1)),B_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1)) # label(fact_883_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 955 (all X_a all Ca all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_2)) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B_1)))) # label(fact_884_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 956 (all X_a all A_2 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_2))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_1))))) # label(fact_885_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 957 (all X_a (linord219039673up_add(X_a) -> (all Aa (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa) = zero_zero(X_a) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_886_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 958 (all X_a (linordered_semidom(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_887_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 959 (all Nat hAPP(nat,nat,nat_size,hAPP(nat,nat,suc,Nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,nat_size,Nat)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_888_nat_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 960 (all X_a (linordered_idom(X_a) -> (all X all Y (ti(X_a,X) != ti(X_a,Y) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_889_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.50 961 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),B_1)) -> (exists B_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_1),A_2)))))) # label(fact_891_psubset__imp__ex__mem) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 962 (all I_1 all Pa all K_1 (hBOOL(hAPP(nat,bool,Pa,K_1)) -> ((all N_1 (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_1))) -> hBOOL(hAPP(nat,bool,Pa,N_1)))) -> hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K_1),I_1)))))) # label(fact_892_zero__induct__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 963 (all N (N != zero_zero(nat) -> (exists M_1 N = hAPP(nat,nat,suc,M_1)))) # label(fact_893_not0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 964 (all N_2 all Pa (hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))) -> ((all N_1 (hBOOL(hAPP(nat,bool,Pa,N_1)) -> hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_1))))) -> hBOOL(hAPP(nat,bool,Pa,N_2))))) # label(fact_894_nat__induct) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 965 (all Y (Y != zero_zero(nat) -> -(all Nat_1 Y != hAPP(nat,nat,suc,Nat_1)))) # label(fact_895_nat_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 966 (all Pa all K_1 (hBOOL(hAPP(nat,bool,Pa,K_1)) -> ((all N_1 (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_1))) -> hBOOL(hAPP(nat,bool,Pa,N_1)))) -> hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))))) # label(fact_896_zero__induct) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 967 (all Nat hAPP(nat,nat,size_size(nat),hAPP(nat,nat,suc,Nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,size_size(nat),Nat)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_897_nat_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 968 (all X_a all Fa all Aa all List hAPP(list(X_a),nat,hAPP(fun(X_a,nat),fun(list(X_a),nat),list_size(X_a),Fa),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Aa),List)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(X_a,nat,Fa,Aa)),hAPP(list(X_a),nat,hAPP(fun(X_a,nat),fun(list(X_a),nat),list_size(X_a),Fa),List))),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_898_list_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 969 (all N hAPP(nat,nat,size_size(nat),N) = N) # label(fact_900_nat__size) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 970 (all X_a all Fa hAPP(list(X_a),nat,hAPP(fun(X_a,nat),fun(list(X_a),nat),list_size(X_a),Fa),nil(X_a)) = zero_zero(nat)) # label(fact_901_list_Osize_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 971 (all X_a all Y_1 all F all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y_1),hAPP(X_a,nat,F,X_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y_1),hAPP(list(X_a),nat,hAPP(fun(X_a,nat),fun(list(X_a),nat),list_size(X_a),F),Xs_1)))))) # label(fact_902_list__size__estimation) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 972 (all X_a all Y_1 all F all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Y_1),hAPP(X_a,nat,F,X_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Y_1),hAPP(list(X_a),nat,hAPP(fun(X_a,nat),fun(list(X_a),nat),list_size(X_a),F),Xs_1)))))) # label(fact_903_list__size__estimation_H) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 973 (all X_a all F all G all Xs_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X_a,nat,F,X_2)),hAPP(X_a,nat,G,X_2))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,hAPP(fun(X_a,nat),fun(list(X_a),nat),list_size(X_a),F),Xs_1)),hAPP(list(X_a),nat,hAPP(fun(X_a,nat),fun(list(X_a),nat),list_size(X_a),G),Xs_1))))) # label(fact_904_list__size__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 974 (all X_a all A_2 all XS hAPP(fun(list(X_a),bool),fun(list(X_a),bool),hAPP(fun(X_a,bool),fun(fun(list(X_a),bool),fun(list(X_a),bool)),set_Cons(X_a),A_2),XS) = hAPP(fun(list(X_a),bool),fun(list(X_a),bool),collect(list(X_a)),hAPP(fun(list(X_a),fun(X_a,bool)),fun(list(X_a),bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(list(X_a),fun(X_a,bool)),fun(list(X_a),bool)),combb(fun(X_a,bool),bool,list(X_a)),fEx(X_a)),hAPP(fun(list(X_a),fun(X_a,fun(list(X_a),bool))),fun(list(X_a),fun(X_a,bool)),hAPP(fun(fun(X_a,fun(list(X_a),bool)),fun(X_a,bool)),fun(fun(list(X_a),fun(X_a,fun(list(X_a),bool))),fun(list(X_a),fun(X_a,bool))),combb(fun(X_a,fun(list(X_a),bool)),fun(X_a,bool),list(X_a)),hAPP(fun(fun(list(X_a),bool),bool),fun(fun(X_a,fun(list(X_a),bool)),fun(X_a,bool)),combb(fun(list(X_a),bool),bool,X_a),fEx(list(X_a)))),hAPP(fun(X_a,fun(list(X_a),bool)),fun(list(X_a),fun(X_a,fun(list(X_a),bool))),hAPP(fun(list(X_a),fun(fun(X_a,fun(list(X_a),bool)),fun(X_a,fun(list(X_a),bool)))),fun(fun(X_a,fun(list(X_a),bool)),fun(list(X_a),fun(X_a,fun(list(X_a),bool)))),combc(list(X_a),fun(X_a,fun(list(X_a),bool)),fun(X_a,fun(list(X_a),bool))),hAPP(fun(list(X_a),fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool)))),fun(list(X_a),fun(fun(X_a,fun(list(X_a),bool)),fun(X_a,fun(list(X_a),bool)))),hAPP(fun(fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool))),fun(fun(X_a,fun(list(X_a),bool)),fun(X_a,fun(list(X_a),bool)))),fun(fun(list(X_a),fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool)))),fun(list(X_a),fun(fun(X_a,fun(list(X_a),bool)),fun(X_a,fun(list(X_a),bool))))),combb(fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool))),fun(fun(X_a,fun(list(X_a),bool)),fun(X_a,fun(list(X_a),bool))),list(X_a)),combs(X_a,fun(list(X_a),bool),fun(list(X_a),bool))),hAPP(fun(list(X_a),fun(X_a,fun(list(X_a),fun(bool,bool)))),fun(list(X_a),fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool)))),hAPP(fun(fun(X_a,fun(list(X_a),fun(bool,bool))),fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool)))),fun(fun(list(X_a),fun(X_a,fun(list(X_a),fun(bool,bool)))),fun(list(X_a),fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool))))),combb(fun(X_a,fun(list(X_a),fun(bool,bool))),fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool))),list(X_a)),hAPP(fun(fun(list(X_a),fun(bool,bool)),fun(fun(list(X_a),bool),fun(list(X_a),bool))),fun(fun(X_a,fun(list(X_a),fun(bool,bool))),fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool)))),combb(fun(list(X_a),fun(bool,bool)),fun(fun(list(X_a),bool),fun(list(X_a),bool)),X_a),combs(list(X_a),bool,bool))),hAPP(fun(list(X_a),fun(X_a,fun(list(X_a),bool))),fun(list(X_a),fun(X_a,fun(list(X_a),fun(bool,bool)))),hAPP(fun(fun(X_a,fun(list(X_a),bool)),fun(X_a,fun(list(X_a),fun(bool,bool)))),fun(fun(list(X_a),fun(X_a,fun(list(X_a),bool))),fun(list(X_a),fun(X_a,fun(list(X_a),fun(bool,bool))))),combb(fun(X_a,fun(list(X_a),bool)),fun(X_a,fun(list(X_a),fun(bool,bool))),list(X_a)),hAPP(fun(fun(list(X_a),bool),fun(list(X_a),fun(bool,bool))),fun(fun(X_a,fun(list(X_a),bool)),fun(X_a,fun(list(X_a),fun(bool,bool)))),combb(fun(list(X_a),bool),fun(list(X_a),fun(bool,bool)),X_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(list(X_a),bool),fun(list(X_a),fun(bool,bool))),combb(bool,fun(bool,bool),list(X_a)),fconj))),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),fun(X_a,fun(list(X_a),bool))),hAPP(fun(list(X_a),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(X_a,fun(list(X_a),bool)))),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),fun(X_a,fun(list(X_a),bool)))),combc(list(X_a),fun(X_a,fun(list(X_a),list(X_a))),fun(X_a,fun(list(X_a),bool))),hAPP(fun(list(X_a),fun(fun(list(X_a),list(X_a)),fun(list(X_a),bool))),fun(list(X_a),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(X_a,fun(list(X_a),bool)))),hAPP(fun(fun(fun(list(X_a),list(X_a)),fun(list(X_a),bool)),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(X_a,fun(list(X_a),bool)))),fun(fun(list(X_a),fun(fun(list(X_a),list(X_a)),fun(list(X_a),bool))),fun(list(X_a),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(X_a,fun(list(X_a),bool))))),combb(fun(fun(list(X_a),list(X_a)),fun(list(X_a),bool)),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(X_a,fun(list(X_a),bool))),list(X_a)),combb(fun(list(X_a),list(X_a)),fun(list(X_a),bool),X_a)),hAPP(fun(list(X_a),fun(list(X_a),bool)),fun(list(X_a),fun(fun(list(X_a),list(X_a)),fun(list(X_a),bool))),hAPP(fun(fun(list(X_a),bool),fun(fun(list(X_a),list(X_a)),fun(list(X_a),bool))),fun(fun(list(X_a),fun(list(X_a),bool)),fun(list(X_a),fun(fun(list(X_a),list(X_a)),fun(list(X_a),bool)))),combb(fun(list(X_a),bool),fun(fun(list(X_a),list(X_a)),fun(list(X_a),bool)),list(X_a)),combb(list(X_a),bool,list(X_a))),fequal(list(X_a))))),cons(X_a)))))),hAPP(fun(list(X_a),bool),fun(X_a,fun(list(X_a),bool)),hAPP(fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool))),fun(fun(list(X_a),bool),fun(X_a,fun(list(X_a),bool))),combc(X_a,fun(list(X_a),bool),fun(list(X_a),bool)),hAPP(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool))),hAPP(fun(fun(bool,bool),fun(fun(list(X_a),bool),fun(list(X_a),bool))),fun(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(list(X_a),bool),fun(list(X_a),bool)))),combb(fun(bool,bool),fun(fun(list(X_a),bool),fun(list(X_a),bool)),X_a),combb(bool,bool,list(X_a))),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_2)))),hAPP(fun(list(X_a),bool),fun(list(X_a),bool),hAPP(fun(list(X_a),fun(fun(list(X_a),bool),bool)),fun(fun(list(X_a),bool),fun(list(X_a),bool)),combc(list(X_a),fun(list(X_a),bool),bool),member(list(X_a))),XS))))))) # label(fact_905_set__Cons__def) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 975 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_906_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 976 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_907_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 977 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))))) # label(fact_908_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 978 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),B)))) # label(fact_909_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 979 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))) # label(fact_910_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 980 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),D_1)))) # label(fact_911_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 981 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),D_1))))) # label(fact_912_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 982 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)))) # label(fact_913_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 983 (all X_a (semiri456707255roduct(X_a) -> (all Ba all Aa (ti(X_a,Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_914_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 984 (all X_a (linordered_field(X_a) -> (all X all Y ((all E (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),E)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),E))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_915_field__le__epsilon) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 985 (all X_a all X_b all Xs_1 all Ys hAPP(list(product_prod(X_a,X_b)),fun(product_prod(X_a,X_b),bool),set(product_prod(X_a,X_b)),hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Xs_1),Ys)) = hAPP(fun(product_prod(X_a,X_b),bool),fun(product_prod(X_a,X_b),bool),collect(product_prod(X_a,X_b)),hAPP(fun(product_prod(X_a,X_b),fun(nat,bool)),fun(product_prod(X_a,X_b),bool),hAPP(fun(fun(nat,bool),bool),fun(fun(product_prod(X_a,X_b),fun(nat,bool)),fun(product_prod(X_a,X_b),bool)),combb(fun(nat,bool),bool,product_prod(X_a,X_b)),fEx(nat)),hAPP(fun(nat,bool),fun(product_prod(X_a,X_b),fun(nat,bool)),hAPP(fun(product_prod(X_a,X_b),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(product_prod(X_a,X_b),fun(nat,bool))),combc(product_prod(X_a,X_b),fun(nat,bool),fun(nat,bool)),hAPP(fun(product_prod(X_a,X_b),fun(nat,fun(bool,bool))),fun(product_prod(X_a,X_b),fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(product_prod(X_a,X_b),fun(nat,fun(bool,bool))),fun(product_prod(X_a,X_b),fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),product_prod(X_a,X_b)),combs(nat,bool,bool)),hAPP(fun(product_prod(X_a,X_b),fun(nat,bool)),fun(product_prod(X_a,X_b),fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(product_prod(X_a,X_b),fun(nat,bool)),fun(product_prod(X_a,X_b),fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),product_prod(X_a,X_b)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),hAPP(fun(nat,product_prod(X_a,X_b)),fun(product_prod(X_a,X_b),fun(nat,bool)),hAPP(fun(product_prod(X_a,X_b),fun(fun(nat,product_prod(X_a,X_b)),fun(nat,bool))),fun(fun(nat,product_prod(X_a,X_b)),fun(product_prod(X_a,X_b),fun(nat,bool))),combc(product_prod(X_a,X_b),fun(nat,product_prod(X_a,X_b)),fun(nat,bool)),hAPP(fun(product_prod(X_a,X_b),fun(product_prod(X_a,X_b),bool)),fun(product_prod(X_a,X_b),fun(fun(nat,product_prod(X_a,X_b)),fun(nat,bool))),hAPP(fun(fun(product_prod(X_a,X_b),bool),fun(fun(nat,product_prod(X_a,X_b)),fun(nat,bool))),fun(fun(product_prod(X_a,X_b),fun(product_prod(X_a,X_b),bool)),fun(product_prod(X_a,X_b),fun(fun(nat,product_prod(X_a,X_b)),fun(nat,bool)))),combb(fun(product_prod(X_a,X_b),bool),fun(fun(nat,product_prod(X_a,X_b)),fun(nat,bool)),product_prod(X_a,X_b)),combb(product_prod(X_a,X_b),bool,nat)),fequal(product_prod(X_a,X_b)))),hAPP(fun(nat,X_b),fun(nat,product_prod(X_a,X_b)),hAPP(fun(nat,fun(X_b,product_prod(X_a,X_b))),fun(fun(nat,X_b),fun(nat,product_prod(X_a,X_b))),combs(nat,X_b,product_prod(X_a,X_b)),hAPP(fun(nat,X_a),fun(nat,fun(X_b,product_prod(X_a,X_b))),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(fun(nat,X_a),fun(nat,fun(X_b,product_prod(X_a,X_b)))),combb(X_a,fun(X_b,product_prod(X_a,X_b)),nat),product_Pair(X_a,X_b)),hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1))),hAPP(list(X_b),fun(nat,X_b),nth(X_b),Ys)))))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)),hAPP(list(X_b),nat,size_size(list(X_b)),Ys))))))) # label(fact_916_set__zip) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 986 (all X_a all X_b all Xs all Ys_1 hAPP(list(product_prod(X_a,X_b)),nat,size_size(list(product_prod(X_a,X_b))),hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Xs),Ys_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),hAPP(list(X_b),nat,size_size(list(X_b)),Ys_1))) # label(fact_917_length__zip) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 987 (all X_a all X_b all Xs all Ys_1 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs) = hAPP(list(X_b),nat,size_size(list(X_b)),Ys_1) -> hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),hAPP(list(X_a),list(X_a),rev(X_a),Xs)),hAPP(list(X_b),list(X_b),rev(X_b),Ys_1)) = hAPP(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b)),rev(product_prod(X_a,X_b)),hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Xs),Ys_1)))) # label(fact_918_zip__rev) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 988 (all X_a all X_b all Ys_1 all Vs_2 all Xs all Us_2 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs) = hAPP(list(X_b),nat,size_size(list(X_b)),Us_2) -> (hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1) = hAPP(list(X_b),nat,size_size(list(X_b)),Vs_2) -> hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)),hAPP(list(X_b),list(X_b),hAPP(list(X_b),fun(list(X_b),list(X_b)),append(X_b),Us_2),Vs_2)) = hAPP(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b)),hAPP(list(product_prod(X_a,X_b)),fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b))),append(product_prod(X_a,X_b)),hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Xs),Us_2)),hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Ys_1),Vs_2))))) # label(fact_919_zip__append) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 989 (all X_b all X_a all X_1 all Xs_1 all Ys hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),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) = hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(fun(X_b,fun(list(X_b),list(product_prod(X_a,X_b)))),fun(list(X_b),list(product_prod(X_a,X_b))),hAPP(list(product_prod(X_a,X_b)),fun(fun(X_b,fun(list(X_b),list(product_prod(X_a,X_b)))),fun(list(X_b),list(product_prod(X_a,X_b)))),list_case(list(product_prod(X_a,X_b)),X_b),nil(product_prod(X_a,X_b))),hAPP(fun(list(X_b),list(product_prod(X_a,X_b))),fun(X_b,fun(list(X_b),list(product_prod(X_a,X_b)))),hAPP(fun(X_b,fun(fun(list(X_b),list(product_prod(X_a,X_b))),fun(list(X_b),list(product_prod(X_a,X_b))))),fun(fun(list(X_b),list(product_prod(X_a,X_b))),fun(X_b,fun(list(X_b),list(product_prod(X_a,X_b))))),combc(X_b,fun(list(X_b),list(product_prod(X_a,X_b))),fun(list(X_b),list(product_prod(X_a,X_b)))),hAPP(fun(X_b,fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b)))),fun(X_b,fun(fun(list(X_b),list(product_prod(X_a,X_b))),fun(list(X_b),list(product_prod(X_a,X_b))))),hAPP(fun(fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b))),fun(fun(list(X_b),list(product_prod(X_a,X_b))),fun(list(X_b),list(product_prod(X_a,X_b))))),fun(fun(X_b,fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b)))),fun(X_b,fun(fun(list(X_b),list(product_prod(X_a,X_b))),fun(list(X_b),list(product_prod(X_a,X_b)))))),combb(fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b))),fun(fun(list(X_b),list(product_prod(X_a,X_b))),fun(list(X_b),list(product_prod(X_a,X_b)))),X_b),combb(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b)),list(X_b))),hAPP(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b)))),hAPP(fun(product_prod(X_a,X_b),fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b)))),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b))))),combb(product_prod(X_a,X_b),fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b))),X_b),cons(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)))),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Xs_1))),Ys)) # label(fact_920_zip__Cons1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 990 (all X_b all X_a all Xs_1 all Y_1 all Ys hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Xs_1),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Y_1),Ys)) = hAPP(list(X_a),list(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(list(X_a),list(product_prod(X_a,X_b)))),fun(list(X_a),list(product_prod(X_a,X_b))),hAPP(list(product_prod(X_a,X_b)),fun(fun(X_a,fun(list(X_a),list(product_prod(X_a,X_b)))),fun(list(X_a),list(product_prod(X_a,X_b)))),list_case(list(product_prod(X_a,X_b)),X_a),nil(product_prod(X_a,X_b))),hAPP(fun(list(X_a),list(product_prod(X_a,X_b))),fun(X_a,fun(list(X_a),list(product_prod(X_a,X_b)))),hAPP(fun(X_a,fun(fun(list(X_a),list(product_prod(X_a,X_b))),fun(list(X_a),list(product_prod(X_a,X_b))))),fun(fun(list(X_a),list(product_prod(X_a,X_b))),fun(X_a,fun(list(X_a),list(product_prod(X_a,X_b))))),combc(X_a,fun(list(X_a),list(product_prod(X_a,X_b))),fun(list(X_a),list(product_prod(X_a,X_b)))),hAPP(fun(X_a,fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b)))),fun(X_a,fun(fun(list(X_a),list(product_prod(X_a,X_b))),fun(list(X_a),list(product_prod(X_a,X_b))))),hAPP(fun(fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b))),fun(fun(list(X_a),list(product_prod(X_a,X_b))),fun(list(X_a),list(product_prod(X_a,X_b))))),fun(fun(X_a,fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b)))),fun(X_a,fun(fun(list(X_a),list(product_prod(X_a,X_b))),fun(list(X_a),list(product_prod(X_a,X_b)))))),combb(fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b))),fun(fun(list(X_a),list(product_prod(X_a,X_b))),fun(list(X_a),list(product_prod(X_a,X_b)))),X_a),combb(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b)),list(X_a))),hAPP(fun(X_a,product_prod(X_a,X_b)),fun(X_a,fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b)))),hAPP(fun(product_prod(X_a,X_b),fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b)))),fun(fun(X_a,product_prod(X_a,X_b)),fun(X_a,fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b))))),combb(product_prod(X_a,X_b),fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b))),X_a),cons(product_prod(X_a,X_b))),hAPP(X_b,fun(X_a,product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_b,fun(X_a,product_prod(X_a,X_b))),combc(X_a,X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b)),Y_1)))),hAPP(list(X_b),fun(list(X_a),list(product_prod(X_a,X_b))),hAPP(fun(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b)))),fun(list(X_b),fun(list(X_a),list(product_prod(X_a,X_b)))),combc(list(X_a),list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b)),Ys))),Xs_1)) # label(fact_921_zip__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 991 (all X_b all X_a all Xs all I_2 all X all Ys_1 all Y hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_2),X)),hAPP(X_b,list(X_b),hAPP(nat,fun(X_b,list(X_b)),hAPP(list(X_b),fun(nat,fun(X_b,list(X_b))),list_update(X_b),Ys_1),I_2),Y)) = hAPP(product_prod(X_a,X_b),list(product_prod(X_a,X_b)),hAPP(nat,fun(product_prod(X_a,X_b),list(product_prod(X_a,X_b))),hAPP(list(product_prod(X_a,X_b)),fun(nat,fun(product_prod(X_a,X_b),list(product_prod(X_a,X_b)))),list_update(product_prod(X_a,X_b)),hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Xs),Ys_1)),I_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),Y))) # label(fact_922_zip__update) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 992 (all X_b all X_a all X all Xs all Y all Ys_1 hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),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_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Y),Ys_1)) = hAPP(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b)),hAPP(product_prod(X_a,X_b),fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b))),cons(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),Y)),hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Xs),Ys_1))) # label(fact_923_zip__Cons__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 993 (all X_a all X_b all X_1 all Y_1 all Xs_1 all Ys (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)),hAPP(list(product_prod(X_a,X_b)),fun(product_prod(X_a,X_b),bool),set(product_prod(X_a,X_b)),hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Xs_1),Ys)))) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),hAPP(list(X_b),fun(X_b,bool),set(X_b),Ys)))))) # label(fact_924_in__set__zipE) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 994 (all X_a all X_b all X_1 all Y_1 all Xs_1 all Ys (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)),hAPP(list(product_prod(X_a,X_b)),fun(product_prod(X_a,X_b),bool),set(product_prod(X_a,X_b)),hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Xs_1),Ys)))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),hAPP(list(X_b),fun(X_b,bool),set(X_b),Ys))))) # label(fact_925_set__zip__rightD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 995 (all X_a all X_b all X_1 all Y_1 all Xs_1 all Ys (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)),hAPP(list(product_prod(X_a,X_b)),fun(product_prod(X_a,X_b),bool),set(product_prod(X_a,X_b)),hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Xs_1),Ys)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_926_set__zip__leftD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 996 (all X_a all Aa all Ba all 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),Aa),Ba)),hAPP(list(product_prod(X_a,X_a)),fun(product_prod(X_a,X_a),bool),set(product_prod(X_a,X_a)),hAPP(list(X_a),list(product_prod(X_a,X_a)),hAPP(list(X_a),fun(list(X_a),list(product_prod(X_a,X_a))),zip(X_a,X_a),Xs_1),Xs_1)))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & ti(X_a,Aa) = ti(X_a,Ba))) # label(fact_927_zip__same) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 997 (all X_b all X_a all Xs hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Xs),nil(X_b)) = nil(product_prod(X_a,X_b))) # label(fact_928_zip_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 998 (all X_b all X_a all Ys_1 hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),nil(X_a)),Ys_1) = nil(product_prod(X_a,X_b))) # label(fact_929_zip__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 999 (all X_b all X_a all Xs all Ys_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Ys_1)) -> hBOOL(hAPP(list(product_prod(X_b,X_a)),bool,distinct(product_prod(X_b,X_a)),hAPP(list(X_a),list(product_prod(X_b,X_a)),hAPP(list(X_b),fun(list(X_a),list(product_prod(X_b,X_a))),zip(X_b,X_a),Xs),Ys_1))))) # label(fact_930_distinct__zipI2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1000 (all X_b all X_a all Ys_1 all Xs (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs)) -> hBOOL(hAPP(list(product_prod(X_a,X_b)),bool,distinct(product_prod(X_a,X_b)),hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Xs),Ys_1))))) # label(fact_931_distinct__zipI1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1001 (all X_a all X_b all N all Xs all Ys_1 hAPP(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b)),hAPP(nat,fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b))),take(product_prod(X_a,X_b)),N),hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Xs),Ys_1)) = hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs)),hAPP(list(X_b),list(X_b),hAPP(nat,fun(list(X_b),list(X_b)),take(X_b),N),Ys_1))) # label(fact_932_take__zip) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1002 (all X_a all X_b all N all Xs all Ys_1 hAPP(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b)),hAPP(nat,fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b))),drop(product_prod(X_a,X_b)),N),hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Xs),Ys_1)) = hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs)),hAPP(list(X_b),list(X_b),hAPP(nat,fun(list(X_b),list(X_b)),drop(X_b),N),Ys_1))) # label(fact_933_drop__zip) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1003 (all X_b all X_a all I_2 all X all J all Y hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),I_2),X)),hAPP(X_b,list(X_b),hAPP(nat,fun(X_b,list(X_b)),replicate(X_b),J),Y)) = hAPP(product_prod(X_a,X_b),list(product_prod(X_a,X_b)),hAPP(nat,fun(product_prod(X_a,X_b),list(product_prod(X_a,X_b))),replicate(product_prod(X_a,X_b)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),I_2),J)),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),Y))) # label(fact_934_zip__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1004 (all X_b all X_a all Ys_1 all I_2 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_b),nat,size_size(list(X_b)),Ys_1))) -> hAPP(nat,product_prod(X_a,X_b),hAPP(list(product_prod(X_a,X_b)),fun(nat,product_prod(X_a,X_b)),nth(product_prod(X_a,X_b)),hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Xs),Ys_1)),I_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),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_2)),hAPP(nat,X_b,hAPP(list(X_b),fun(nat,X_b),nth(X_b),Ys_1),I_2))))) # label(fact_935_nth__zip) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1005 (all X_b all X_a all Xs all Ys_1 all Zs_2 hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1)),Zs_2) = hAPP(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b)),hAPP(list(product_prod(X_a,X_b)),fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b))),append(product_prod(X_a,X_b)),hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Xs),hAPP(list(X_b),list(X_b),hAPP(nat,fun(list(X_b),list(X_b)),take(X_b),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),Zs_2))),hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Ys_1),hAPP(list(X_b),list(X_b),hAPP(nat,fun(list(X_b),list(X_b)),drop(X_b),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),Zs_2)))) # label(fact_936_zip__append1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1006 (all X_b all X_a all Xs all Ys_1 all Zs_2 hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Xs),hAPP(list(X_b),list(X_b),hAPP(list(X_b),fun(list(X_b),list(X_b)),append(X_b),Ys_1),Zs_2)) = hAPP(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b)),hAPP(list(product_prod(X_a,X_b)),fun(list(product_prod(X_a,X_b)),list(product_prod(X_a,X_b))),append(product_prod(X_a,X_b)),hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(list(X_b),nat,size_size(list(X_b)),Ys_1)),Xs)),Ys_1)),hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(list(X_b),nat,size_size(list(X_b)),Ys_1)),Xs)),Zs_2))) # label(fact_937_zip__append2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1007 (all X_a all X_b all Pa all Xs_1 all Ys ((all Zs all Ws all N_1 (hAPP(list(X_a),nat,size_size(list(X_a)),Zs) = hAPP(list(X_b),nat,size_size(list(X_b)),Ws) -> (N_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)),hAPP(list(X_b),nat,size_size(list(X_b)),Ys)) -> (Zs = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs_1) -> (Ws = hAPP(list(X_b),list(X_b),hAPP(nat,fun(list(X_b),list(X_b)),take(X_b),N_1),Ys) -> hBOOL(hAPP(list(product_prod(X_a,X_b)),bool,Pa,hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Zs),Ws)))))))) -> hBOOL(hAPP(list(product_prod(X_a,X_b)),bool,Pa,hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Xs_1),Ys))))) # label(fact_938_zip__obtain__same__length) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1008 (all X_a all Xs_1 all Ys all R_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)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_1))) <-> hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(list(X_a),nat,size_size(list(X_a)),Ys) & (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)),X_2),hAPP(list(product_prod(X_a,X_a)),fun(product_prod(X_a,X_a),bool),set(product_prod(X_a,X_a)),hAPP(list(X_a),list(product_prod(X_a,X_a)),hAPP(list(X_a),fun(list(X_a),list(product_prod(X_a,X_a))),zip(X_a,X_a),Xs_1),Ys)))) -> hBOOL(hAPP(product_prod(X_a,X_a),bool,hAPP(fun(X_a,fun(X_a,bool)),fun(product_prod(X_a,X_a),bool),product_prod_case(X_a,X_a,bool),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_1)),X_2)))))) # label(fact_939_listrel__iff__zip) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1009 (all X_a all A_2 all R_1 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(fun(X_a,bool),fun(fun(product_prod(X_a,X_a),bool),bool),refl_on(X_a),A_2),R_1)) <-> (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)),X_2),R_1)) -> hBOOL(hAPP(product_prod(X_a,X_a),bool,hAPP(fun(X_a,fun(X_a,bool)),fun(product_prod(X_a,X_a),bool),product_prod_case(X_a,X_a,bool),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(X_a,fun(X_a,bool))),combc(X_a,fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),combb(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),X_a),combb(bool,bool,X_a)),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_2)))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_2))),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),A_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_1)))))) # label(fact_940_refl__on__def_H) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1010 (all X_a all Xs_1 all Ys (Xs_1 = Ys <-> hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(list(X_a),nat,size_size(list(X_a)),Ys) & (all 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)),X_2),hAPP(list(product_prod(X_a,X_a)),fun(product_prod(X_a,X_a),bool),set(product_prod(X_a,X_a)),hAPP(list(X_a),list(product_prod(X_a,X_a)),hAPP(list(X_a),fun(list(X_a),list(product_prod(X_a,X_a))),zip(X_a,X_a),Xs_1),Ys)))) -> hBOOL(hAPP(product_prod(X_a,X_a),bool,hAPP(fun(X_a,fun(X_a,bool)),fun(product_prod(X_a,X_a),bool),product_prod_case(X_a,X_a,bool),fequal(X_a)),X_2)))))) # label(fact_941_list__eq__iff__zip__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1011 (all X_b all X_a all Pa all Xs_1 all Ys (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Xs_1),Ys)) <-> hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(list(X_b),nat,size_size(list(X_b)),Ys) & (all X_2 (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)),X_2),hAPP(list(product_prod(X_a,X_b)),fun(product_prod(X_a,X_b),bool),set(product_prod(X_a,X_b)),hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),Xs_1),Ys)))) -> 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),Pa),X_2)))))) # label(fact_942_list__all2__def) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1012 (all X_a all A_2 all As_1 hAPP(list(fun(X_a,bool)),fun(list(X_a),bool),listset(X_a),hAPP(list(fun(X_a,bool)),list(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(list(fun(X_a,bool)),list(fun(X_a,bool))),cons(fun(X_a,bool)),A_2),As_1)) = hAPP(fun(list(X_a),bool),fun(list(X_a),bool),hAPP(fun(X_a,bool),fun(fun(list(X_a),bool),fun(list(X_a),bool)),set_Cons(X_a),A_2),hAPP(list(fun(X_a,bool)),fun(list(X_a),bool),listset(X_a),As_1))) # label(fact_943_listset_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1013 (all X_b all X_a all Ca all D all Pa all Aa all Ba (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Aa),Ba)) -> (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Ca),D)) -> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Aa),Ca)),hAPP(list(X_b),list(X_b),hAPP(list(X_b),fun(list(X_b),list(X_b)),append(X_b),Ba),D)))))) # label(fact_944_list__all2__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1014 (all X_b all X_a all Pa all Ys (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),nil(X_a)),Ys)) <-> Ys = nil(X_b))) # label(fact_945_list__all2__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1015 (all X_b all X_a all Pa all Xs_1 (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Xs_1),nil(X_b))) <-> Xs_1 = nil(X_a))) # label(fact_946_list__all2__Nil2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1016 (all X_b all X_a all Pa all X_1 all Xs_1 all Y_1 all Ys (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),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_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Y_1),Ys))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_1),Y_1)) & hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Xs_1),Ys)))) # label(fact_947_list__all2__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1017 (all X_b all X_a all N_2 all Pa all As all Bs (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),As),Bs)) -> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_2),As)),hAPP(list(X_b),list(X_b),hAPP(nat,fun(list(X_b),list(X_b)),drop(X_b),N_2),Bs))))) # label(fact_948_list__all2__dropI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1018 (all X_b all X_a all Pa all Xs_1 all Ys (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)),hAPP(list(X_b),list(X_b),rev(X_b),Ys))) <-> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Xs_1),Ys)))) # label(fact_949_list__all2__rev) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1019 (all X_b all X_a all Pa all Xs_1 all Ys (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)),Ys)) <-> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Xs_1),hAPP(list(X_b),list(X_b),rev(X_b),Ys))))) # label(fact_950_list__all2__rev1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1020 (all X_b all X_a all N_2 all Pa all Xs_1 all Ys (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Xs_1),Ys)) -> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_2),Xs_1)),hAPP(list(X_b),list(X_b),hAPP(nat,fun(list(X_b),list(X_b)),take(X_b),N_2),Ys))))) # label(fact_951_list__all2__takeI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1021 (all X_b all X_a all Pa all Xs_1 all Ys (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Xs_1),Ys)) -> hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(list(X_b),nat,size_size(list(X_b)),Ys))) # label(fact_952_list__all2__lengthD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1022 (all X_a all X_b all Pa all Us_1 all Vs_1 all Xs_1 all Ys (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(list(X_b),nat,size_size(list(X_b)),Ys) -> (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),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_b),list(X_b),hAPP(list(X_b),fun(list(X_b),list(X_b)),append(X_b),Ys),Vs_1))) <-> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Xs_1),Ys)) & hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Us_1),Vs_1))))) # label(fact_953_list__all2__append) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1023 (all X_b all X_a all Pa all Xs_1 all Ys (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Xs_1),Ys)) <-> hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(list(X_b),nat,size_size(list(X_b)),Ys) & (all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I)),hAPP(nat,X_b,hAPP(list(X_b),fun(nat,X_b),nth(X_b),Ys),I))))))) # label(fact_954_list__all2__conv__all__nth) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1024 (all X_b all X_a all P_1 all Pa all Xs_1 all Ys (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Xs_1),Ys)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),P_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),P_1)),hAPP(nat,X_b,hAPP(list(X_b),fun(nat,X_b),nth(X_b),Ys),P_1)))))) # label(fact_955_list__all2__nthD) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1025 (all X_b all X_a all P_1 all Pa all Xs_1 all Ys (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Xs_1),Ys)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),P_1),hAPP(list(X_b),nat,size_size(list(X_b)),Ys))) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),P_1)),hAPP(nat,X_b,hAPP(list(X_b),fun(nat,X_b),nth(X_b),Ys),P_1)))))) # label(fact_956_list__all2__nthD2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1026 (all X_a all Xs_1 all Ys (Xs_1 = Ys <-> hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),list_all2(X_a,X_a),fequal(X_a)),Xs_1),Ys)))) # label(fact_957_list__all2__eq) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1027 (all X_b all X_a all I_1 all X_1 all Y_1 all Pa all Xs_1 all Ys (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Xs_1),Ys)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_1),Y_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_b),nat,size_size(list(X_b)),Ys))) -> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs_1),I_1),X_1)),hAPP(X_b,list(X_b),hAPP(nat,fun(X_b,list(X_b)),hAPP(list(X_b),fun(nat,fun(X_b,list(X_b))),list_update(X_b),Ys),I_1),Y_1))))))) # label(fact_958_list__all2__update__cong2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1028 (all X_b all X_a all X_1 all Y_1 all Pa all Ys all I_1 all Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) -> (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Xs_1),Ys)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_1),Y_1)) -> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs_1),I_1),X_1)),hAPP(X_b,list(X_b),hAPP(nat,fun(X_b,list(X_b)),hAPP(list(X_b),fun(nat,fun(X_b,list(X_b))),list_update(X_b),Ys),I_1),Y_1))))))) # label(fact_959_list__all2__update__cong) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.51 1029 (all X_a all X_b all Pa all Aa all Ba ((all X_2 (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)),X_2),hAPP(list(product_prod(X_a,X_b)),fun(product_prod(X_a,X_b),bool),set(product_prod(X_a,X_b)),hAPP(list(X_b),list(product_prod(X_a,X_b)),hAPP(list(X_a),fun(list(X_b),list(product_prod(X_a,X_b))),zip(X_a,X_b),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),Pa),X_2)))) -> (hAPP(list(X_a),nat,size_size(list(X_a)),Aa) = hAPP(list(X_b),nat,size_size(list(X_b)),Ba) -> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Aa),Ba))))) # label(fact_960_list__all2I) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1030 (all X_a all X_b all Pa all Aa all Ba (hAPP(list(X_a),nat,size_size(list(X_a)),Aa) = hAPP(list(X_b),nat,size_size(list(X_b)),Ba) -> ((all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Aa))) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Aa),N_1)),hAPP(nat,X_b,hAPP(list(X_b),fun(nat,X_b),nth(X_b),Ba),N_1))))) -> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Aa),Ba))))) # label(fact_961_list__all2__all__nthI) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1031 (all X_b all X_a all Pa all Xs_1 all Ys all Zs_1 (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Xs_1),hAPP(list(X_b),list(X_b),hAPP(list(X_b),fun(list(X_b),list(X_b)),append(X_b),Ys),Zs_1))) <-> (exists Us exists 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),Vs) & hAPP(list(X_a),nat,size_size(list(X_a)),Us) = hAPP(list(X_b),nat,size_size(list(X_b)),Ys) & hAPP(list(X_a),nat,size_size(list(X_a)),Vs) = hAPP(list(X_b),nat,size_size(list(X_b)),Zs_1) & hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Us),Ys)) & hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Vs),Zs_1)))))) # label(fact_962_list__all2__append2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1032 (all X_b all X_a all Pa all Xs_1 all Ys all Zs_1 (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),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)),Zs_1)) <-> (exists Us exists Vs (Zs_1 = hAPP(list(X_b),list(X_b),hAPP(list(X_b),fun(list(X_b),list(X_b)),append(X_b),Us),Vs) & hAPP(list(X_b),nat,size_size(list(X_b)),Us) = hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) & hAPP(list(X_b),nat,size_size(list(X_b)),Vs) = hAPP(list(X_a),nat,size_size(list(X_a)),Ys) & hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Xs_1),Us)) & hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Ys),Vs)))))) # label(fact_963_list__all2__append1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1033 (all X_b all X_a all Pa all Xs_1 all Y_1 all Ys (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Xs_1),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Y_1),Ys))) <-> (exists Z exists Zs (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Z),Zs) & hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,Z),Y_1)) & hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Zs),Ys)))))) # label(fact_964_list__all2__Cons2) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1034 (all X_b all X_a all Pa all X_1 all Xs_1 all Ys (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),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)),Ys)) <-> (exists Z exists Zs (Ys = hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Z),Zs) & hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_1),Z)) & hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),hAPP(fun(X_a,fun(X_b,bool)),fun(list(X_a),fun(list(X_b),bool)),list_all2(X_a,X_b),Pa),Xs_1),Zs)))))) # label(fact_965_list__all2__Cons1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1035 (all X_a all X all K all Xs (Xs != nil(X_a) -> (K = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat)) -> hAPP(list(X_a),X_a,last(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),K),X)) = ti(X_a,X)) & (K != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat)) -> hAPP(list(X_a),X_a,last(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),K),X)) = hAPP(list(X_a),X_a,last(X_a),Xs)))) # label(fact_966_last__list__update) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1036 (all X_a all N all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(list(X_a),nat,size_size(list(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)),take(X_a),N),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),Xs))) # label(fact_967_butlast__take) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1037 (all X_a (linordered_semidom(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))))))) # label(fact_968_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1038 (all X_a (linordered_semidom(X_a) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),zero_zero(X_a))))) # label(fact_969_not__one__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1039 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),one_one(X_a))))) # label(fact_970_zero__le__one) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1040 (all X_a (zero_neq_one(X_a) -> zero_zero(X_a) != one_one(X_a))) # label(fact_971_zero__neq__one) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1041 (all X_a (zero_neq_one(X_a) -> one_one(X_a) != zero_zero(X_a))) # label(fact_972_one__neq__zero) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1042 (all X_a (linordered_semidom(X_a) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a))))) # label(fact_973_not__one__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1043 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),one_one(X_a))))) # label(fact_974_zero__less__one) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1044 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)))))) # label(fact_975_zero__less__two) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1045 (all X_a (one(X_a) -> (all X_1 (one_one(X_a) = ti(X_a,X_1) <-> ti(X_a,X_1) = one_one(X_a))))) # label(fact_977_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1046 (all N hAPP(nat,nat,suc,N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))) # label(fact_978_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1047 (all N hAPP(nat,nat,suc,N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N)) # label(fact_979_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1048 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N)),one_one(nat)) = N) # label(fact_980_diff__Suc__1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1049 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N)) # label(fact_981_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1050 (all X_a all X all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),one_one(nat)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a))) # label(fact_982_take__1__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1051 (all X_a all X all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),one_one(nat)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = Xs) # label(fact_983_drop__1__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1052 (all X_a all Xs hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat))) # label(fact_984_length__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1053 (all X_a all Xs hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),tl(X_a),Xs)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat))) # label(fact_985_length__tl) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1054 (all X_a all N all Xs hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),hAPP(list(X_a),list(X_a),tl(X_a),Xs))) # label(fact_986_tl__take) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1055 (all X_a all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat))) -> hAPP(list(X_a),list(X_a),rotate1(X_a),Xs) = Xs)) # label(fact_987_rotate1__length01) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1056 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))))) # label(fact_988_Suc__pred_H) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1057 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))) = N)) # label(fact_989_Suc__diff__1) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1058 (all N all M ((M = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = N) & (M != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N))))) # label(fact_990_add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1059 (all X_a all X all Xs all N ((N = zero_zero(nat) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),N) = ti(X_a,X)) & (N != zero_zero(nat) -> hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),N) = hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))))) # label(fact_991_nth__Cons_H) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1060 (all X_a all X all Xs all N ((N = zero_zero(nat) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) & (N != zero_zero(nat) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),Xs)))) # label(fact_992_drop__Cons_H) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1061 (all X_a all Xs hAPP(list(X_a),list(X_a),butlast(X_a),Xs) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat))),Xs)) # label(fact_993_butlast__conv__take) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1062 (all X_a all X all K all Xs ((K = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat)) -> hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),K),X)) = hAPP(list(X_a),list(X_a),butlast(X_a),Xs)) & (K != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat)) -> hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),K),X)) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)),K),X)))) # label(fact_994_butlast__list__update) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1063 (all X_a all X all N (N != zero_zero(nat) -> hAPP(list(X_a),list(X_a),tl(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),X))) # label(fact_995_tl__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1064 (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].
% 1.98/2.52 1065 (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].
% 1.98/2.52 1066 (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].
% 1.98/2.52 1067 (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].
% 1.98/2.52 1068 (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].
% 1.98/2.52 1069 (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].
% 1.98/2.52 1070 (all T_2 all T_1 (minus(T_1) -> minus(fun(T_2,T_1)))) # label(arity_fun___Groups_Ominus) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1071 (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].
% 1.98/2.52 1072 (all T_1 cl_HOL_Oequal(list(T_1))) # label(arity_List_Olist___HOL_Oequal) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1073 (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].
% 1.98/2.52 1074 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1075 (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].
% 1.98/2.52 1076 (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].
% 1.98/2.52 1077 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_If_3_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1078 (all X_a all P all X (-hBOOL(hAPP(X_a,bool,P,X)) | hBOOL(hAPP(fun(X_a,bool),bool,fEx(X_a),P)))) # label(help_fEx_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1079 (all P (-hBOOL(hAPP(bool,bool,fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1080 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1081 (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].
% 1.98/2.52 1082 (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].
% 1.98/2.52 1083 (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].
% 1.98/2.52 1084 (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].
% 1.98/2.52 1085 (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].
% 1.98/2.52 1086 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fTrue_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1087 (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].
% 1.98/2.52 1088 (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].
% 1.98/2.52 1089 (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].
% 1.98/2.52 1090 (all Q all P (-hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1091 (all P all Q (-hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1092 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | hBOOL(P) | hBOOL(Q))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1093 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.98/2.52 1094 (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].
% 1.98/2.52 1095 (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].
% 1.98/2.52 1096 -(all I (hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I))) <-> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),c)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I)),c),b))))) # label(conj_0) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.81/3.02
% 2.81/3.02 ============================== end of process non-clausal formulas ===
% 2.81/3.02
% 2.81/3.02 ============================== PROCESS INITIAL CLAUSES ===============
% 2.81/3.02
% 2.81/3.02 ============================== PREDICATE ELIMINATION =================
% 2.81/3.02 1097 one(nat) # label(arity_Nat_Onat___Groups_Oone) # label(axiom). [assumption].
% 2.81/3.02 1098 -one(A) | one_one(A) = ti(A,one_one(A)) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom). [clausify(9)].
% 2.81/3.02 Derived: one_one(nat) = ti(nat,one_one(nat)). [resolve(1097,a,1098,a)].
% 2.81/3.02 1099 monoid_add(nat) # label(arity_Nat_Onat___Groups_Omonoid__add) # label(axiom). [assumption].
% 2.81/3.02 1100 -monoid_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom). [clausify(10)].
% 2.81/3.02 1101 -monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_729_add__0__left) # label(axiom). [clausify(800)].
% 2.81/3.02 1102 -monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_732_add__0__right) # label(axiom). [clausify(803)].
% 2.81/3.02 Derived: plus_plus(nat) = ti(fun(nat,fun(nat,nat)),plus_plus(nat)). [resolve(1099,a,1100,a)].
% 2.81/3.02 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),A) = ti(nat,A). [resolve(1099,a,1101,a)].
% 2.81/3.02 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),zero_zero(nat)) = ti(nat,A). [resolve(1099,a,1102,a)].
% 2.81/3.02 1103 ab_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 2.81/3.02 1104 -ab_semigroup_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom). [clausify(11)].
% 2.81/3.02 1105 -ab_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_664_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom). [clausify(735)].
% 2.81/3.02 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)). [resolve(1103,a,1105,a)].
% 2.81/3.02 1106 cancel_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.81/3.02 1107 -cancel_semigroup_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_2_res) # label(axiom). [clausify(12)].
% 2.81/3.02 1108 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C) | ti(A,B) = ti(A,D) # label(fact_659_add__right__imp__eq) # label(axiom). [clausify(730)].
% 2.81/3.02 1109 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) = ti(A,D) # label(fact_661_add__left__imp__eq) # label(axiom). [clausify(732)].
% 2.81/3.02 1110 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C) | ti(A,B) = ti(A,D) # label(fact_662_add__right__cancel) # label(axiom). [clausify(733)].
% 3.05/3.26 1111 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C) | ti(A,B) != ti(A,D) # label(fact_662_add__right__cancel) # label(axiom). [clausify(733)].
% 3.05/3.26 1112 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) = ti(A,D) # label(fact_663_add__left__cancel) # label(axiom). [clausify(734)].
% 3.05/3.26 1113 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) != ti(A,D) # label(fact_663_add__left__cancel) # label(axiom). [clausify(734)].
% 3.05/3.26 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B) | ti(nat,A) = ti(nat,C). [resolve(1106,a,1108,a)].
% 3.05/3.26 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C) | ti(nat,B) = ti(nat,C). [resolve(1106,a,1109,a)].
% 3.05/3.26 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B) | ti(nat,A) != ti(nat,C). [resolve(1106,a,1111,a)].
% 3.05/3.26 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C) | ti(nat,B) != ti(nat,C). [resolve(1106,a,1113,a)].
% 3.05/3.26 1114 zero(nat) # label(arity_Nat_Onat___Groups_Ozero) # label(axiom). [assumption].
% 3.05/3.26 1115 -zero(A) | zero_zero(A) = ti(A,zero_zero(A)) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom). [clausify(13)].
% 3.05/3.26 Derived: zero_zero(nat) = ti(nat,zero_zero(nat)). [resolve(1114,a,1115,a)].
% 3.05/3.26 1116 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom). [assumption].
% 3.05/3.26 1117 -linorder(A) | linorder_sorted(A) = ti(fun(list(A),bool),linorder_sorted(A)) # label(tsy_c_List_Olinorder__class_Osorted_res) # label(axiom). [clausify(29)].
% 3.05/3.26 1118 -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_93_sorted__single) # label(axiom). [clausify(165)].
% 3.05/3.26 1119 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),nil(A))) # label(fact_97_sorted_ONil) # label(axiom). [clausify(169)].
% 3.05/3.26 1120 -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_98_sorted__butlast) # label(axiom). [clausify(170)].
% 3.05/3.26 1121 -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_135_sorted__takeWhile) # label(axiom). [clausify(207)].
% 3.05/3.26 1122 -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_184_sorted__dropWhile) # label(axiom). [clausify(255)].
% 3.05/3.26 1123 -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_211_sorted__tl) # label(axiom). [clausify(282)].
% 3.05/3.26 1124 -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_266_sorted__drop) # label(axiom). [clausify(337)].
% 3.05/3.26 1125 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | -hBOOL(hAPP(list(A),bool,distinct(A),B)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | -hBOOL(hAPP(list(A),bool,distinct(A),C)) | hAPP(list(A),fun(A,bool),set(A),C) != hAPP(list(A),fun(A,bool),set(A),B) | C = B # label(fact_303_sorted__distinct__set__unique) # label(axiom). [clausify(374)].
% 3.05/3.26 1126 -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_354_linorder__le__cases) # label(axiom). [clausify(425)].
% 3.05/3.26 1127 -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_376_linorder__linear) # label(axiom). [clausify(447)].
% 3.05/3.26 1128 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(nat,fun(list(A),list(A)),take(A),C),B))) # label(fact_386_sorted__take) # label(axiom). [clausify(457)].
% 3.05/3.26 1129 -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_393_sorted__many) # label(axiom). [clausify(464)].
% 3.05/3.26 1130 -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_394_sorted__many__eq) # label(axiom). [clausify(465)].
% 3.05/3.26 1131 -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_394_sorted__many__eq) # label(axiom). [clausify(465)].
% 3.05/3.26 1132 -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_394_sorted__many__eq) # label(axiom). [clausify(465)].
% 3.05/3.26 1133 -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_398_sorted__Cons) # label(axiom). [clausify(469)].
% 3.05/3.26 1134 -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_398_sorted__Cons) # label(axiom). [clausify(469)].
% 3.05/3.26 1135 -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),f207(A,B,C)),hAPP(list(A),fun(A,bool),set(A),C))) # label(fact_398_sorted__Cons) # label(axiom). [clausify(469)].
% 3.05/3.26 1136 -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),f207(A,B,C))) # label(fact_398_sorted__Cons) # label(axiom). [clausify(469)].
% 3.05/3.26 1137 -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_399_sorted__append) # label(axiom). [clausify(470)].
% 3.05/3.26 1138 -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_399_sorted__append) # label(axiom). [clausify(470)].
% 3.05/3.26 1139 -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_399_sorted__append) # label(axiom). [clausify(470)].
% 3.05/3.26 1140 -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),f208(A,B,C)),hAPP(list(A),fun(A,bool),set(A),B))) # label(fact_399_sorted__append) # label(axiom). [clausify(470)].
% 3.05/3.26 1141 -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),f209(A,B,C)),hAPP(list(A),fun(A,bool),set(A),C))) # label(fact_399_sorted__append) # label(axiom). [clausify(470)].
% 3.05/3.26 1142 -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),f208(A,B,C)),f209(A,B,C))) # label(fact_399_sorted__append) # label(axiom). [clausify(470)].
% 3.05/3.26 1143 -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),f211(A,B)),f210(A,B)) = B # label(fact_401_sorted_Osimps) # label(axiom). [clausify(472)].
% 3.05/3.26 1144 -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),f210(A,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f211(A,B)),C)) # label(fact_401_sorted_Osimps) # label(axiom). [clausify(472)].
% 3.05/3.26 1145 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | nil(A) = B | hBOOL(hAPP(list(A),bool,linorder_sorted(A),f210(A,B))) # label(fact_401_sorted_Osimps) # label(axiom). [clausify(472)].
% 3.05/3.26 1146 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | nil(A) != B # label(fact_401_sorted_Osimps) # label(axiom). [clausify(472)].
% 3.05/3.26 1147 -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),f212(A,B,D,C)),hAPP(list(A),fun(A,bool),set(A),D))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),D)) # label(fact_401_sorted_Osimps) # label(axiom). [clausify(472)].
% 3.05/3.26 1148 -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),f212(A,B,D,C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),D)) # label(fact_401_sorted_Osimps) # label(axiom). [clausify(472)].
% 3.05/3.26 1149 -linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f213(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_402_sorted_OCons) # label(axiom). [clausify(473)].
% 3.05/3.26 1150 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f213(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_402_sorted_OCons) # label(axiom). [clausify(473)].
% 3.05/3.26 1151 -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_438_linorder__not__less) # label(axiom). [clausify(509)].
% 3.05/3.26 1152 -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_438_linorder__not__less) # label(axiom). [clausify(509)].
% 3.05/3.26 1153 -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(510)].
% 3.05/3.26 1154 -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(510)].
% 3.05/3.26 1155 -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_440_linorder__le__less__linear) # label(axiom). [clausify(511)].
% 3.05/3.26 1156 -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_444_leI) # label(axiom). [clausify(515)].
% 3.05/3.26 1157 -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_445_not__leE) # label(axiom). [clausify(516)].
% 3.05/3.26 1158 -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_446_linorder__antisym__conv1) # label(axiom). [clausify(517)].
% 3.05/3.26 1159 -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_446_linorder__antisym__conv1) # label(axiom). [clausify(517)].
% 3.05/3.26 1160 -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_449_leD) # label(axiom). [clausify(520)].
% 3.05/3.26 1161 -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_451_linorder__antisym__conv2) # label(axiom). [clausify(522)].
% 3.05/3.26 1162 -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_451_linorder__antisym__conv2) # label(axiom). [clausify(522)].
% 3.05/3.26 1163 -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_460_linorder__neq__iff) # label(axiom). [clausify(531)].
% 3.05/3.26 1164 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_460_linorder__neq__iff) # label(axiom). [clausify(531)].
% 3.05/3.26 1165 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_460_linorder__neq__iff) # label(axiom). [clausify(531)].
% 3.05/3.26 1166 -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_461_not__less__iff__gr__or__eq) # label(axiom). [clausify(532)].
% 3.05/3.26 1167 -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_461_not__less__iff__gr__or__eq) # label(axiom). [clausify(532)].
% 3.05/3.26 1168 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_461_not__less__iff__gr__or__eq) # label(axiom). [clausify(532)].
% 3.05/3.26 1169 -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_462_linorder__less__linear) # label(axiom). [clausify(533)].
% 3.05/3.26 1170 -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_463_linorder__antisym__conv3) # label(axiom). [clausify(534)].
% 3.05/3.26 1171 -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_463_linorder__antisym__conv3) # label(axiom). [clausify(534)].
% 3.05/3.26 1172 -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_464_linorder__neqE) # label(axiom). [clausify(535)].
% 3.05/3.26 1173 -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_480_linorder__cases) # label(axiom). [clausify(551)].
% 3.05/3.26 1174 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),D),hAPP(list(A),nat,size_size(list(A)),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),C)),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),D))) # label(fact_587_sorted__nth__mono) # label(axiom). [clausify(658)].
% 3.05/3.26 1175 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),hAPP(list(A),nat,size_size(list(A)),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),D)),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),C))) # label(fact_588_sorted__equals__nth__mono) # label(axiom). [clausify(659)].
% 3.05/3.26 1176 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f258(A,B)),hAPP(list(A),nat,size_size(list(A)),B))) # label(fact_588_sorted__equals__nth__mono) # label(axiom). [clausify(659)].
% 3.05/3.26 1177 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f259(A,B)),f258(A,B))) # label(fact_588_sorted__equals__nth__mono) # label(axiom). [clausify(659)].
% 3.05/3.26 1178 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),f259(A,B))),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),f258(A,B)))) # label(fact_588_sorted__equals__nth__mono) # label(axiom). [clausify(659)].
% 3.05/3.26 1179 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),rev(A),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),D),hAPP(list(A),nat,size_size(list(A)),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),D)),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),C))) # label(fact_592_sorted__rev__nth__mono) # label(axiom). [clausify(663)].
% 3.05/3.26 1180 -linorder(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f263(A,B)),f264(A,B))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) # label(fact_595_sorted__nth__monoI) # label(axiom). [clausify(666)].
% 3.05/3.26 1181 -linorder(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f264(A,B)),hAPP(list(A),nat,size_size(list(A)),B))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) # label(fact_595_sorted__nth__monoI) # label(axiom). [clausify(666)].
% 3.05/3.26 1182 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),f263(A,B))),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),f264(A,B)))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) # label(fact_595_sorted__nth__monoI) # label(axiom). [clausify(666)].
% 3.05/3.26 1183 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_606_min__less__iff__conj) # label(axiom). [clausify(677)].
% 3.05/3.26 1184 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_606_min__less__iff__conj) # label(axiom). [clausify(677)].
% 3.05/3.26 1185 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_606_min__less__iff__conj) # label(axiom). [clausify(677)].
% 3.05/3.26 1186 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_607_min__less__iff__disj) # label(axiom). [clausify(678)].
% 3.05/3.26 1187 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_607_min__less__iff__disj) # label(axiom). [clausify(678)].
% 3.05/3.26 1188 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_607_min__less__iff__disj) # label(axiom). [clausify(678)].
% 3.05/3.26 1189 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_621_min__le__iff__disj) # label(axiom). [clausify(692)].
% 3.05/3.26 1190 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_621_min__le__iff__disj) # label(axiom). [clausify(692)].
% 3.05/3.26 1191 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_621_min__le__iff__disj) # label(axiom). [clausify(692)].
% 3.05/3.26 1192 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),B)),C)) # label(fact_685_min__max_Oless__infI2) # label(axiom). [clausify(756)].
% 3.05/3.26 1193 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C)) # label(fact_686_min__max_Oless__infI1) # label(axiom). [clausify(757)].
% 3.05/3.26 1194 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_687_min__max_Oinf__assoc) # label(axiom). [clausify(758)].
% 3.05/3.26 1195 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_688_min__max_Oinf_Oassoc) # label(axiom). [clausify(759)].
% 3.05/3.26 1196 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_689_min__max_Oinf__left__commute) # label(axiom). [clausify(760)].
% 3.05/3.26 1197 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_690_min__max_Oinf_Oleft__commute) # label(axiom). [clausify(761)].
% 3.05/3.26 1198 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) # label(fact_691_min__max_Oinf__left__idem) # label(axiom). [clausify(762)].
% 3.05/3.26 1199 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) # label(fact_692_min__max_Oinf_Oleft__idem) # label(axiom). [clausify(763)].
% 3.05/3.26 1200 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),B) # label(fact_693_min__max_Oinf__commute) # label(axiom). [clausify(764)].
% 3.05/3.26 1201 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),B) # label(fact_694_min__max_Oinf_Ocommute) # label(axiom). [clausify(765)].
% 3.05/3.26 1202 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),B) = ti(A,B) # label(fact_695_min__max_Oinf_Oidem) # label(axiom). [clausify(766)].
% 3.05/3.26 1203 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),B)) # label(fact_696_min__max_Oinf__le1) # label(axiom). [clausify(767)].
% 3.05/3.26 1204 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),C)) # label(fact_697_min__max_Oinf__le2) # label(axiom). [clausify(768)].
% 3.05/3.26 1205 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) = ti(A,B) # label(fact_698_min__max_Ole__iff__inf) # label(axiom). [clausify(769)].
% 3.05/3.26 1206 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) != ti(A,B) # label(fact_698_min__max_Ole__iff__inf) # label(axiom). [clausify(769)].
% 3.05/3.26 1207 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_699_min__max_Ole__inf__iff) # label(axiom). [clausify(770)].
% 3.05/3.26 1208 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_699_min__max_Ole__inf__iff) # label(axiom). [clausify(770)].
% 3.05/3.26 1209 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_699_min__max_Ole__inf__iff) # label(axiom). [clausify(770)].
% 3.05/3.26 1210 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C)) # label(fact_700_min__max_Ole__infI1) # label(axiom). [clausify(771)].
% 3.05/3.26 1211 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),B)),C)) # label(fact_701_min__max_Ole__infI2) # label(axiom). [clausify(772)].
% 3.05/3.26 1212 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) = ti(A,B) # label(fact_702_min__max_Oinf__absorb1) # label(axiom). [clausify(773)].
% 3.05/3.26 1213 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),B) = ti(A,B) # label(fact_703_min__max_Oinf__absorb2) # label(axiom). [clausify(774)].
% 3.05/3.26 1214 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) # label(fact_704_min__max_Ole__infI) # label(axiom). [clausify(775)].
% 3.05/3.26 1215 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) # label(fact_705_min__max_Oinf__greatest) # label(axiom). [clausify(776)].
% 3.05/3.26 1216 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),E))) # label(fact_706_min__max_Oinf__mono) # label(axiom). [clausify(777)].
% 3.05/3.26 1217 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_707_min__max_Ole__infE) # label(axiom). [clausify(778)].
% 3.05/3.26 1218 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_707_min__max_Ole__infE) # label(axiom). [clausify(778)].
% 3.05/3.26 Derived: linorder_sorted(nat) = ti(fun(list(nat),bool),linorder_sorted(nat)). [resolve(1116,a,1117,a)].
% 3.05/3.26 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(1116,a,1118,a)].
% 3.05/3.26 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),nil(nat))). [resolve(1116,a,1119,a)].
% 3.05/3.26 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(1116,a,1120,a)].
% 3.05/3.26 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(1116,a,1121,a)].
% 3.05/3.26 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(1116,a,1122,a)].
% 3.05/3.26 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(1116,a,1123,a)].
% 3.05/3.26 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(1116,a,1124,a)].
% 3.05/3.26 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(1116,a,1125,a)].
% 3.05/3.26 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(1116,a,1126,a)].
% 3.05/3.26 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(1116,a,1128,a)].
% 3.05/3.26 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(1116,a,1129,a)].
% 3.05/3.26 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(1116,a,1130,a)].
% 3.05/3.26 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(1116,a,1131,a)].
% 3.05/3.26 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(1116,a,1133,a)].
% 3.05/3.26 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(1116,a,1134,a)].
% 3.05/3.26 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),f207(nat,A,B)),hAPP(list(nat),fun(nat,bool),set(nat),B))). [resolve(1116,a,1135,a)].
% 3.05/3.26 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),f207(nat,A,B))). [resolve(1116,a,1136,a)].
% 3.05/3.26 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(1116,a,1137,a)].
% 3.05/3.26 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(1116,a,1138,a)].
% 3.05/3.26 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(1116,a,1139,a)].
% 3.05/3.26 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),f208(nat,A,B)),hAPP(list(nat),fun(nat,bool),set(nat),A))). [resolve(1116,a,1140,a)].
% 3.05/3.26 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),f209(nat,A,B)),hAPP(list(nat),fun(nat,bool),set(nat),B))). [resolve(1116,a,1141,a)].
% 3.05/3.26 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),f208(nat,A,B)),f209(nat,A,B))). [resolve(1116,a,1142,a)].
% 3.05/3.26 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),f211(nat,A)),f210(nat,A)) = A. [resolve(1116,a,1143,a)].
% 3.05/3.26 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),f210(nat,A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f211(nat,A)),B)). [resolve(1116,a,1144,a)].
% 3.05/3.26 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | nil(nat) = A | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),f210(nat,A))). [resolve(1116,a,1145,a)].
% 3.05/3.26 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | nil(nat) != A. [resolve(1116,a,1146,a)].
% 3.05/3.26 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),f212(nat,A,C,B)),hAPP(list(nat),fun(nat,bool),set(nat),C))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),C)). [resolve(1116,a,1147,a)].
% 3.05/3.26 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),f212(nat,A,C,B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),C)). [resolve(1116,a,1148,a)].
% 3.05/3.26 Derived: hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f213(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(1116,a,1149,a)].
% 3.05/3.26 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f213(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(1116,a,1150,a)].
% 3.05/3.26 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),B),A)). [resolve(1116,a,1151,a)].
% 3.05/3.26 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),B),A)). [resolve(1116,a,1152,a)].
% 3.05/3.26 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(1116,a,1158,a)].
% 3.05/3.26 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(1116,a,1159,a)].
% 3.05/3.26 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(1116,a,1162,a)].
% 3.05/3.26 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(1116,a,1163,a)].
% 3.05/3.26 Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(1116,a,1164,a)].
% 3.05/3.26 Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1116,a,1165,a)].
% 3.05/3.26 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(1116,a,1167,a)].
% 3.05/3.26 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),hAPP(list(nat),nat,size_size(list(nat)),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),nth(nat),A),B)),hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),nth(nat),A),C))). [resolve(1116,a,1174,a)].
% 3.05/3.26 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f258(nat,A)),hAPP(list(nat),nat,size_size(list(nat)),A))). [resolve(1116,a,1176,a)].
% 3.05/3.26 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f259(nat,A)),f258(nat,A))). [resolve(1116,a,1177,a)].
% 3.05/3.26 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),nth(nat),A),f259(nat,A))),hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),nth(nat),A),f258(nat,A)))). [resolve(1116,a,1178,a)].
% 3.05/3.26 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),rev(nat),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),hAPP(list(nat),nat,size_size(list(nat)),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),nth(nat),A),C)),hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),nth(nat),A),B))). [resolve(1116,a,1179,a)].
% 3.05/3.26 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f263(nat,A)),f264(nat,A))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)). [resolve(1116,a,1180,a)].
% 3.05/3.26 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f264(nat,A)),hAPP(list(nat),nat,size_size(list(nat)),A))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)). [resolve(1116,a,1181,a)].
% 3.05/3.26 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),nth(nat),A),f263(nat,A))),hAPP(nat,nat,hAPP(list(nat),fun(nat,nat),nth(nat),A),f264(nat,A)))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)). [resolve(1116,a,1182,a)].
% 3.05/3.26 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1116,a,1183,a)].
% 3.05/3.26 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1116,a,1184,a)].
% 3.05/3.26 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1116,a,1185,a)].
% 3.05/3.26 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(1116,a,1186,a)].
% 3.05/3.26 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1116,a,1187,a)].
% 3.05/3.26 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(1116,a,1188,a)].
% 3.05/3.26 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1116,a,1189,a)].
% 3.05/3.26 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1116,a,1190,a)].
% 3.05/3.26 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1116,a,1191,a)].
% 3.05/3.26 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)). [resolve(1116,a,1194,a)].
% 3.05/3.26 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)). [resolve(1116,a,1196,a)].
% 3.05/3.26 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B). [resolve(1116,a,1198,a)].
% 3.05/3.26 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),A). [resolve(1116,a,1200,a)].
% 3.05/3.26 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),A) = ti(nat,A). [resolve(1116,a,1202,a)].
% 3.05/3.26 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),A)). [resolve(1116,a,1203,a)].
% 3.05/3.26 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),B)). [resolve(1116,a,1204,a)].
% 3.05/3.26 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B) = ti(nat,A). [resolve(1116,a,1205,a)].
% 3.05/3.26 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B) != ti(nat,A). [resolve(1116,a,1206,a)].
% 3.28/3.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1116,a,1207,a)].
% 3.28/3.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1116,a,1208,a)].
% 3.28/3.48 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1116,a,1209,a)].
% 3.28/3.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),A) = ti(nat,A). [resolve(1116,a,1213,a)].
% 3.28/3.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),D))). [resolve(1116,a,1216,a)].
% 3.28/3.48 1219 ordere223160158up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.28/3.48 1220 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_658_add__less__le__mono) # label(axiom). [clausify(729)].
% 3.28/3.48 1221 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_674_add__strict__right__mono) # label(axiom). [clausify(745)].
% 3.28/3.48 1222 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_675_add__strict__left__mono) # label(axiom). [clausify(746)].
% 3.28/3.48 1223 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_676_add__strict__mono) # label(axiom). [clausify(747)].
% 3.28/3.48 1224 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_680_add__le__less__mono) # label(axiom). [clausify(751)].
% 3.28/3.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))). [resolve(1219,a,1220,a)].
% 3.28/3.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))). [resolve(1219,a,1221,a)].
% 3.28/3.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))). [resolve(1219,a,1222,a)].
% 3.28/3.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))). [resolve(1219,a,1223,a)].
% 3.49/3.69 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))). [resolve(1219,a,1224,a)].
% 3.49/3.69 1225 cancel146912293up_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.49/3.69 1226 -cancel146912293up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) = ti(A,D) # label(fact_660_add__imp__eq) # label(axiom). [clausify(731)].
% 3.49/3.69 1227 ordere236663937imp_le(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 3.49/3.69 1228 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_665_add__le__cancel__right) # label(axiom). [clausify(736)].
% 3.49/3.69 1229 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_665_add__le__cancel__right) # label(axiom). [clausify(736)].
% 3.49/3.69 1230 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_666_add__le__cancel__left) # label(axiom). [clausify(737)].
% 3.49/3.69 1231 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_666_add__le__cancel__left) # label(axiom). [clausify(737)].
% 3.49/3.69 1232 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_670_add__le__imp__le__right) # label(axiom). [clausify(741)].
% 3.49/3.69 1233 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_671_add__le__imp__le__left) # label(axiom). [clausify(742)].
% 3.49/3.69 1234 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_672_add__less__cancel__right) # label(axiom). [clausify(743)].
% 3.49/3.69 1235 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_672_add__less__cancel__right) # label(axiom). [clausify(743)].
% 3.49/3.69 1236 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_673_add__less__cancel__left) # label(axiom). [clausify(744)].
% 3.49/3.69 1237 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_673_add__less__cancel__left) # label(axiom). [clausify(744)].
% 3.58/3.80 1238 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_677_add__less__imp__less__right) # label(axiom). [clausify(748)].
% 3.58/3.80 1239 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_678_add__less__imp__less__left) # label(axiom). [clausify(749)].
% 3.58/3.80 1240 -ordere236663937imp_le(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C) # label(fact_679_min__add__distrib__left) # label(axiom). [clausify(750)].
% 3.58/3.80 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1227,a,1228,a)].
% 3.58/3.80 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1227,a,1229,a)].
% 3.58/3.80 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1227,a,1230,a)].
% 3.58/3.80 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1227,a,1231,a)].
% 3.58/3.80 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1227,a,1234,a)].
% 3.58/3.80 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(1227,a,1236,a)].
% 3.58/3.80 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),B). [resolve(1227,a,1240,a)].
% 3.58/3.80 1241 ordere779506340up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 3.58/3.80 1242 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_667_add__right__mono) # label(axiom). [clausify(738)].
% 3.58/3.80 1243 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_668_add__left__mono) # label(axiom). [clausify(739)].
% 3.58/3.80 1244 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_669_add__mono) # label(axiom). [clausify(740)].
% 4.18/4.42 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))). [resolve(1241,a,1244,a)].
% 4.18/4.42 1245 comm_monoid_add(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 4.18/4.42 1246 -comm_monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_730_add__0) # label(axiom). [clausify(801)].
% 4.18/4.42 1247 -comm_monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_733_add_Ocomm__neutral) # label(axiom). [clausify(804)].
% 4.18/4.42 1248 ordere216010020id_add(nat) # label(arity_Nat_Onat___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 4.18/4.42 1249 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_816_add__neg__neg) # label(axiom). [clausify(887)].
% 4.18/4.42 1250 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_817_add__pos__pos) # label(axiom). [clausify(888)].
% 4.18/4.42 1251 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_821_add__nonpos__nonpos) # label(axiom). [clausify(892)].
% 4.18/4.42 1252 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B))) # label(fact_822_add__increasing2) # label(axiom). [clausify(893)].
% 4.18/4.42 1253 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_823_add__increasing) # label(axiom). [clausify(894)].
% 4.18/4.42 1254 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_824_add__nonneg__eq__0__iff) # label(axiom). [clausify(895)].
% 4.18/4.42 1255 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != zero_zero(A) | zero_zero(A) = ti(A,C) # label(fact_824_add__nonneg__eq__0__iff) # label(axiom). [clausify(895)].
% 4.18/4.42 1256 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = zero_zero(A) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_824_add__nonneg__eq__0__iff) # label(axiom). [clausify(895)].
% 4.18/4.42 1257 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_825_add__nonneg__nonneg) # label(axiom). [clausify(896)].
% 4.18/4.42 1258 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_855_add__pos__nonneg) # label(axiom). [clausify(926)].
% 4.18/4.42 1259 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_856_add__nonneg__pos) # label(axiom). [clausify(927)].
% 4.18/4.42 1260 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_857_add__strict__increasing) # label(axiom). [clausify(928)].
% 4.18/4.42 1261 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_858_add__strict__increasing2) # label(axiom). [clausify(929)].
% 4.18/4.42 1262 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_859_add__neg__nonpos) # label(axiom). [clausify(930)].
% 4.18/4.42 1263 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_860_add__nonpos__neg) # label(axiom). [clausify(931)].
% 4.18/4.42 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))). [resolve(1248,a,1249,a)].
% 4.18/4.42 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))). [resolve(1248,a,1250,a)].
% 4.18/4.42 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))). [resolve(1248,a,1251,a)].
% 4.18/4.42 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),A))). [resolve(1248,a,1252,a)].
% 4.18/4.42 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(1248,a,1253,a)].
% 4.18/4.42 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != zero_zero(nat) | zero_zero(nat) = ti(nat,A). [resolve(1248,a,1254,a)].
% 4.18/4.42 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != zero_zero(nat) | zero_zero(nat) = ti(nat,B). [resolve(1248,a,1255,a)].
% 4.38/4.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = zero_zero(nat) | zero_zero(nat) != ti(nat,A) | zero_zero(nat) != ti(nat,B). [resolve(1248,a,1256,a)].
% 4.38/4.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))). [resolve(1248,a,1258,a)].
% 4.38/4.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))). [resolve(1248,a,1259,a)].
% 4.38/4.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(1248,a,1260,a)].
% 4.38/4.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(1248,a,1261,a)].
% 4.38/4.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))). [resolve(1248,a,1262,a)].
% 4.38/4.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))). [resolve(1248,a,1263,a)].
% 4.38/4.62 1264 linordered_semidom(nat) # label(arity_Nat_Onat___Rings_Olinordered__semidom) # label(axiom). [assumption].
% 4.38/4.62 1265 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_887_pos__add__strict) # label(axiom). [clausify(958)].
% 4.38/4.62 1266 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A)))) # label(fact_968_less__add__one) # label(axiom). [clausify(1037)].
% 4.38/4.62 1267 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),zero_zero(A))) # label(fact_969_not__one__le__zero) # label(axiom). [clausify(1038)].
% 4.38/4.62 1268 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),one_one(A))) # label(fact_970_zero__le__one) # label(axiom). [clausify(1039)].
% 4.38/4.62 1269 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),zero_zero(A))) # label(fact_973_not__one__less__zero) # label(axiom). [clausify(1042)].
% 4.38/4.62 1270 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),one_one(A))) # label(fact_974_zero__less__one) # label(axiom). [clausify(1043)].
% 4.38/4.62 1271 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A)))) # label(fact_975_zero__less__two) # label(axiom). [clausify(1044)].
% 4.38/4.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(1264,a,1265,a)].
% 4.47/4.72 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat)))). [resolve(1264,a,1266,a)].
% 4.47/4.72 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),zero_zero(nat))). [resolve(1264,a,1267,a)].
% 4.47/4.72 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),one_one(nat))). [resolve(1264,a,1268,a)].
% 4.47/4.72 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),zero_zero(nat))). [resolve(1264,a,1269,a)].
% 4.47/4.72 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),one_one(nat))). [resolve(1264,a,1270,a)].
% 4.47/4.72 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat)))). [resolve(1264,a,1271,a)].
% 4.47/4.72 1272 comm_semiring_1(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 4.47/4.72 1273 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_906_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom). [clausify(975)].
% 4.47/4.72 1274 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_907_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom). [clausify(976)].
% 4.47/4.72 1275 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E)) # label(fact_908_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom). [clausify(977)].
% 4.47/4.72 1276 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_909_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom). [clausify(978)].
% 4.47/4.72 1277 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_910_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom). [clausify(979)].
% 4.47/4.72 1278 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_911_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom). [clausify(980)].
% 4.47/4.72 1279 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)) # label(fact_912_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom). [clausify(981)].
% 4.47/4.72 1280 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B) # label(fact_913_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom). [clausify(982)].
% 4.47/4.72 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D)). [resolve(1272,a,1275,a)].
% 4.47/4.72 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),B). [resolve(1272,a,1276,a)].
% 5.70/5.93 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)). [resolve(1272,a,1279,a)].
% 5.70/5.93 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),A). [resolve(1272,a,1280,a)].
% 5.70/5.93 1281 semiri456707255roduct(nat) # label(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption].
% 5.70/5.93 1282 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != ti(A,B) | zero_zero(A) = ti(A,C) # label(fact_914_add__0__iff) # label(axiom). [clausify(983)].
% 5.70/5.93 1283 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_914_add__0__iff) # label(axiom). [clausify(983)].
% 5.70/5.93 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != ti(nat,A) | zero_zero(nat) = ti(nat,B). [resolve(1281,a,1282,a)].
% 5.70/5.93 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = ti(nat,A) | zero_zero(nat) != ti(nat,B). [resolve(1281,a,1283,a)].
% 5.70/5.93 1284 zero_neq_one(nat) # label(arity_Nat_Onat___Rings_Ozero__neq__one) # label(axiom). [assumption].
% 5.70/5.93 1285 -zero_neq_one(A) | zero_zero(A) != one_one(A) # label(fact_971_zero__neq__one) # label(axiom). [clausify(1040)].
% 5.70/5.93 1286 -zero_neq_one(A) | zero_zero(A) != one_one(A) # label(fact_972_one__neq__zero) # label(axiom). [clausify(1041)].
% 5.70/5.93 Derived: zero_zero(nat) != one_one(nat). [resolve(1284,a,1285,a)].
% 5.70/5.93
% 5.70/5.93 ============================== end predicate elimination =============
% 5.70/5.93
% 5.70/5.93 Auto_denials: (non-Horn, no changes).
% 5.70/5.93
% 5.70/5.93 Term ordering decisions:
% 5.70/5.93 Function symbol KB weights: bool=1. nat=1. arrow_2142409994le_alt=1. arrow_1998540521e_indi=1. suc=1. arrow_1568854078le_Lin=1. arrow_301600364e_Prof=1. arrow_1665824030_below=1. fconj=1. arrow_357225482_above=1. f=1. b=1. a=1. arrow_1541970350le_IIA=1. p=1. arrow_708804735ctator=1. c=1. fNot=1. fFalse=1. fTrue=1. arrow_1066301521nimity=1. arrow_1622070166_mkbot=1. arrow_1770777252_mktop=1. fdisj=1. nat_size=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. list_all2=1. zip=1. pi=1. combk=1. list_case=1. lex_prod=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. f89=1. f90=1. f92=1. f107=1. f108=1. f109=1. f110=1. f135=1. f210=1. f211=1. f231=1. f232=1. f233=1. f256=1. f257=1. f258=1. f259=1. f263=1. f264=1. f276=1. f277=1. f278=1. f281=1. f289=1. f293=1. f294=1. f299=1. f301=1. list=1. member=1. ord_less_eq=1. ord_less=1. cons=1. size_size=1. append=1. nil=1. plus_plus=1. zero_zero=1. minus_minus=1. set=1. nth=1. take=1. transitive_rtrancl=1. drop=1. linorder_sorted=1. listrel1=1. ord_min=1. rev=1. distinct=1. list_update=1. listrel=1. replicate=1. takeWhile=1. lexord=1. butlast=1. dropWhile=1. last=1. one_one=1. top_top=1. tl=1. fequal=1. listrelp=1. hd=1. collect=1. lex=1. refl_on=1. sublist=1. nat_case=1. rotate1=1. equal_equal=1. list_size=1. null=1. fEx=1. insert=1. splice=1. combi=1. if=1. partition=1. reflp=1. lexn=1. listset=1. measure=1. mlex_prod=1. set_Cons=1. lenlex=1. min=1. order_215145569der_on=1. undefined=1. f8=1. f9=1. f10=1. f11=1. f13=1. f14=1. f15=1. f91=1. f285=1. f286=1. f290=1. f295=1. f298=1. f300=1. combb=1. combc=1. product_prod_case=1. combs=1. product_curry=1. produc1605651328_split=1. product_prod_rec=1. f1=1. f2=1. f3=1. f25=1. f26=1. f27=1. f68=1. f69=1. f70=1. f71=1. f74=1. f75=1. f76=1. f78=1. f79=1. f82=1. f87=1. f88=1. f140=1. f141=1. f147=1. f148=1. f149=1. f150=1. f151=1. f152=1. f153=1. f154=1. f155=1. f164=1. f165=1. f166=1. f167=1. f168=1. f169=1. f170=1. f171=1. f172=1. f173=1. f174=1. f175=1. f176=1. f177=1. f178=1. f179=1. f181=1. f182=1. f183=1. f184=1. f200=1. f201=1. f202=1. f203=1. f204=1. f205=1. f207=1. f208=1. f209=1. f213=1. f214=1. f219=1. f220=1. f221=1. f222=1. f223=1. f229=1. f230=1. f252=1. f253=1. f254=1. f255=1. f270=1. f271=1. f272=1. f279=1. f280=1. f282=1. f283=1. f287=1. f288=1. f296=1. f297=1. f308=1. f309=1. f310=1. hAPP=1. product_map_pair=1. f12=1. f59=1. f60=1. f61=1. f72=1. f73=1. f77=1. f80=1. f81=1. f93=1. f94=1. f95=1. f96=1. f119=1. f120=1. f121=1. f122=1. f131=1. f132=1. f133=1. f134=1. f136=1. f137=1. f138=1. f139=1. f145=1. f146=1. f162=1. f163=1. f196=1. f197=1. f198=1. f199=1. f206=1. f212=1. f216=1. f217=1. f218=1. f224=1. f225=1. f226=1. f227=1. f228=1. f260=1. f261=1. f262=1. f265=1. f266=1. f267=1. f268=1. f269=1. f273=1. f274=1. f275=1. f291=1. f292=1. f302=1. f307=1. f7=1. f50=1. f51=1. f52=1. f53=1. f54=1. f62=1. f63=1. f64=1. f65=1. f66=1. f83=1. f84=1. f85=1. f86=1. f97=1. f98=1. f99=1. f100=1. f101=1. f102=1. f111=1. f112=1. f113=1. f114=1. f115=1. f116=1. f117=1. f118=1. f142=1. f143=1. f144=1. f156=1. f157=1. f158=1. f159=1. f160=1. f161=1. f185=1. f215=1. f284=1. f304=1. f305=1. f306=1. f311=1. f312=1. f313=1. f314=1. f4=1. f5=1. f40=1. f41=1. f42=1. f43=1. f44=1. f55=1. f56=1. f57=1. f58=1. f67=1. f103=1. f104=1. f123=1. f124=1. f125=1. f126=1. f127=1. f128=1. f129=1. f130=1. f180=1. f236=1. f237=1. f238=1. f239=1. f240=1. f241=1. f242=1. f243=1. f244=1. f245=1. f246=1. f247=1. f248=1. f249=1. f250=1. f251=1. f315=1. f316=1. f317=1. f318=1. f319=1. f320=1. f321=1. f322=1. f34=1. f35=1. f36=1. f37=1. f38=1. f39=1. f45=1. f46=1. f47=1. f48=1. f49=1. f105=1. f106=1. f186=1. f187=1. f28=1. f29=1. f30=1. f31=1. f32=1. f33=1. f188=1. f189=1. f190=1. f191=1. f192=1. f193=1. f194=1. f195=1.
% 8.81/9.05
% 8.81/9.05 ============================== end of process initial clauses ========
% 8.81/9.05
% 8.81/9.05 ============================== CLAUSES FOR SEARCH ====================
% 8.81/9.05
% 8.81/9.05 ============================== end of clauses for search =============
% 8.81/9.05
% 8.81/9.05 ============================== SEARCH ================================
% 8.81/9.05
% 8.81/9.05 % Starting search at 3.75 seconds.
% 8.81/9.05
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% 8.81/9.05 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 119 (0.00 of 6.23 sec).
% 8.81/9.05
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% 119.78/119.97
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% 119.78/119.97 Low Water (displace): id=6926, wt=199.000
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% 119.78/119.97 Low Water (keep): wt=40.000, iters=3355
% 119.78/119.97
% 119.78/119.97 Low Water (keep): wt=39.000, iters=3334
% 119.78/119.97
% 119.78/119.97 Low Water (keep): wt=38.000, iters=3334
% 119.78/119.97
% 119.78/119.97 Low Water (keep): wt=37.000, iters=3335
% 119.78/119.97
% 119.78/119.97 Low Water (keep): wt=36.000, iters=3508
% 119.78/119.97
% 119.78/119.97 Low Water (keep): wt=35.000, iters=3362
% 119.78/119.97
% 119.78/119.97 Low Water (keep): wt=34.000, iters=3343
% 119.78/119.97
% 119.78/119.97 Low Water (keep): wt=33.000, iters=3373
% 119.78/119.97
% 119.78/119.97 Low Water (keep): wt=32.000, iters=3379
% 119.78/119.97
% 119.78/119.97 Low Water (keep): wt=31.000, iters=3337
% 119.78/119.97
% 119.78/119.97 Low Water (keep): wt=30.000, iters=3488
% 119.78/119.97
% 119.78/119.97 Low Water (keep): wt=29.000, iters=3381
% 119.78/119.97
% 119.78/119.97 Low Water (keep): wt=28.000, iters=3432
% 119.78/119.97
% 119.78/119.97 ============================== STATISTICS ============================
% 119.78/119.97
% 119.78/119.97 Given=6274. Generated=1286247. Kept=226974. proofs=0.
% 119.78/119.97 Usable=6002. Sos=9999. Demods=792. Limbo=27, Disabled=212838. Hints=0.
% 119.78/119.97 Kept_by_rule=0, Deleted_by_rule=157980.
% 119.78/119.97 Forward_subsumed=157105. Back_subsumed=52.
% 119.78/119.97 Sos_limit_deleted=744188. Sos_displaced=209270. Sos_removed=0.
% 119.78/119.97 New_demodulators=1518 (0 lex), Back_demodulated=1622. Back_unit_deleted=2.
% 119.78/119.97 Demod_attempts=107594831. Demod_rewrites=325319.
% 119.78/119.97 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
% 119.78/119.97 Nonunit_fsub_feature_tests=3201897. Nonunit_bsub_feature_tests=12493.
% 119.78/119.97 Megabytes=419.43.
% 119.78/119.97 User_CPU=116.94, System_CPU=0.85, Wall_clock=118.
% 119.78/119.97
% 119.78/119.97 Megs malloced by palloc(): 400.
% 119.78/119.97 type (bytes each) gets frees in use bytes
% 119.78/119.97 chunk ( 104) 102141 102141 0 0.0 K
% 119.78/119.97 string_buf ( 8) 91346 91346 0 0.0 K
% 119.78/119.97 token ( 20) 234139 234139 0 0.0 K
% 119.78/119.97 pterm ( 16) 164326 164326 0 0.0 K
% 119.78/119.97 hashtab ( 8) 1096 1096 0 0.0 K
% 119.78/119.97 hashnode ( 8) 4385 4385 0 0.0 K
% 119.78/119.98 term ( 20) 140127902 134314873 5813029 113535.7 K
% 119.78/119.98 term arg arrays: 24915.7 K
% 119.78/119.98 attribute ( 12) 9444 308 9136 107.1 K
% 119.78/119.98 ilist ( 8) 1104196626 1103070638 1125988 8796.8 K
% 119.78/119.98 plist ( 8) 3834447 3572989 261458 2042.6 K
% 119.78/119.98 i2list ( 12) 9587976 9587976 0 0.0 K
% 119.78/119.98 just ( 12) 1610337 1360525 249812 2927.5 K
% 119.78/119.98 parajust ( 16) 1004355 894130 110225 1722.3 K
% 119.78/119.98 instancejust ( 8) 0 0 0 0.0 K
% 119.78/119.98 ivyjust ( 24) 0 0 0 0.0 K
% 119.78/119.98 formula ( 28) 48156 31502 16654 455.4 K
% 119.78/119.98 formula arg arrays: 56.5 K
% 119.78/119.98 topform ( 52) 1289287 1059273 230014 11680.4 K
% 119.78/119.98 clist_pos ( 20) 677981 448323 229658 4485.5 K
% 119.78/119.98 clist ( 16) 8 1 7 0.1 K
% 119.78/119.98 context ( 808) 9777530 9777528 2 1.6 K
% 119.78/119.98 trail ( 12) 8272336 8272335 1 0.0 K
% 119.78/119.98 ac_match_pos (70044) 0 0 0 0.0 K
% 119.78/119.98 ac_match_free_vars_pos (20020)
% 119.78/119.98 0 0 0 0.0 K
% 119.78/119.98 btm_state ( 60) 0 0 0 0.0 K
% 119.78/119.98 btu_state ( 60) 0 0 0 0.0 K
% 119.78/119.98 ac_position (285432) 0 0 0 0.0 K
% 119.78/119.98 fpa_trie ( 20) 976702 645665 331037 6465.6 K
% 119.78/119.98 fpa_state ( 28) 5297640 5297639 1 0.0 K
% 119.78/119.98 fpa_index ( 12) 10 0 10 0.1 K
% 119.78/119.98 fpa_chunk ( 20) 1518554 1375249 143305 2798.9 K
% 119.78/119.98 fpa_list ( 16) 727916 0 727916 11373.7 K
% 119.78/119.98 fpa_list chunks: 10579.8 K
% 119.78/119.98 discrim ( 12) 1136529 1053196 83333 976.6 K
% 119.78/119.98 discrim_pos ( 16) 367470 367470 0 0.0 K
% 119.78/119.98 flat2 ( 32) 65013501 65013501 0 0.0 K
% 119.78/119.98 flat ( 48) 0 0 0 0.0 K
% 119.78/119.98 flatterm ( 32) 146761688 146761688 0 0.0 K
% 119.78/119.98 mindex ( 28) 13 0 13 0.4 K
% 119.78/119.98 mindex_pos ( 56) 6330452 6330451 1 0.1 K
% 119.78/119.98 lindex ( 12) 5 0 5 0.1 K
% 119.78/119.98 clash ( 40) 0 0 0 0.0 K
% 119.78/119.98 di_tree ( 12) 86258992 74030517 12228475 143302.4 K
% 119.78/119.98 avl_node ( 20) 451971 431973 19998 390.6 K
% 119.78/119.98
% 119.78/119.98 Memory report, 20 @ 20 = 400 megs (400.00 megs used).
% 119.78/119.98 List 1, length 7, 0.0 K
% 119.78/119.98 List 2, length 1752, 13.7 K
% 119.78/119.98 List 3, length 5014155, 58759.6 K
% 119.78/119.98 List 4, length 9, 0.1 K
% 119.78/119.98 List 8, length 1298, 40.6 K
% 119.78/119.98 List 9, length 26, 0.9 K
% 119.78/119.98 List 10, length 4, 0.2 K
% 119.78/119.98 List 11, length 43, 1.8 K
% 119.78/119.98 List 12, length 54, 2.5 K
% 119.78/119.98 List 14, length 1, 0.1 K
% 119.78/119.98 List 15, length 2, 0.1 K
% 119.78/119.98 List 16, length 2451, 153.2 K
% 119.78/119.98 List 26, length 1270, 129.0 K
% 119.78/119.98 List 32, length 737, 92.1 K
% 119.78/119.98 List 64, length 140, 35.0 K
% 119.78/119.98 List 128, length 121, 60.5 K
% 119.78/119.98 List 202, length 2, 1.6 K
% 119.78/119.98 List 256, length 7, 7.0 K
% 119.78/119.98
% 119.78/119.98 ============================== SELECTOR REPORT =======================
% 119.78/119.98 Sos_deleted=744188, Sos_displaced=209270, Sos_size=9999
% 119.78/119.98 SELECTOR PART PRIORITY ORDER SIZE SELECTED
% 119.78/119.98 I 2147483647 high age 0 1541
% 119.78/119.98 H 1 high weight 0 0
% 119.78/119.98 A 1 low age 9999 526
% 119.78/119.98 F 4 low weight 189 2104
% 119.78/119.98 T 4 low weight 9810 2103
% 119.78/119.98 ============================== end of selector report ================
% 119.78/119.98
% 119.78/119.98 ============================== end of statistics =====================
% 119.78/119.98
% 119.78/119.98 Exiting with failure.
% 119.78/119.98
% 119.78/119.98 Process 18461 exit (max_megs) Sat Jul 2 09:30:52 2022
% 119.78/119.98 Prover9 interrupted
%------------------------------------------------------------------------------