TSTP Solution File: SWW472+6 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW472+6 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 01:17:08 EDT 2022
% Result : Unknown 129.14s 129.44s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW472+6 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 4 10:55:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.48/1.77 ============================== Prover9 ===============================
% 1.48/1.77 Prover9 (32) version 2009-11A, November 2009.
% 1.48/1.77 Process 16557 was started by sandbox on n020.cluster.edu,
% 1.48/1.77 Sat Jun 4 10:55:09 2022
% 1.48/1.77 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16404_n020.cluster.edu".
% 1.48/1.77 ============================== end of head ===========================
% 1.48/1.77
% 1.48/1.77 ============================== INPUT =================================
% 1.48/1.77
% 1.48/1.77 % Reading from file /tmp/Prover9_16404_n020.cluster.edu
% 1.48/1.77
% 1.48/1.77 set(prolog_style_variables).
% 1.48/1.77 set(auto2).
% 1.48/1.77 % set(auto2) -> set(auto).
% 1.48/1.77 % set(auto) -> set(auto_inference).
% 1.48/1.77 % set(auto) -> set(auto_setup).
% 1.48/1.77 % set(auto_setup) -> set(predicate_elim).
% 1.48/1.77 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.48/1.77 % set(auto) -> set(auto_limits).
% 1.48/1.77 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.48/1.77 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.48/1.77 % set(auto) -> set(auto_denials).
% 1.48/1.77 % set(auto) -> set(auto_process).
% 1.48/1.77 % set(auto2) -> assign(new_constants, 1).
% 1.48/1.77 % set(auto2) -> assign(fold_denial_max, 3).
% 1.48/1.77 % set(auto2) -> assign(max_weight, "200.000").
% 1.48/1.77 % set(auto2) -> assign(max_hours, 1).
% 1.48/1.77 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.48/1.77 % set(auto2) -> assign(max_seconds, 0).
% 1.48/1.77 % set(auto2) -> assign(max_minutes, 5).
% 1.48/1.77 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.48/1.77 % set(auto2) -> set(sort_initial_sos).
% 1.48/1.77 % set(auto2) -> assign(sos_limit, -1).
% 1.48/1.77 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.48/1.77 % set(auto2) -> assign(max_megs, 400).
% 1.48/1.77 % set(auto2) -> assign(stats, some).
% 1.48/1.77 % set(auto2) -> clear(echo_input).
% 1.48/1.77 % set(auto2) -> set(quiet).
% 1.48/1.77 % set(auto2) -> clear(print_initial_clauses).
% 1.48/1.77 % set(auto2) -> clear(print_given).
% 1.48/1.77 assign(lrs_ticks,-1).
% 1.48/1.77 assign(sos_limit,10000).
% 1.48/1.77 assign(order,kbo).
% 1.48/1.77 set(lex_order_vars).
% 1.48/1.77 clear(print_given).
% 1.48/1.77
% 1.48/1.77 % formulas(sos). % not echoed (617 formulas)
% 1.48/1.77
% 1.48/1.77 ============================== end of input ==========================
% 1.48/1.77
% 1.48/1.77 % From the command line: assign(max_seconds, 300).
% 1.48/1.77
% 1.48/1.77 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.48/1.77
% 1.48/1.77 % Formulas that are not ordinary clauses:
% 1.48/1.77 1 (all X_a all X_b (comm_monoid_add(X_b) -> ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),big_co1399186613setsum(X_a,X_b)) = big_co1399186613setsum(X_a,X_b))) # label(tsy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 2 (all X_a all X_b (comm_monoid_mult(X_b) -> ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),big_co302546470etprod(X_a,X_b)) = big_co302546470etprod(X_a,X_b))) # label(tsy_c_Big__Operators_Ocomm__monoid__mult__class_Osetprod_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 3 (all X_a (linorder(X_a) -> ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a)),big_Inf_fin(X_a)) = big_Inf_fin(X_a))) # label(tsy_c_Big__Operators_Olattice_OInf__fin_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 4 (all X_a (linorder(X_a) -> ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a)),big_Sup_fin(X_a)) = big_Sup_fin(X_a))) # label(tsy_c_Big__Operators_Olattice_OSup__fin_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 5 (all X_a (linorder(X_a) -> ti(fun(fun(X_a,bool),X_a),big_linorder_Max(X_a)) = big_linorder_Max(X_a))) # label(tsy_c_Big__Operators_Olinorder__class_OMax_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 6 (all X_a (linorder(X_a) -> ti(fun(fun(X_a,bool),X_a),big_linorder_Min(X_a)) = big_linorder_Min(X_a))) # label(tsy_c_Big__Operators_Olinorder__class_OMin_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 7 (all X_a ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool)),big_semilattice_big(X_a)) = big_semilattice_big(X_a)) # label(tsy_c_Big__Operators_Osemilattice__big_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 8 (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].
% 1.48/1.77 9 (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].
% 1.48/1.77 10 (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].
% 1.48/1.77 11 (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].
% 1.48/1.77 12 (all X_a ti(fun(X_a,fun(fun(vname,fun(fun(state,nat),X_a)),fun(fun(loc,fun(fun(state,nat),fun(com,X_a))),fun(fun(com,fun(com,X_a)),fun(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a))))))))),com_case(X_a)) = com_case(X_a)) # label(tsy_c_Com_Ocom_Ocom__case_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 13 (all X_a all X_b ti(fun(fun(X_a,fun(X_b,X_b)),bool),finite100568337ommute(X_a,X_b)) = finite100568337ommute(X_a,X_b)) # label(tsy_c_Finite__Set_Ocomp__fun__commute_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 14 (all X_a all X_b ti(fun(fun(X_a,fun(X_b,X_b)),bool),finite_comp_fun_idem(X_a,X_b)) = finite_comp_fun_idem(X_a,X_b)) # label(tsy_c_Finite__Set_Ocomp__fun__idem_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 15 (all X_a ti(fun(fun(X_a,bool),bool),finite_finite_1(X_a)) = finite_finite_1(X_a)) # label(tsy_c_Finite__Set_Ofinite_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 16 (all X_a all X_b ti(fun(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold(X_a,X_b)) = finite_fold(X_a,X_b)) # label(tsy_c_Finite__Set_Ofold_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 17 (all X_a ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a)),finite_fold1(X_a)) = finite_fold1(X_a)) # label(tsy_c_Finite__Set_Ofold1_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 18 (all X_a ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool))),finite_fold1Set(X_a)) = finite_fold1Set(X_a)) # label(tsy_c_Finite__Set_Ofold1Set_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 19 (all X_a all X_b ti(fun(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool)))),finite_fold_graph(X_a,X_b)) = finite_fold_graph(X_a,X_b)) # label(tsy_c_Finite__Set_Ofold__graph_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 20 (all X_a all X_b ti(fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)))),finite1357897459simple(X_a,X_b)) = finite1357897459simple(X_a,X_b)) # label(tsy_c_Finite__Set_Ofolding__image__simple_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 21 (all X_a all X_b ti(fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)))),finite908156982e_idem(X_a,X_b)) = finite908156982e_idem(X_a,X_b)) # label(tsy_c_Finite__Set_Ofolding__image__simple__idem_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 22 (all X_a ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool)),finite_folding_one(X_a)) = finite_folding_one(X_a)) # label(tsy_c_Finite__Set_Ofolding__one_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 23 (all X_a ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool)),finite2073411215e_idem(X_a)) = finite2073411215e_idem(X_a)) # label(tsy_c_Finite__Set_Ofolding__one__idem_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 24 (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].
% 1.48/1.77 25 (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_0_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 26 (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].
% 1.48/1.77 27 (all X_a (semiring(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_0_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 28 (all X_a (ab_semigroup_mult(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_1_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 29 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 30 (all X_a ti(fun(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool)),hoare_279057269derivs(X_a)) = hoare_279057269derivs(X_a)) # label(tsy_c_Hoare__Mirabelle__nrugjuseim_Ohoare__derivs_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 31 (all X_a ti(fun(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool)),hoare_2027193591valids(X_a)) = hoare_2027193591valids(X_a)) # label(tsy_c_Hoare__Mirabelle__nrugjuseim_Ohoare__valids_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 32 (all X_a ti(fun(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),hoare_246368825triple(X_a)) = hoare_246368825triple(X_a)) # label(tsy_c_Hoare__Mirabelle__nrugjuseim_Otriple_Otriple_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 33 (all X_b all X_a ti(fun(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a))),fun(hoare_1656922687triple(X_b),X_a)),hoare_1312322281e_case(X_b,X_a)) = hoare_1312322281e_case(X_b,X_a)) # label(tsy_c_Hoare__Mirabelle__nrugjuseim_Otriple_Otriple__case_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 34 (all X_b all X_a ti(fun(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a))),fun(hoare_1656922687triple(X_b),X_a)),hoare_1632998903le_rec(X_b,X_a)) = hoare_1632998903le_rec(X_b,X_a)) # label(tsy_c_Hoare__Mirabelle__nrugjuseim_Otriple_Otriple__rec_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 35 (all X_a all X_b ti(fun(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool)))),fold_graph(X_a,X_b)) = fold_graph(X_a,X_b)) # label(tsy_c_Nitpick_Ofold__graph_H_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 36 (all X_a (bot(X_a) -> ti(X_a,bot_bot(X_a)) = bot_bot(X_a))) # label(tsy_c_Orderings_Obot__class_Obot_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 37 (all X_a (ord(X_a) -> ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a))),max(X_a)) = max(X_a))) # label(tsy_c_Orderings_Oord_Omax_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 38 (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].
% 1.48/1.77 39 (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].
% 1.48/1.77 40 (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].
% 1.48/1.77 41 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,X_a)),ord_max(X_a)) = ord_max(X_a))) # label(tsy_c_Orderings_Oord__class_Omax_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 42 (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].
% 1.48/1.77 43 (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].
% 1.48/1.77 44 (all X_a ti(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),insert(X_a)) = insert(X_a)) # label(tsy_c_Set_Oinsert_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 45 (all X_a ti(fun(fun(X_a,bool),X_a),the_elem(X_a)) = the_elem(X_a)) # label(tsy_c_Set_Othe__elem_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 46 (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].
% 1.48/1.77 47 (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].
% 1.48/1.77 48 (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].
% 1.48/1.77 49 (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].
% 1.48/1.77 50 (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].
% 1.48/1.77 51 (all X_a ti(fun(X_a,fun(fun(X_a,bool),bool)),member(X_a)) = member(X_a)) # label(tsy_c_member_res) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 52 (all X_a all G_2 hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),bot_bot(fun(hoare_1656922687triple(X_a),bool))))) # label(fact_0_empty) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 53 (all X_a all Fun1_1 all Com_1 all Fun2_1 all Fun1_2 all Com_2 all Fun2_2 (hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),Fun1_1),Com_1),Fun2_1) = hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),Fun1_2),Com_2),Fun2_2) <-> Fun1_1 = Fun1_2 & Com_1 = Com_2 & Fun2_1 = Fun2_2)) # label(fact_1_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 54 (all X_a all G_2 all Ts (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),Ts)) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_2027193591valids(X_a),G_2),Ts)))) # label(fact_2_hoare__sound) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 55 (all X_a all G_2 all G_1 all Ts (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),Ts)) -> (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),G_1)) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),Ts))))) # label(fact_3_cut) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 56 (all X_a all Ts all G_2 all T_3 (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),T_3),bot_bot(fun(hoare_1656922687triple(X_a),bool))))) -> (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),Ts)) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),T_3),Ts)))))) # label(fact_4_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 57 (all X_a all G_2 all T_3 all Ts (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),T_3),Ts))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),T_3),bot_bot(fun(hoare_1656922687triple(X_a),bool))))) & hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),Ts)))) # label(fact_5_derivs__insertD) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 58 (all X_a all Qa all G_2 all Pa all Ca all Q_2 (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),Pa),Ca),Q_2)),bot_bot(fun(hoare_1656922687triple(X_a),bool))))) -> ((all Z_3 all S (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Q_2,Z_3),S)) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Qa,Z_3),S)))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),Pa),Ca),Qa)),bot_bot(fun(hoare_1656922687triple(X_a),bool)))))))) # label(fact_6_conseq2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 59 (all X_a all Pa all G_2 all P_2 all Ca all Qa (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),P_2),Ca),Qa)),bot_bot(fun(hoare_1656922687triple(X_a),bool))))) -> ((all Z_3 all S (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Pa,Z_3),S)) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),P_2,Z_3),S)))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),Pa),Ca),Qa)),bot_bot(fun(hoare_1656922687triple(X_a),bool)))))))) # label(fact_7_conseq1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 60 (all X_a all A_1 all B all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),A_2))) -> (ti(X_a,A_1) != ti(X_a,B) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2))))) # label(fact_8_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 61 (all X_a all B all A_1 all B_1 ((-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),B_1)) -> ti(X_a,A_1) = ti(X_a,B)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),B_1))))) # label(fact_9_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 62 (all X_a all Qa all Pa all G_2 all P_2 all Ca all Q_2 (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),P_2),Ca),Q_2)),bot_bot(fun(hoare_1656922687triple(X_a),bool))))) -> ((all Z_3 all S (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Pa,Z_3),S)) -> (all S_1 ((all Z_4 (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),P_2,Z_4),S)) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Q_2,Z_4),S_1)))) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Qa,Z_3),S_1)))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),Pa),Ca),Qa)),bot_bot(fun(hoare_1656922687triple(X_a),bool)))))))) # label(fact_10_conseq12) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 63 (all X_a all A_1 -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),bot_bot(fun(X_a,bool))))) # label(fact_11_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 64 (all X_b all X_a all F1 all Fun1_1 all Com_1 all Fun2_1 hAPP(hoare_1656922687triple(X_b),X_a,hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a))),fun(hoare_1656922687triple(X_b),X_a),hoare_1632998903le_rec(X_b,X_a),F1),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Fun1_1),Com_1),Fun2_1)) = hAPP(fun(X_b,fun(state,bool)),X_a,hAPP(com,fun(fun(X_b,fun(state,bool)),X_a),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a)),F1,Fun1_1),Com_1),Fun2_1)) # label(fact_12_triple_Orecs) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 65 (all X_b all X_a all F1 all Fun1_1 all Com_1 all Fun2_1 hAPP(hoare_1656922687triple(X_b),X_a,hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a))),fun(hoare_1656922687triple(X_b),X_a),hoare_1312322281e_case(X_b,X_a),F1),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Fun1_1),Com_1),Fun2_1)) = hAPP(fun(X_b,fun(state,bool)),X_a,hAPP(com,fun(fun(X_b,fun(state,bool)),X_a),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a)),F1,Fun1_1),Com_1),Fun2_1)) # label(fact_13_triple_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 66 (all X_a all A_1 all A_2 bot_bot(fun(X_a,bool)) != hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2)) # label(fact_14_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 67 (all X_a all A_1 all A_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2) != bot_bot(fun(X_a,bool))) # label(fact_15_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 68 (all X_a all B all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))))) <-> ti(X_a,B) = ti(X_a,A_1))) # label(fact_16_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 69 (all X_a all A_1 all B all Ca all D (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),bot_bot(fun(X_a,bool)))) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),D),bot_bot(fun(X_a,bool)))) <-> ti(X_a,A_1) = ti(X_a,Ca) & ti(X_a,B) = ti(X_a,D) | ti(X_a,A_1) = ti(X_a,D) & ti(X_a,B) = ti(X_a,Ca))) # label(fact_17_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 70 (all X_a all A_1 all A_2 (ti(fun(X_a,bool),A_2) = bot_bot(fun(X_a,bool)) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)))) # label(fact_18_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 71 (all X_a all Pa (hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa) = bot_bot(fun(X_a,bool)) <-> (all X_1 -hBOOL(hAPP(X_a,bool,Pa,X_1))))) # label(fact_19_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 72 (all X_a all Ca -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),bot_bot(fun(X_a,bool))))) # label(fact_20_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 73 (all X_a all Pa (bot_bot(fun(X_a,bool)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa) <-> (all X_1 -hBOOL(hAPP(X_a,bool,Pa,X_1))))) # label(fact_21_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 74 (all X_a all A_2 ((exists 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))) <-> ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)))) # label(fact_22_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 75 (all X_a all A_2 ((all 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))) <-> ti(fun(X_a,bool),A_2) = bot_bot(fun(X_a,bool)))) # label(fact_23_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 76 (all X_a bot_bot(fun(X_a,bool)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(bool,fun(X_a,bool),combk(bool,X_a),fFalse))) # label(fact_24_empty__def) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 77 (all X_a all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2) = ti(fun(X_a,bool),A_2))) # label(fact_25_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 78 (all X_a all B all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),B_1))))) # label(fact_26_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 79 (all X_a all B_1 all X_2 all A_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)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),B_1) <-> ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_1))))) # label(fact_27_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 80 (all X_a all Y_2 all A_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_2),A_2),X_2)) <-> ti(X_a,Y_2) = ti(X_a,X_2) | hBOOL(hAPP(X_a,bool,A_2,X_2)))) # label(fact_28_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 81 (all X_a all A_1 all B all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),A_2))) <-> ti(X_a,A_1) = ti(X_a,B) | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)))) # label(fact_29_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 82 (all X_a all X_2 all Y_2 all A_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_2),A_2)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2))) # label(fact_30_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 83 (all X_a all X_2 all A_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) # label(fact_31_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 84 (all X_a all A_1 all Pa hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa)) = 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),fimplies),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)),A_1)))),Pa))) # label(fact_32_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 85 (all X_a all A_1 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),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),fdisj),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)),A_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_1)))) # label(fact_33_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 86 (all X_a all A_1 all B_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),B_1)))) # label(fact_34_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 87 (all X_a all A_1 all B (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),bot_bot(fun(X_a,bool))) -> ti(X_a,A_1) = ti(X_a,B))) # label(fact_35_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 88 (all X_a all B all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))))) -> ti(X_a,B) = ti(X_a,A_1))) # label(fact_36_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 89 (all X_a all X_2 hAPP(fun(X_a,bool),X_a,the_elem(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = ti(X_a,X_2)) # label(fact_37_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 90 (all X_b all X_a (bot(X_a) -> (all X_2 hAPP(X_b,X_a,bot_bot(fun(X_b,X_a)),X_2) = bot_bot(X_a)))) # label(fact_38_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 91 (all X_a all X_b (bot(X_b) -> (all X_1 hAPP(X_a,X_b,bot_bot(fun(X_a,X_b)),X_1) = bot_bot(X_b)))) # label(fact_39_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 92 (all X_a all G_2 all Pa hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),Pa),skip),Pa)),bot_bot(fun(hoare_1656922687triple(X_a),bool)))))) # label(fact_40_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 93 (all X_a all D all R_1 all G_2 all Pa all Ca all Qa (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),Pa),Ca),Qa)),bot_bot(fun(hoare_1656922687triple(X_a),bool))))) -> (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),Qa),D),R_1)),bot_bot(fun(hoare_1656922687triple(X_a),bool))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),Pa),hAPP(com,com,hAPP(com,fun(com,com),semi,Ca),D)),R_1)),bot_bot(fun(hoare_1656922687triple(X_a),bool)))))))) # label(fact_41_Comp) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 94 (all X_a all Y_2 -(all Fun1 all Com all Fun2 Y_2 != hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),Fun1),Com),Fun2))) # label(fact_42_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 95 (all X_a all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> -(all B_4 (ti(fun(X_a,bool),A_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),B_4) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B_4)))))) # label(fact_43_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 96 (all X_a all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> (exists B_4 (ti(fun(X_a,bool),A_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),B_4) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),B_4)))))) # label(fact_44_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 97 (all X_a all A_2 ((all Y_1 -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_2))) -> ti(fun(X_a,bool),A_2) = bot_bot(fun(X_a,bool)))) # label(fact_45_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 98 (all X_a all Qa all G_2 all Ca all Pa ((all Z_3 all S (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Pa,Z_3),S)) -> (exists P_1 exists Q_1 (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),P_1),Ca),Q_1)),bot_bot(fun(hoare_1656922687triple(X_a),bool))))) & (all S_1 ((all Z_4 (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),P_1,Z_4),S)) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Q_1,Z_4),S_1)))) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Qa,Z_3),S_1)))))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),Pa),Ca),Qa)),bot_bot(fun(hoare_1656922687triple(X_a),bool))))))) # label(fact_46_conseq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 99 (all X_a all A_2 (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) <-> (exists X_1 exists B_4 (ti(fun(X_a,bool),A_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),B_4) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_4)))))) # label(fact_47_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 100 (all Com1_2 all Com2_2 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2) != skip) # label(fact_48_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 101 (all Com1_2 all Com2_2 skip != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2)) # label(fact_49_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 102 (all Com1 all Com2 all Com1_1 all Com2_1 (hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2) = hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1) <-> Com1 = Com1_1 & Com2 = Com2_1)) # label(fact_50_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 103 (all X_a all F all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool)),finite_fold1Set(X_a),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool)))),B)) <-> ti(X_a,A_1) = ti(X_a,B))) # label(fact_51_fold1Set__sing) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 104 (all X_a all X_2 all F all F_1 (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),F_1)) -> hAPP(fun(X_a,bool),X_a,F_1,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = ti(X_a,X_2))) # label(fact_52_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 105 (all X_a all X_1 (hBOOL(hAPP(X_a,bool,bot_bot(fun(X_a,bool)),X_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),bot_bot(fun(X_a,bool)))))) # label(fact_53_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 106 (all X_a all F all A_1 hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool)))) = ti(X_a,A_1)) # label(fact_54_fold1__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 107 (all X_a all A_1 all G all F (G = hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),F) -> hAPP(fun(X_a,bool),X_a,G,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool)))) = ti(X_a,A_1))) # label(fact_55_fold1__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 108 (all X_a all F all X_2 -hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool)),finite_fold1Set(X_a),F),bot_bot(fun(X_a,bool))),X_2))) # label(fact_56_empty__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 109 (all X_a all F all A_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool)),finite_fold1Set(X_a),F),A_2),X_2)) -> ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)))) # label(fact_57_fold1Set__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.77 110 (all X_a all F all A_1 all A_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),finite_fold_graph(X_a,X_a),F),A_1),A_2),X_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool)),finite_fold1Set(X_a),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2)),X_2))))) # label(fact_58_fold1Set_Ointros) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 111 (all X_a all X_2 all A_2 all F all F_1 (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),F_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,F_1,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),hAPP(fun(X_a,bool),X_a,F_1,A_2))))))) # label(fact_59_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 112 (all X_a all A_2 all F all F_1 (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),F_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_a,F_1,A_2) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),F),A_2)))) # label(fact_60_folding__one_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 113 (all X_a all A_2 all F all F_1 (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),F_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> ((all X_1 all Y_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_1),Y_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_1),bot_bot(fun(X_a,bool))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(fun(X_a,bool),X_a,F_1,A_2)),A_2))))))) # label(fact_61_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 114 (all X_a all F1 all F2 all F3 all F4 all F5 all F6 all F7 all F8 hAPP(com,X_a,hAPP(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a),hAPP(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a)),hAPP(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a))),hAPP(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a)))),hAPP(fun(com,fun(com,X_a)),fun(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a))))),hAPP(fun(loc,fun(fun(state,nat),fun(com,X_a))),fun(fun(com,fun(com,X_a)),fun(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a)))))),hAPP(fun(vname,fun(fun(state,nat),X_a)),fun(fun(loc,fun(fun(state,nat),fun(com,X_a))),fun(fun(com,fun(com,X_a)),fun(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a))))))),hAPP(X_a,fun(fun(vname,fun(fun(state,nat),X_a)),fun(fun(loc,fun(fun(state,nat),fun(com,X_a))),fun(fun(com,fun(com,X_a)),fun(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a)))))))),com_case(X_a),F1),F2),F3),F4),F5),F6),F7),F8),skip) = ti(X_a,F1)) # label(fact_62_com_Osimps_I64_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 115 (all X_a all F1 all F2 all F3 all F4 all F5 all F6 all F7 all F8 all Com1 all Com2 hAPP(com,X_a,hAPP(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a),hAPP(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a)),hAPP(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a))),hAPP(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a)))),hAPP(fun(com,fun(com,X_a)),fun(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a))))),hAPP(fun(loc,fun(fun(state,nat),fun(com,X_a))),fun(fun(com,fun(com,X_a)),fun(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a)))))),hAPP(fun(vname,fun(fun(state,nat),X_a)),fun(fun(loc,fun(fun(state,nat),fun(com,X_a))),fun(fun(com,fun(com,X_a)),fun(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a))))))),hAPP(X_a,fun(fun(vname,fun(fun(state,nat),X_a)),fun(fun(loc,fun(fun(state,nat),fun(com,X_a))),fun(fun(com,fun(com,X_a)),fun(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a)))))))),com_case(X_a),F1),F2),F3),F4),F5),F6),F7),F8),hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2)) = hAPP(com,X_a,hAPP(com,fun(com,X_a),F4,Com1),Com2)) # label(fact_63_com_Osimps_I67_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 116 (all X_a all F all A_1 all X_3 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool)),finite_fold1Set(X_a),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),X_3)),X_2)) -> -(all A_5 all A_4 (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),X_3) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_5),A_4) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),finite_fold_graph(X_a,X_a),F),A_5),A_4),X_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_5),A_4))))))) # label(fact_64_insert__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 117 (all X_a all A_2 all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))) -> ti(fun(X_a,bool),A_2) = bot_bot(fun(X_a,bool)) | ti(fun(X_a,bool),A_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))) # label(fact_65_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 118 (all X_b all X_a all F all Z_1 all G all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z_1),G),F_1)) -> hAPP(fun(X_b,bool),X_a,F_1,bot_bot(fun(X_b,bool))) = ti(X_a,Z_1))) # label(fact_66_folding__image__simple_Oempty) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 119 (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_67_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 120 (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_68_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 121 (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_69_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 122 (all X_a hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),bot_bot(fun(X_a,bool))))) # label(fact_70_finite_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 123 (all X_a all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2))))) # label(fact_71_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 124 (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)),bot_bot(fun(X_a,bool))),A_2))) # label(fact_72_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 125 (all X_a all Qa all Pa all X_2 (hBOOL(hAPP(X_a,bool,Pa,X_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),Pa),Qa)) -> hBOOL(hAPP(X_a,bool,Qa,X_2))))) # label(fact_73_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 126 (all X_a all X_2 all Pa all Qa (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),Qa)) -> (hBOOL(hAPP(X_a,bool,Pa,X_2)) -> hBOOL(hAPP(X_a,bool,Qa,X_2))))) # label(fact_74_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 127 (all X_a all X_b all F all G ((all X_1 hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,G,X_1)) -> ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G))) # label(fact_75_ext) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 128 (all X_a all X_2 all A_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(X_a,bool,A_2,X_2)))) # label(fact_76_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 129 (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].
% 1.48/1.78 130 (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_78_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 131 (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_79_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 132 (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_80_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 133 (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_81_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 134 (all X_a all X_2 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_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))))) # label(fact_82_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 135 (all X_a all B_1 all X_2 all A_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(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_2),B_1))))) # label(fact_83_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 136 (all X_a all X_2 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_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))))) # label(fact_84_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 137 (all X_a all C 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)) -> 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))))) # label(fact_85_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 138 (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_86_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 139 (all X_a (finite_finite(X_a) -> (all A_2 hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2))))) # label(fact_87_finite) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 140 (all X_a (finite_finite(X_a) -> (all A_2 hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2))))) # label(fact_88_finite__code) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 141 (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_1 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_89_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 142 (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_90_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 143 (all X_a (order(X_a) -> (all X_2 all Y_2 (ti(X_a,X_2) = ti(X_a,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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_2)))))) # label(fact_91_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 144 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),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,finite_finite_1(X_a),A_2))))) # label(fact_92_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 145 (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_93_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 146 (all X_a all X_b (ord(X_b) -> (all X_2 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_2)),hAPP(X_a,X_b,G,X_2))))))) # label(fact_94_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 147 (all X_a (order(X_a) -> (all Y_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) <-> ti(X_a,X_2) = ti(X_a,Y_2)))))) # label(fact_95_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 148 (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,finite_finite_1(X_a),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2))))) # label(fact_96_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 149 (all X_a (ord(X_a) -> (all C_1 all A_3 all B_3 (ti(X_a,A_3) = ti(X_a,B_3) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_3),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),C_1))))))) # label(fact_97_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 150 (all X_a (order(X_a) -> (all C_1 all A_3 all B_3 (ti(X_a,A_3) = ti(X_a,B_3) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),B_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_3))))))) # label(fact_98_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 151 (all X_a (ord(X_a) -> (all C_1 all A_3 all B_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_3)) -> (ti(X_a,B_3) = ti(X_a,C_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),C_1))))))) # label(fact_99_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 152 (all X_a (order(X_a) -> (all C_1 all B_3 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_3),A_3)) -> (ti(X_a,B_3) = ti(X_a,C_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_3))))))) # label(fact_100_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 153 (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_101_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 154 (all X_a (preorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z))))))) # label(fact_102_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 155 (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_103_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 156 (all X_a (order(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X))))))) # label(fact_104_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 157 (all X_a all X_b (ord(X_b) -> (all X_2 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_2)),hAPP(X_a,X_b,G,X_2))))))) # label(fact_105_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 158 (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_106_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 159 (all X_b all X_a all X_2 all A_2 all F all Z_1 all G all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z_1),G),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_2)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_2)) -> hAPP(fun(X_b,bool),X_a,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_b,X_a,G,X_2)),hAPP(fun(X_b,bool),X_a,F_1,A_2)))))) # label(fact_107_folding__image__simple_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 160 (all X_a (bot(X_a) -> (all A_3 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),bot_bot(X_a)),A_3))))) # label(fact_108_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 161 (all X_a (bot(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),bot_bot(X_a))) <-> ti(X_a,A_1) = bot_bot(X_a))))) # label(fact_109_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 162 (all X_a (bot(X_a) -> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),bot_bot(X_a))) -> ti(X_a,A_3) = bot_bot(X_a))))) # label(fact_110_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 163 (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),bot_bot(fun(X_a,bool)))) <-> ti(fun(X_a,bool),A_2) = bot_bot(fun(X_a,bool)))) # label(fact_111_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 164 (all X_a all B_1 all A_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),B_1)))) # label(fact_112_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 165 (all X_a all X_2 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(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)),B_1)) <-> 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_113_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 166 (all X_a all B_1 all X_2 all A_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(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(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_114_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 167 (all X_a all B 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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),B_1))))) # label(fact_115_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 168 (all X_a all A_1 all C all D_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)),C),D_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(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),C)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),D_2))))) # label(fact_116_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 169 (all X_a all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)))) # label(fact_117_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 170 (all X_a all Ts all G_2 (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),ord_less_eq(fun(hoare_1656922687triple(X_a),bool)),Ts),G_2)) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),Ts)))) # label(fact_118_asm) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 171 (all X_a all Ts all G_2 all Ts_1 (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),Ts_1)) -> (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),ord_less_eq(fun(hoare_1656922687triple(X_a),bool)),Ts),Ts_1)) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),Ts))))) # label(fact_119_weaken) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 172 (all X_a all G_2 all G_1 all Ts (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),Ts)) -> (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),ord_less_eq(fun(hoare_1656922687triple(X_a),bool)),G_1),G_2)) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),Ts))))) # label(fact_120_thin) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 173 (all X_b all X_a all F all Z_1 hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F),Z_1),bot_bot(fun(X_a,bool))),Z_1))) # label(fact_121_fold__graph_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 174 (all X_b all X_a all F all Z_1 all X_2 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F),Z_1),bot_bot(fun(X_a,bool))),X_2)) -> ti(X_b,X_2) = ti(X_b,Z_1))) # label(fact_122_empty__fold__graphE) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 175 (all X_b all X_a all F all Z_1 all Y_2 all X_2 all A_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(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F),Z_1),A_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F),Z_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)),hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),Y_2)))))) # label(fact_123_fold__graph_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 176 (all X_a all Pa all A_2 all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_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)),F_1),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,Pa,bot_bot(fun(X_a,bool)))) -> ((all A_5 all F_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_5),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_5),F_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,Pa,F_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,Pa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_5),F_2)))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,Pa,F_1))))))) # label(fact_124_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 177 (all X_a all F all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> (exists X1 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool)),finite_fold1Set(X_a),F),A_2),X1)))))) # label(fact_125_finite__nonempty__imp__fold1Set) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 178 (all X_a all B_1 all A_2 ((all 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)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),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_126_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 179 (all X_a all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) <-> ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)) | (exists A_4 exists A_5 (ti(fun(X_a,bool),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_5),A_4) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_4)))))) # label(fact_127_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 180 (all X_a all Pa all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,Pa,bot_bot(fun(X_a,bool)))) -> ((all X_1 all F_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),F_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,Pa,F_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,Pa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),F_2))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,Pa,F_1)))))) # label(fact_128_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 181 (all X_b all X_a all A_2 all F all Z_1 all G all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z_1),G),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_2)) -> ((all X_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_2)) -> hAPP(X_b,X_a,G,X_1) = ti(X_a,Z_1))) -> hAPP(fun(X_b,bool),X_a,F_1,A_2) = ti(X_a,Z_1))))) # label(fact_129_folding__image__simple_Oneutral) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 182 (all X_b all X_a all F all Z_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (exists X1 hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F),Z_1),A_2),X1))))) # label(fact_130_finite__imp__fold__graph) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 183 (all X_a all X_b (ord(X_b) -> (all F all G ((all X_1 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)))) -> 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_131_le__funI) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 184 (all X_a all F all A1 all A2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool)),finite_fold1Set(X_a),F),A1),A2)) <-> (exists A_5 exists A_4 exists X_1 (ti(fun(X_a,bool),A1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_5),A_4) & ti(X_a,A2) = ti(X_a,X_1) & hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),finite_fold_graph(X_a,X_a),F),A_5),A_4),X_1)) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_5),A_4)))))) # label(fact_132_fold1Set_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 185 (all X_b all X_a all F all Z_1 all A1 all A2 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F),Z_1),A1),A2)) <-> ti(fun(X_a,bool),A1) = bot_bot(fun(X_a,bool)) & ti(X_b,A2) = ti(X_b,Z_1) | (exists X_1 exists A_4 exists Y_1 (ti(fun(X_a,bool),A1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),A_4) & ti(X_b,A2) = hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_1),Y_1) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_4)) & hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F),Z_1),A_4),Y_1)))))) # label(fact_133_fold__graph_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 186 (all X_a all B_1 all A_2 all F all F_1 (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F),F_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> (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)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_a,bool),X_a,F_1,B_1)),hAPP(fun(X_a,bool),X_a,F_1,A_2)) = hAPP(fun(X_a,bool),X_a,F_1,A_2)))))) # label(fact_134_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 187 (all X_a all X_2 all A_2 all F all F_1 (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F),F_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,F_1,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),hAPP(fun(X_a,bool),X_a,F_1,A_2)))))) # label(fact_135_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 188 (all X_a all Pa all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_1)) -> (ti(fun(X_a,bool),F_1) != bot_bot(fun(X_a,bool)) -> ((all X_1 hBOOL(hAPP(fun(X_a,bool),bool,Pa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),bot_bot(fun(X_a,bool)))))) -> ((all X_1 all F_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_2)) -> (ti(fun(X_a,bool),F_2) != bot_bot(fun(X_a,bool)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),F_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,Pa,F_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,Pa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),F_2)))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,Pa,F_1))))))) # label(fact_136_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 189 (all X_b all X_a all B_1 all A_2 all F all Z_1 all G all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z_1),G),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_1),A_2)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,F_1,B_1)),hAPP(fun(X_b,bool),X_a,F_1,A_2)) = hAPP(fun(X_b,bool),X_a,F_1,A_2))))) # label(fact_137_folding__image__simple__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 190 (all X_b all X_a all X_2 all A_2 all F all Z_1 all G all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z_1),G),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_2)) -> hAPP(fun(X_b,bool),X_a,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_b,X_a,G,X_2)),hAPP(fun(X_b,bool),X_a,F_1,A_2))))) # label(fact_138_folding__image__simple__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 191 (all X_a all Qa all Pa ((all X_1 (hBOOL(hAPP(X_a,bool,Pa,X_1)) -> hBOOL(hAPP(X_a,bool,Qa,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(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Qa))))) # label(fact_139_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 192 (all X_b all X_a all X_2 all F all Z_1 all G all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z_1),G),F_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),X_2) = ti(X_a,X_2))) # label(fact_140_folding__image__simple__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 193 (all X_a all X_2 all F all F_1 (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F),F_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),X_2) = ti(X_a,X_2))) # label(fact_141_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 194 (all X_a all X_2 all A_2 all F all F_1 (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F),F_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),hAPP(fun(X_a,bool),X_a,F_1,A_2)) = hAPP(fun(X_a,bool),X_a,F_1,A_2))))) # label(fact_142_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 195 (all X_b all X_a all X_2 all A_2 all F all Z_1 all G all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z_1),G),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_2)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_b,X_a,G,X_2)),hAPP(fun(X_b,bool),X_a,F_1,A_2)) = hAPP(fun(X_b,bool),X_a,F_1,A_2))))) # label(fact_143_folding__image__simple__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 196 (all X_a all Qa all Pa ((all X_1 (hBOOL(hAPP(X_a,bool,Pa,X_1)) -> hBOOL(hAPP(X_a,bool,Qa,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),Qa)))) # label(fact_144_predicate1I) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 197 (all X_b all X_a (order(X_a) & order(X_b) -> (all Ca all F all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),hAPP(X_a,X_b,F,B))) -> ((all X_1 all Y_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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Y_1)),hAPP(X_a,X_b,F,X_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),hAPP(X_a,X_b,F,A_1))))))))) # label(fact_145_xt3) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 198 (all X_a (order(X_a) -> (all F all Ca 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)) -> (hAPP(X_a,X_a,F,B) = ti(X_a,Ca) -> ((all X_1 all Y_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),hAPP(X_a,X_a,F,Y_1)),hAPP(X_a,X_a,F,X_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),hAPP(X_a,X_a,F,A_1))))))))) # label(fact_146_xt1_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 199 (all X_a all X_b (ord(X_b) & ord(X_a) -> (all F all Ca 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)) -> (hAPP(X_a,X_b,F,B) = ti(X_b,Ca) -> ((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_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,F,Y_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,A_1)),Ca)))))))) # label(fact_147_ord__le__eq__subst) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 200 (all X_a all X_b (order(X_b) & order(X_a) -> (all F all Ca 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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,B)),Ca)) -> ((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_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,F,Y_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,A_1)),Ca)))))))) # label(fact_148_order__subst2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 201 (all X_a all X_b (ord(X_b) & ord(X_a) -> (all Ca all A_1 all F all B (ti(X_a,A_1) = hAPP(X_b,X_a,F,B) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B),Ca)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_1)),hAPP(X_b,X_a,F,Y_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),hAPP(X_b,X_a,F,Ca))))))))) # label(fact_149_ord__eq__le__subst) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 202 (all X_b all X_a (order(X_a) & ord(X_b) -> (all Ca all F all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,B)),A_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),B)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Y_1)),hAPP(X_b,X_a,F,X_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Ca)),A_1)))))))) # label(fact_150_xt2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 203 (all X_a (order(X_a) -> (all Ca all A_1 all F all B (ti(X_a,A_1) = hAPP(X_a,X_a,F,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),B)) -> ((all X_1 all Y_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),hAPP(X_a,X_a,F,Y_1)),hAPP(X_a,X_a,F,X_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,F,Ca)),A_1)))))))) # label(fact_151_xt1_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 204 (all X_a all X_b (order(X_b) & order(X_a) -> (all Ca all A_1 all F all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),hAPP(X_b,X_a,F,B))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B),Ca)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_1)),hAPP(X_b,X_a,F,Y_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),hAPP(X_b,X_a,F,Ca))))))))) # label(fact_152_order__subst1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 205 (all X_a all A_2 all F all F_1 (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),big_semilattice_big(X_a),F),F_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_a,F_1,A_2) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),F),A_2)))) # label(fact_153_semilattice__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 206 (all X_a all X_2 all A_2 all F all F_1 (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),F_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,F_1,A_2) = ti(X_a,X_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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,F_1,A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),hAPP(fun(X_a,bool),X_a,F_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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))))))))) # label(fact_154_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 207 (all X_a all X_2 all A_2 all F all F_1 (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),F_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,F_1,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = ti(X_a,X_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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,F_1,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),hAPP(fun(X_a,bool),X_a,F_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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))))))) # label(fact_155_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 208 (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_156_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 209 (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_157_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 210 (all X_a all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),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_158_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 211 (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_159_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 212 (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_160_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 213 (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_161_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 214 (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_162_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 215 (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_163_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 216 (all X_a all A_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)),bot_bot(fun(X_a,bool))),A_2) = bot_bot(fun(X_a,bool))) # label(fact_164_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 217 (all X_a all A_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)),A_2),bot_bot(fun(X_a,bool))) = ti(fun(X_a,bool),A_2)) # label(fact_165_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 218 (all X_a all A_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)),A_2),A_2) = bot_bot(fun(X_a,bool))) # label(fact_166_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 219 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),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,finite_finite_1(X_a),A_2))))) # label(fact_167_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 220 (all X_a all A_2 all X_2 all B_1 ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_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)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),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)),A_2),B_1)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_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)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)),B_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_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)),A_2),B_1))))) # label(fact_168_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 221 (all X_a all A_2 all X_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_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)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),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)),A_2),B_1))) # label(fact_169_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 222 (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_170_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 223 (all X_a all D_2 all B_1 all A_2 all C (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),C)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),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),D_2)))))) # label(fact_171_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 224 (all X_a all C 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)) -> 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),A_2)) = ti(fun(X_a,bool),A_2)))) # label(fact_172_double__diff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 225 (all X_a all A_2 all A_1 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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_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)),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(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))))) # label(fact_173_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 226 (all X_a all A_2 all A_1 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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_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)),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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))))),B_1)) # label(fact_174_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 227 (all X_a all A_1 all A_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))))) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2)) # label(fact_175_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 228 (all X_a all X_2 all A_2 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_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)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = ti(fun(X_a,bool),A_2))) # label(fact_176_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 229 (all X_a all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))))) = ti(fun(X_a,bool),A_2))) # label(fact_177_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 230 (all X_a all A_2 all A_1 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),B_1)))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),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_178_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 231 (all X_a all A_2 all X_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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),B_1))) <-> (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(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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))),B_1))) & (-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(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1))))) # label(fact_179_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 232 (all X_a all A_2 all X_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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))),B_1)) -> (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(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),B_1)))))) # label(fact_180_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 233 (all X_b all X_a all X_2 all A_2 all F all Z_1 all G all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z_1),G),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_2)) -> hAPP(fun(X_b,bool),X_a,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_b,X_a,G,X_2)),hAPP(fun(X_b,bool),X_a,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool))))))))) # label(fact_181_folding__image__simple_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 234 (all X_b all X_a all X_2 all A_2 all F all Z_1 all G all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z_1),G),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_2)) -> hAPP(fun(X_b,bool),X_a,F_1,A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_b,X_a,G,X_2)),hAPP(fun(X_b,bool),X_a,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))))))))) # label(fact_182_folding__image__simple_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 235 (all X_a all Pa all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,Pa,A_2)) -> ((all A_5 all A_4 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_4)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_5),A_4)) -> (hBOOL(hAPP(fun(X_a,bool),bool,Pa,A_4)) -> hBOOL(hAPP(fun(X_a,bool),bool,Pa,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_4),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_5),bot_bot(fun(X_a,bool)))))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,Pa,bot_bot(fun(X_a,bool)))))))) # label(fact_183_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 236 (all X_b all X_a (minus(X_a) -> (all A_2 all B_1 all X_2 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_2) = 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_2)),hAPP(X_b,X_a,B_1,X_2))))) # label(fact_184_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 237 (all X_a all X_b (minus(X_b) -> (all A_2 all B_1 all X_1 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_1) = 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_1)),hAPP(X_a,X_b,B_1,X_1))))) # label(fact_185_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.78 238 (all X_a (ordered_ab_group_add(X_a) -> (all A_1 all B all Ca all D (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B) = 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),A_1),B)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),D))))))) # label(fact_186_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 239 (all X_a (linorder(X_a) -> (all B_1 all A_2 (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> (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,finite_finite_1(X_a),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),ord_min(X_a)),B_1)),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),ord_min(X_a)),A_2))))))))) # label(fact_187_fold1__antimono) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 240 (all X_a all X_b all A_1 all Z_1 all A_2 all Y_2 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite100568337ommute(X_a,X_b),F)) -> (hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F),Z_1),A_2),Y_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> (exists Y_3 (ti(X_b,Y_2) = hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,A_1),Y_3) & hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F),Z_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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))))),Y_3)))))))) # label(fact_188_comp__fun__commute_Ofold__graph__insertE__aux) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 241 (all X_a (ordered_ab_group_add(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z))))) # label(fact_189_min__diff__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 242 (all X_a (linorder(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),X) = ti(X_a,X)))) # label(fact_190_Min_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 243 (all X_a all X_b all X_2 all Y_2 all Z_1 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite100568337ommute(X_a,X_b),F)) -> hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,Y_2),Z_1)) = hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,Y_2),hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),Z_1)))) # label(fact_191_comp__fun__commute_Ofun__left__comm) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 244 (all X_a (linorder(X_a) -> (all A_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),A_3) = ti(X_a,A_3)))) # label(fact_192_min__max_Oinf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 245 (all X_a (linorder(X_a) -> (all A_3 all B_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),B_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B_3),A_3)))) # label(fact_193_min__max_Oinf_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 246 (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_194_min__max_Oinf__commute) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 247 (all X_a (linorder(X_a) -> (all A_3 all B_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),B_3)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),B_3)))) # label(fact_195_min__max_Oinf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 248 (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_196_min__max_Oinf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 249 (all X_a (linorder(X_a) -> (all B_3 all A_3 all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B_3),C_1))))) # label(fact_197_min__max_Oinf_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 250 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z)) = 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))))) # label(fact_198_min__max_Oinf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 251 (all X_a (linorder(X_a) -> (all A_3 all B_3 all C_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),A_3),B_3)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B_3),C_1))))) # label(fact_199_min__max_Oinf_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 252 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z))))) # label(fact_200_min__max_Oinf__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 253 (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_201_min__max_Oinf__le1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 254 (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_202_min__max_Oinf__le2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 255 (all X_a (linorder(X_a) -> (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)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),Y_2) = ti(X_a,X_2))))) # label(fact_203_min__max_Ole__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 256 (all X_a (linorder(X_a) -> (all X_2 all Y_2 all Z_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y_2),Z_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z_1)))))) # label(fact_204_min__max_Ole__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 257 (all X_a (linorder(X_a) -> (all B_3 all A_3 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),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_3),B_3)),X)))))) # label(fact_205_min__max_Ole__infI1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 258 (all X_a (linorder(X_a) -> (all A_3 all B_3 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_3),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_3),B_3)),X)))))) # label(fact_206_min__max_Ole__infI2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 259 (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_207_min__max_Oinf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 260 (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_208_min__max_Oinf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 261 (all X_a (linorder(X_a) -> (all B_3 all X all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_3)) -> 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_3),B_3)))))))) # label(fact_209_min__max_Ole__infI) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 262 (all X_a (linorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z)) -> 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)))))))) # label(fact_210_min__max_Oinf__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 263 (all X_a (linorder(X_a) -> (all B_3 all D_1 all A_3 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_3),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_3),B_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),C_1),D_1)))))))) # label(fact_211_min__max_Oinf__mono) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 264 (all X_a (linorder(X_a) -> (all X all A_3 all B_3 (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_3),B_3))) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_3)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_3))))))) # label(fact_212_min__max_Ole__infE) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 265 (all X_a (linorder(X_a) -> (all X_2 all Y_2 all Z_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),Y_2)),Z_1)) <-> 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_2),Z_1)))))) # label(fact_213_min__le__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 266 (all X_a all X_b all Y_2 all Z_1 all A_2 all X_2 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite100568337ommute(X_a,X_b),F)) -> (hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F),Z_1),A_2),X_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F),Z_1),A_2),Y_2)) -> ti(X_b,Y_2) = ti(X_b,X_2))))) # label(fact_214_comp__fun__commute_Ofold__graph__determ) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 267 (all X_a (linorder(X_a) -> (all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),ord_min(X_a)),A_2)),A_1))))))) # label(fact_215_min__max_Ofold1__belowI) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 268 (all X_a (ab_group_add(X_a) -> (all A_1 all B all Ca all D (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Ca),D) -> (ti(X_a,A_1) = ti(X_a,B) <-> ti(X_a,Ca) = ti(X_a,D)))))) # label(fact_216_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 269 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),ord_min(X_a)),A_2)),X_2)) <-> (exists 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)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),X_2)))))))))) # label(fact_217_fold1__below__iff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 270 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),ord_min(X_a)),A_2))) <-> (all 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)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),X_1)))))))))) # label(fact_218_min__max_Obelow__fold1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 271 (all X_a all X_b all Z_1 all X_2 all A_2 all V all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite100568337ommute(X_a,X_b),F)) -> (hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F),Z_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)),V)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> -(all Y_1 (ti(X_b,V) = hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),Y_1) -> -hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F),Z_1),A_2),Y_1)))))))) # label(fact_219_comp__fun__commute_Ofold__graph__insertE) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 272 (all X_a (order(X_a) -> (all X all Least ((all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_1))) -> 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_220_min__leastR) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 273 (all X_a (ord(X_a) -> (all X all Least ((all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_1))) -> 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_221_min__leastL) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 274 (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_222_min__ord__min) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 275 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_2) = ti(X_a,X_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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))))))))) # label(fact_223_Min_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 276 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_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(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_2)),X_2))))))) # label(fact_224_Min__le) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 277 (all X_a (linorder(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_2)),A_2))))))) # label(fact_225_Min__in) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 278 (all X_a (linorder(X_a) -> (all X_2 hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = ti(X_a,X_2)))) # label(fact_226_Min_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 279 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_2)) = hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_2)))))) # label(fact_227_Min_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 280 (all X_a (linorder(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_2) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),ord_min(X_a)),A_2))))) # label(fact_228_Min_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 281 (all X_a (linorder(X_a) -> (all M_1 all N (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),M_1),N)) -> (ti(fun(X_a,bool),M_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),N)),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),M_1))))))))) # label(fact_229_Min__antimono) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 282 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_2)))))))) # label(fact_230_Min_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 283 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_2))))))) # label(fact_231_Min__insert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 284 (all X_a (linorder(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> (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)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),B_1)),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_2)) = hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_2))))))) # label(fact_232_Min_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 285 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = ti(X_a,X_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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))))))))) # label(fact_233_Min_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 286 (all X_a (linorder(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> ((all X_1 all Y_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_1),bot_bot(fun(X_a,bool))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_2)),A_2)))))))) # label(fact_234_Min_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 287 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> ((all Y_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),A_2) = ti(X_a,X_2))))))) # label(fact_235_Min__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 288 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = ti(X_a,X_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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))))))))) # label(fact_236_min__max_OInf__fin_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 289 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_2) = ti(X_a,X_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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))))))))) # label(fact_237_min__max_OInf__fin_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 290 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_2)) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_2)))))) # label(fact_238_min__max_OInf__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 291 (all X_a (linorder(X_a) -> (all X_2 hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = ti(X_a,X_2)))) # label(fact_239_min__max_OInf__fin_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 292 (all X_a (linorder(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_2) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),ord_min(X_a)),A_2))))) # label(fact_240_min__max_OInf__fin_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 293 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_2)))))))) # label(fact_241_min__max_OInf__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 294 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_2))))))) # label(fact_242_min__max_OInf__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 295 (all X_a (linorder(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> (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)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),B_1)),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_2)) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_2))))))) # label(fact_243_min__max_OInf__fin_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 296 (all X_a (linorder(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> ((all X_1 all Y_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_1),bot_bot(fun(X_a,bool))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_2)),A_2)))))))) # label(fact_244_min__max_OInf__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 297 (all X_a all X_b all Z_1 all X_2 all A_2 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite100568337ommute(X_a,X_b),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))))))) # label(fact_245_comp__fun__commute_Ofold__insert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 298 (all X_a all X_b all Z_1 all X_2 all A_2 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite100568337ommute(X_a,X_b),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_1),A_2) = hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))))))) # label(fact_246_comp__fun__commute_Ofold__rec) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 299 (all X_a (linorder(X_a) -> (all M_1 all N (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),M_1),N)) -> (ti(fun(X_a,bool),M_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),M_1)),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),N))))))))) # label(fact_247_Max__mono) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 300 (all X_b all X_a all F all Z_1 hAPP(fun(X_b,bool),X_a,hAPP(X_a,fun(fun(X_b,bool),X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,bool),X_a)),finite_fold(X_b,X_a),F),Z_1),bot_bot(fun(X_b,bool))) = ti(X_a,Z_1)) # label(fact_248_fold__empty) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 301 (all X_a all X_b all X_2 all Z_1 all A_2 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite100568337ommute(X_a,X_b),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_1),A_2)) = hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),Z_1)),A_2)))) # label(fact_249_comp__fun__commute_Ofold__fun__comm) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 302 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_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(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_2)))))))) # label(fact_250_Max__ge) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 303 (all X_a (linorder(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_2)),A_2))))))) # label(fact_251_Max__in) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 304 (all X_a (linorder(X_a) -> (all X_2 hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = ti(X_a,X_2)))) # label(fact_252_Max_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 305 (all X_a all X_b all Z_1 all A_2 all Y_2 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite100568337ommute(X_a,X_b),F)) -> (hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F),Z_1),A_2),Y_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_1),A_2) = ti(X_b,Y_2)))) # label(fact_253_comp__fun__commute_Ofold__equality) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 306 (all X_a (linorder(X_a) -> (all B all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_min(X_a)),B),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)))))))) # label(fact_254_min__max_Ofold__inf__le__inf) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 307 (all X_a (linorder(X_a) -> (all B all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_min(X_a)),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_min(X_a)),B),A_2)))))) # label(fact_255_min__max_Ofold__inf__insert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 308 (all X_a all X_b all Z_1 all X_2 all A_2 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite100568337ommute(X_a,X_b),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),Z_1)),A_2))))) # label(fact_256_comp__fun__commute_Ofold__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 309 (all X_a all X_b all Z_1 all X_2 all A_2 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite100568337ommute(X_a,X_b),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_1),A_2)))))) # label(fact_257_comp__fun__commute_Ofold__insert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 310 (all X_a all X_2 all A_2 all F all F_1 (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),F_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(fun(X_a,bool),X_a,F_1,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),F),X_2),A_2))))) # label(fact_258_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 311 (all X_a all A_1 all A_2 all F all F_1 (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F),F_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_a,F_1,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),F),A_1),A_2)))) # label(fact_259_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 312 (all X_a all X_b all Z_1 all A_2 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite100568337ommute(X_a,X_b),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F),Z_1),A_2),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_1),A_2)))))) # label(fact_260_comp__fun__commute_Ofold__graph__fold) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 313 (all X_a (linorder(X_a) -> (all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_min(X_a)),A_1),A_2))))) # label(fact_261_Min_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 314 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Min(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_min(X_a)),X_2),A_2)))))) # label(fact_262_Min_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 315 (all X_a (linorder(X_a) -> (all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_min(X_a)),A_1),A_2))))) # label(fact_263_min__max_OInf__fin_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 316 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_min(X_a)),X_2),A_2)))))) # label(fact_264_min__max_OInf__fin_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 317 (all X_a (linorder(X_a) -> (all Ca all B all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> ((all 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)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X_1)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),Ca)),hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_min(X_a)),Ca),A_2)))))))) # label(fact_265_min__max_Oinf__le__fold__inf) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 318 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> ((all Y_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),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)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_2) = ti(X_a,X_2))))))) # label(fact_266_Max__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 319 (all X_a all X_b all Z_1 all X_2 all A_2 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_a,X_b),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_1),A_2))))) # label(fact_267_comp__fun__idem_Ofold__insert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 320 (all X_a all X_b all Z_1 all X_2 all A_2 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_a,X_b),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),Z_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),finite_fold(X_a,X_b),F),hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),Z_1)),A_2)))) # label(fact_268_comp__fun__idem_Ofold__insert__idem2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 321 (all X_a all X_b all X_2 all Z_1 all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_a,X_b),F)) -> hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),Z_1)) = hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),Z_1))) # label(fact_269_comp__fun__idem_Ofun__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 322 (all X_a hBOOL(hAPP(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),bool,finite_comp_fun_idem(X_a,fun(X_a,bool)),insert(X_a)))) # label(fact_270_comp__fun__idem__insert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 323 (all X_a (linorder(X_a) -> hBOOL(hAPP(fun(X_a,fun(X_a,X_a)),bool,finite_comp_fun_idem(X_a,X_a),ord_min(X_a))))) # label(fact_271_min__max_Ocomp__fun__idem__inf) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 324 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_2) = ti(X_a,X_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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))))))))) # label(fact_272_Max_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 325 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = ti(X_a,X_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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))))))))) # label(fact_273_Max_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 326 (all X_b all X_a all F all Z_1 all Y_2 all X_2 all A_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(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),fold_graph(X_a,X_b),F),Z_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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),fold_graph(X_a,X_b),F),Z_1),A_2),hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),Y_2)))))) # label(fact_274_fold__graph_H_Ointros_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 327 (all X_a all X_b (ring(X_b) -> (all F all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_2)),hAPP(X_a,X_b,F,A_1))))))) # label(fact_275_setsum__diff1__ring) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 328 (all X_a (linorder(X_a) -> hBOOL(hAPP(fun(X_a,fun(X_a,X_a)),bool,finite_comp_fun_idem(X_a,X_a),ord_max(X_a))))) # label(fact_276_min__max_Ocomp__fun__idem__sup) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 329 (all X_b all X_a all F all Z_1 hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),fold_graph(X_a,X_b),F),Z_1),bot_bot(fun(X_a,bool))),Z_1))) # label(fact_277_fold__graph_H_Ointros_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 330 (all X_a (ordered_ab_group_add(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z))))) # label(fact_278_max__diff__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 331 (all X_a (linorder(X_a) -> (all A_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),A_3) = ti(X_a,A_3)))) # label(fact_279_min__max_Osup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 332 (all X_a (linorder(X_a) -> (all A_3 all B_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),B_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_3),A_3)))) # label(fact_280_min__max_Osup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 333 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),X)))) # label(fact_281_min__max_Osup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 334 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)) = ti(X_a,X)))) # label(fact_282_min__max_Osup__inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 335 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)) = ti(X_a,X)))) # label(fact_283_min__max_Oinf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 336 (all X_a (linorder(X_a) -> (all A_3 all B_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),B_3)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),B_3)))) # label(fact_284_min__max_Osup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 337 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))) # label(fact_285_min__max_Osup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 338 (all X_a (linorder(X_a) -> (all B_3 all A_3 all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_3),C_1))))) # label(fact_286_min__max_Osup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 339 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z))))) # label(fact_287_min__max_Osup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 340 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z))))) # label(fact_288_min__max_Osup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 341 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z))))) # label(fact_289_min__max_Oinf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 342 (all X_a (linorder(X_a) -> (all A_3 all B_3 all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),B_3)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_3),C_1))))) # label(fact_290_min__max_Osup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 343 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z))))) # label(fact_291_min__max_Osup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 344 (all X_a (linorder(X_a) -> (all Y all Z all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Z),X))))) # label(fact_292_min__max_Osup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 345 (all X_a (linorder(X_a) -> (all Y all Z all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Z),X))))) # label(fact_293_min__max_Oinf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 346 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))))) # label(fact_294_le__maxI1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 347 (all X_a (linorder(X_a) -> (all Y all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))))) # label(fact_295_le__maxI2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 348 (all X_a (linorder(X_a) -> (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)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),Y_2) = ti(X_a,Y_2))))) # label(fact_296_min__max_Ole__iff__sup) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 349 (all X_a (linorder(X_a) -> (all X_2 all Y_2 all Z_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),Y_2)),Z_1)) <-> 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_2),Z_1)))))) # label(fact_297_min__max_Ole__sup__iff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 350 (all X_a (linorder(X_a) -> (all B_3 all X all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),B_3))))))) # label(fact_298_min__max_Ole__supI1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 351 (all X_a (linorder(X_a) -> (all A_3 all X all B_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),B_3))))))) # label(fact_299_min__max_Ole__supI2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 352 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y) = ti(X_a,Y))))) # label(fact_300_min__max_Osup__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 353 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y) = ti(X_a,X))))) # label(fact_301_min__max_Osup__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 354 (all X_a (linorder(X_a) -> (all B_3 all A_3 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_3),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),B_3)),X))))))) # label(fact_302_min__max_Ole__supI) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 355 (all X_a (linorder(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)),X))))))) # label(fact_303_min__max_Osup__least) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 356 (all X_a (linorder(X_a) -> (all B_3 all D_1 all A_3 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_3),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),B_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),C_1),D_1)))))))) # label(fact_304_min__max_Osup__mono) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 357 (all X_a (linorder(X_a) -> (all A_3 all B_3 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),B_3)),X)) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),X)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_3),X))))))) # label(fact_305_min__max_Ole__supE) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 358 (all X_a (linorder(X_a) -> (all Z_1 all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),Y_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),X_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),Y_2)))))) # label(fact_306_le__max__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 359 (all X_a (linorder(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),X) = ti(X_a,X)))) # label(fact_307_Max_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 360 (all X_a (linorder(X_a) -> (all X all Y all Z hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z))))))) # label(fact_308_min__max_Odistrib__inf__le) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 361 (all X_a (linorder(X_a) -> (all X all Y all Z hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z))))))) # label(fact_309_min__max_Odistrib__sup__le) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 362 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_2)) = hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_2)))))) # label(fact_310_Max_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 363 (all X_a all F all A_1 all A_2 ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_2)),hAPP(X_a,nat,F,A_1))) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))))) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_2)))) # label(fact_311_setsum__diff1__nat) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 364 (all X_a all F all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),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)) -> hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),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(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_2)),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),B_1))))) # label(fact_312_setsum__diff__nat) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 365 (all X_a (linorder(X_a) -> (all B all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_max(X_a)),B),A_2)))))))) # label(fact_313_min__max_Osup__le__fold__sup) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 366 (all X_a (linorder(X_a) -> (all B all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_max(X_a)),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_max(X_a)),B),A_2)))))) # label(fact_314_min__max_Ofold__sup__insert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 367 (all X_a (linorder(X_a) -> (all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_2)) = ti(X_a,A_1)))))) # label(fact_315_min__max_Osup__Inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 368 (all X_a (linorder(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_2) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),ord_max(X_a)),A_2))))) # label(fact_316_Max_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 369 (all X_a all X_b (ab_group_add(X_b) -> (all F all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),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)),B_1),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),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(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),B_1))))))) # label(fact_317_setsum__diff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 370 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_2)))))))) # label(fact_318_Max_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 371 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_2))))))) # label(fact_319_Max__insert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 372 (all X_a (linorder(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> (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)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),B_1)),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_2)) = hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_2))))))) # label(fact_320_Max_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 373 (all X_a (linorder(X_a) -> (all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_max(X_a)),A_1),A_2))))) # label(fact_321_Max_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 374 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_max(X_a)),X_2),A_2)))))) # label(fact_322_Max_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.79 375 (all X_a all X_b (ab_group_add(X_b) -> (all F all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_2)),hAPP(X_a,X_b,F,A_1))) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))))) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_2)))))) # label(fact_323_setsum__diff1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 376 (all X_a (linorder(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> ((all X_1 all Y_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_1),bot_bot(fun(X_a,bool))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(fun(X_a,bool),X_a,big_linorder_Max(X_a),A_2)),A_2)))))))) # label(fact_324_Max_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 377 (all X_a (linorder(X_a) -> (all Ca all B all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> ((all 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)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),B)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_max(X_a)),Ca),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),Ca)))))))) # label(fact_325_min__max_Ofold__sup__le__sup) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 378 (all X_a (linorder(X_a) -> (all X all Y all Z ((all X_1 all Y_1 all Z_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(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)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Z_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z)))))) # label(fact_326_min__max_Odistrib__imp2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 379 (all X_a (linorder(X_a) -> (all X all Y all Z ((all X_1 all Y_1 all Z_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y_1),Z_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(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),Z_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z)))))) # label(fact_327_min__max_Odistrib__imp1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 380 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all H all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> ((all 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)) -> hAPP(X_a,X_b,G,X_1) = hAPP(X_a,X_b,H,X_1))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_2) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),H),A_2)))))) # label(fact_328_setsum_Ocong) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 381 (all X_a (order(X_a) -> (all X all Least ((all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_1))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Least) = ti(X_a,X))))) # label(fact_329_max__leastR) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 382 (all X_a (ord(X_a) -> (all X all Least ((all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_1))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Least),X) = ti(X_a,X))))) # label(fact_330_max__leastL) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 383 (all X_a (ord(X_a) -> ord_max(X_a) = hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),max(X_a),ord_less_eq(X_a)))) # label(fact_331_max__ord__max) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 384 (all X_a (linorder(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Inf_fin(X_a),ord_min(X_a)),A_2)),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),A_2)))))))) # label(fact_332_min__max_OInf__le__Sup) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 385 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = ti(X_a,X_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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),hAPP(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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))))))))) # label(fact_333_min__max_OSup__fin_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 386 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),A_2)) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),A_2)))))) # label(fact_334_min__max_OSup__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 387 (all X_a (linorder(X_a) -> (all X_2 hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = ti(X_a,X_2)))) # label(fact_335_min__max_OSup__fin_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 388 (all X_a (linorder(X_a) -> (all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),A_2)) = ti(X_a,A_1)))))) # label(fact_336_min__max_Oinf__Sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 389 (all X_a (linorder(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),A_2) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),ord_max(X_a)),A_2))))) # label(fact_337_min__max_OSup__fin_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 390 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),A_2))))))) # label(fact_338_min__max_OSup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 391 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),A_2)))))))) # label(fact_339_min__max_OSup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 392 (all X_a (linorder(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),B_1) != bot_bot(fun(X_a,bool)) -> (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)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),B_1)),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),A_2)) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),A_2))))))) # label(fact_340_min__max_OSup__fin_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 393 (all X_a (linorder(X_a) -> (all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_max(X_a)),A_1),A_2))))) # label(fact_341_min__max_OSup__fin_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 394 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),ord_max(X_a)),X_2),A_2)))))) # label(fact_342_min__max_OSup__fin_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 395 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),A_2) = ti(X_a,X_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)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),hAPP(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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))))))))) # label(fact_343_min__max_OSup__fin_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 396 (all X_a (linorder(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> ((all X_1 all Y_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_1),bot_bot(fun(X_a,bool))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),big_Sup_fin(X_a),ord_max(X_a)),A_2)),A_2)))))))) # label(fact_344_min__max_OSup__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 397 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_a,X_b,G,X_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))))))))) # label(fact_345_setsum_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 398 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_a,X_b,F,A_1)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))))))))))) # label(fact_346_setsum__diff1_H) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 399 (all X_a (group_add(X_a) -> (all A_3 all B_3 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_3),B_3)),B_3) = ti(X_a,A_3)))) # label(fact_347_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 400 (all X_a (group_add(X_a) -> (all A_3 all B_3 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_3),B_3)),B_3) = ti(X_a,A_3)))) # label(fact_348_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 401 (all X_a (ab_semigroup_add(X_a) -> (all A_3 all B_3 all C_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_3),B_3)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_3),C_1))))) # label(fact_349_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 402 (all X_a (cancel_semigroup_add(X_a) -> (all A_1 all B all Ca (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),Ca) <-> ti(X_a,B) = ti(X_a,Ca))))) # label(fact_350_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 403 (all X_a (cancel_semigroup_add(X_a) -> (all B all A_1 all Ca (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),Ca),A_1) <-> ti(X_a,B) = ti(X_a,Ca))))) # label(fact_351_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 404 (all X_a (cancel_semigroup_add(X_a) -> (all A_3 all B_3 all C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),B_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),C_1) -> ti(X_a,B_3) = ti(X_a,C_1))))) # label(fact_352_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 405 (all X_a (cancel146912293up_add(X_a) -> (all A_3 all B_3 all C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),B_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),C_1) -> ti(X_a,B_3) = ti(X_a,C_1))))) # label(fact_353_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 406 (all X_a (cancel_semigroup_add(X_a) -> (all B_3 all A_3 all C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_3),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_3) -> ti(X_a,B_3) = ti(X_a,C_1))))) # label(fact_354_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 407 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all Ca 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),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),Ca))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_355_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 408 (all X_a (ordere236663937imp_le(X_a) -> (all Ca 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),Ca),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),B))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_356_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 409 (all X_a (ordere779506340up_add(X_a) -> (all C_1 all A_3 all B_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_3)) -> 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_3),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_3),C_1))))))) # label(fact_357_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 410 (all X_a (ordere779506340up_add(X_a) -> (all C_1 all A_3 all B_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B_3))))))) # label(fact_358_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 411 (all X_a (ordere779506340up_add(X_a) -> (all C_1 all D_1 all A_3 all B_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),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_3),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_3),D_1)))))))) # label(fact_359_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 412 (all X_a (ordere236663937imp_le(X_a) -> (all A_3 all C_1 all B_3 (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_3),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_3),C_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_3)))))) # label(fact_360_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 413 (all X_a (ordere236663937imp_le(X_a) -> (all C_1 all A_3 all B_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B_3))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_3)))))) # label(fact_361_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 414 (all X_a (ordere236663937imp_le(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z))))) # label(fact_362_min__add__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 415 (all X_a (ordere236663937imp_le(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z))))) # label(fact_363_max__add__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 416 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_a,X_b,G,X_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_2))))))) # label(fact_364_setsum_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 417 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all A_1 all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),F_1)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),F_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_a,X_b,F,A_1)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),F_1))))))) # label(fact_365_setsum__insert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 418 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_a,X_b,G,X_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))))))) # label(fact_366_setsum_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 419 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all G all A_2 ((all 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)) -> hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,G,X_1))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_2) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_2))))) # label(fact_367_setsum__cong2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 420 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all G all A_2 all B_1 (ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_1) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_1)) -> hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,G,X_1))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_2) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),B_1)))))) # label(fact_368_setsum__cong) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 421 (all X_a all X_b (comm_monoid_add(X_b) -> (all H all G all A_2 all B_1 (ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_1) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_1)) -> hAPP(X_a,X_b,H,X_1) = hAPP(X_a,X_b,G,X_1))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),H),A_2) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),B_1)))))) # label(fact_369_setsum_OF__cong) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 422 (all X_a (ab_sem1668676832m_mult(X_a) -> (all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),times_times(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),times_times(X_a)),A_1),A_2))))) # label(fact_370_fold1__eq__fold__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 423 (all X_a (ab_semigroup_mult(X_a) -> (all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),times_times(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2)) = hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),X_a)),finite_fold(X_a,X_a),times_times(X_a)),A_1),A_2)))))) # label(fact_371_fold1__eq__fold) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 424 (all X_a (ab_sem1668676832m_mult(X_a) -> (all A_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),A_3) = ti(X_a,A_3)))) # label(fact_372_times_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 425 (all X_a (ab_sem1668676832m_mult(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X) = ti(X_a,X)))) # label(fact_373_mult__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 426 (all X_a (ab_sem1668676832m_mult(X_a) -> (all A_3 all B_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),B_3)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),B_3)))) # label(fact_374_mult__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 427 (all X_a (ab_semigroup_mult(X_a) -> (all A_3 all B_3 all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),B_3)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_3),C_1))))) # label(fact_375_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 428 (all X_a (ab_semigroup_mult(X_a) -> hBOOL(hAPP(fun(X_a,fun(X_a,X_a)),bool,finite100568337ommute(X_a,X_a),times_times(X_a))))) # label(fact_376_comp__fun__commute) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 429 (all X_a (ab_sem1668676832m_mult(X_a) -> hBOOL(hAPP(fun(X_a,fun(X_a,X_a)),bool,finite_comp_fun_idem(X_a,X_a),times_times(X_a))))) # label(fact_377_comp__fun__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 430 (all X_a (ab_semigroup_mult(X_a) -> (all Z_1 all B all A_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),finite_fold_graph(X_a,X_a),times_times(X_a)),B),A_2),Y_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),finite_fold_graph(X_a,X_a),times_times(X_a)),Z_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y_2)))))))) # label(fact_378_fold__graph__insert__swap) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 431 (all X_a (ab_sem1668676832m_mult(X_a) -> (all X_2 all A_2 (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),times_times(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),times_times(X_a)),A_2))))))) # label(fact_379_fold1__insert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 432 (all X_a (ab_semigroup_mult(X_a) -> (all X_2 all A_2 (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),times_times(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),times_times(X_a)),A_2)))))))) # label(fact_380_fold1__insert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 433 (all X_a (ab_semigroup_mult(X_a) -> (all A_1 all B all A_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),finite_fold_graph(X_a,X_a),times_times(X_a)),B),A_2),X_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),finite_fold_graph(X_a,X_a),times_times(X_a)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool)))))),X_2)))))))) # label(fact_381_fold__graph__permute__diff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 434 (all X_a (ab_semigroup_mult(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> ((all X_1 all Y_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Y_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_1),bot_bot(fun(X_a,bool))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),times_times(X_a)),A_2)),A_2)))))))) # label(fact_382_fold1__in) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 435 (all X_a (ordered_ring(X_a) -> (all A_1 all E all Ca all B all D (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),E)),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),E)),D))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),E)),Ca)),D)))))) # label(fact_383_le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 436 (all X_a (semiring(X_a) -> (all A_3 all E_1 all B_3 all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),E_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_3),E_1)),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),B_3)),E_1)),C_1)))) # label(fact_384_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 437 (all X_a (comm_semiring(X_a) -> (all A_3 all B_3 all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),B_3)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_3),C_1))))) # label(fact_385_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 438 (all X_a (ring(X_a) -> (all A_1 all E all Ca all B all D (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),E)),Ca) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),E)),D) <-> ti(X_a,Ca) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1)),E)),D))))) # label(fact_386_eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 439 (all X_a (ring(X_a) -> (all A_1 all E all Ca all B all D (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),E)),Ca) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),E)),D) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),E)),Ca) = ti(X_a,D))))) # label(fact_387_eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 440 (all X_a (ordered_ring(X_a) -> (all A_1 all E all Ca all B all D (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),E)),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),E)),D))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1)),E)),D))))))) # label(fact_388_le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 441 (all X_a (semiri456707255roduct(X_a) -> (all W_1 all Y_2 all X_2 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),times_times(X_a),W_1),Y_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),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),times_times(X_a),W_1),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),Y_2)) <-> ti(X_a,W_1) = ti(X_a,X_2) | ti(X_a,Y_2) = ti(X_a,Z_1))))) # label(fact_389_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 442 (all X_a (comm_semiring_1(X_a) -> (all A_3 all M all B_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),M)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_3),M)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),B_3)),M)))) # label(fact_390_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 443 (all X_a (comm_semiring_1(X_a) -> (all A_3 all B_3 all C_1 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_3),B_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),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_3),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_3),D_1))))) # label(fact_391_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 444 (all X_a (comm_semiring_1(X_a) -> (all A_3 all B_3 all C_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_3),B_3)),C_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_3),C_1)),B_3)))) # label(fact_392_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 445 (all X_a (comm_semiring_1(X_a) -> (all A_3 all B_3 all C_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_3),B_3)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_3),C_1))))) # label(fact_393_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 446 (all X_a (comm_semiring_1(X_a) -> (all A_3 all C_1 all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),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_3),C_1)),D_1)))) # label(fact_394_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 447 (all X_a (comm_semiring_1(X_a) -> (all A_3 all C_1 all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),D_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),D_1))))) # label(fact_395_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 448 (all X_a (comm_semiring_1(X_a) -> (all A_3 all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_3)))) # label(fact_396_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 449 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Ry))))) # label(fact_397_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 450 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Ry))))) # label(fact_398_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 451 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)))))) # label(fact_399_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 452 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ly)))) # label(fact_400_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 453 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Rx))))) # label(fact_401_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 454 (all X_a (comm_semiring_1(X_a) -> (all Lx all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ry)))) # label(fact_402_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 455 (all X_a (comm_semiring_1(X_a) -> (all Lx all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ry))))) # label(fact_403_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 456 (all X_a (comm_semiring_1(X_a) -> (all A_3 all B_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),B_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_3),A_3)))) # label(fact_404_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 457 (all X_a (comm_semiring_1(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z))))) # label(fact_405_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 458 (all X_a (semiri456707255roduct(X_a) -> (all Ca all D all A_1 all B (ti(X_a,A_1) != ti(X_a,B) & ti(X_a,Ca) != ti(X_a,D) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),D)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),Ca)))))) # label(fact_406_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 459 (all X_a (comm_semiring_1(X_a) -> (all A_3 all B_3 all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),B_3)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_3),C_1))))) # label(fact_407_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 460 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_a,X_b,G,X_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))))))))) # label(fact_408_setprod_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 461 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_a,X_b,G,X_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))))))) # label(fact_409_setprod_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 462 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_a,X_b,G,X_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_2))))))) # label(fact_410_setprod_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 463 (all X_a all X_b (comm_monoid_mult(X_b) -> (all F all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_a,X_b,F,A_1)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_2))))))) # label(fact_411_setprod__insert) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 464 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all H all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> ((all 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)) -> hAPP(X_a,X_b,G,X_1) = hAPP(X_a,X_b,H,X_1))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_2) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),H),A_2)))))) # label(fact_412_setprod_Ocong) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 465 (all X_a all X_b (comm_monoid_mult(X_b) -> (all H all G all A_2 all B_1 (ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_1) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_1)) -> hAPP(X_a,X_b,H,X_1) = hAPP(X_a,X_b,G,X_1))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),H),A_2) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),B_1)))))) # label(fact_413_setprod_OF__cong) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 466 (all X_a all X_b (comm_monoid_mult(X_b) -> (all F all G all A_2 all B_1 (ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_1) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_1)) -> hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,G,X_1))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_2) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),B_1)))))) # label(fact_414_setprod__cong) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 467 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),ord_min(X_a)),A_2))) <-> (all 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)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),X_1)))))))))) # label(fact_415_strict__below__fold1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 468 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all Ca 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),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),Ca))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_416_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 469 (all X_a (ordere236663937imp_le(X_a) -> (all Ca 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),Ca),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),B))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_417_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 470 (all X_a (ordere223160158up_add(X_a) -> (all C_1 all A_3 all B_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_3)) -> 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_3),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_3),C_1))))))) # label(fact_418_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 471 (all X_a (ordere223160158up_add(X_a) -> (all C_1 all A_3 all B_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B_3))))))) # label(fact_419_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 472 (all X_a (ordere223160158up_add(X_a) -> (all C_1 all D_1 all A_3 all B_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),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_3),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_3),D_1)))))))) # label(fact_420_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 473 (all X_a (ordere236663937imp_le(X_a) -> (all A_3 all C_1 all B_3 (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_3),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_3),C_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_3)))))) # label(fact_421_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 474 (all X_a (ordere236663937imp_le(X_a) -> (all C_1 all A_3 all B_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B_3))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_3)))))) # label(fact_422_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 475 (all X_a (ordere223160158up_add(X_a) -> (all C_1 all D_1 all A_3 all B_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),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_3),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_3),D_1)))))))) # label(fact_423_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 476 (all X_a (ordere223160158up_add(X_a) -> (all C_1 all D_1 all A_3 all B_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),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_3),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_3),D_1)))))))) # label(fact_424_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 477 (all X_a (linorder(X_a) -> (all B_3 all X all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),B_3))))))) # label(fact_425_min__max_Oless__supI1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 478 (all X_a (linorder(X_a) -> (all A_3 all X all B_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),B_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_3),B_3))))))) # label(fact_426_min__max_Oless__supI2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 479 (all X_a (linorder(X_a) -> (all Z_1 all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),Y_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y_2)))))) # label(fact_427_less__max__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 480 (all X_a (linorder(X_a) -> (all X_2 all Y_2 all Z_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),Y_2)),Z_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),Z_1)))))) # label(fact_428_max__less__iff__conj) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 481 (all X_a (bot(X_a) -> (all A_3 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),bot_bot(X_a)))))) # label(fact_429_not__less__bot) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 482 (all X_a (bot(X_a) -> (all A_1 (ti(X_a,A_1) != bot_bot(X_a) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),bot_bot(X_a)),A_1)))))) # label(fact_430_bot__less) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 483 (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(fun(X_a,bool)),A_2),bot_bot(fun(X_a,bool))))) # label(fact_431_not__psubset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 484 (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_432_psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 485 (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_433_subset__iff__psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 486 (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_434_psubset__imp__subset) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 487 (all X_a all C 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)) -> 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))))) # label(fact_435_psubset__subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 488 (all X_a all C 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)) -> 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))))) # label(fact_436_subset__psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 489 (all X_a (linorder(X_a) -> (all A_3 all B_3 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_3),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_3),B_3)),X)))))) # label(fact_437_min__max_Oless__infI2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 490 (all X_a (linorder(X_a) -> (all B_3 all A_3 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),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_3),B_3)),X)))))) # label(fact_438_min__max_Oless__infI1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 491 (all X_a (linorder(X_a) -> (all Z_1 all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),Y_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y_2)))))) # label(fact_439_min__less__iff__conj) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 492 (all X_a (linorder(X_a) -> (all X_2 all Y_2 all Z_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),Y_2)),Z_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),Z_1)))))) # label(fact_440_min__less__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 493 (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_441_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 494 (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_442_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 495 (all X_a (order(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))))))) # label(fact_443_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 496 (all X_a (preorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))))))) # label(fact_444_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 497 (all X_a (order(X_a) -> (all C_1 all B_3 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_3),A_3)) -> (ti(X_a,B_3) = ti(X_a,C_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_3))))))) # label(fact_445_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 498 (all X_a (ord(X_a) -> (all C_1 all A_3 all B_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_3)) -> (ti(X_a,B_3) = ti(X_a,C_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),C_1))))))) # label(fact_446_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 499 (all X_a (order(X_a) -> (all C_1 all A_3 all B_3 (ti(X_a,A_3) = ti(X_a,B_3) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),B_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_3))))))) # label(fact_447_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 500 (all X_a (ord(X_a) -> (all C_1 all A_3 all B_3 (ti(X_a,A_3) = ti(X_a,B_3) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_3),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),C_1))))))) # label(fact_448_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 501 (all X_a (order(X_a) -> (all B_3 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_3),A_3)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_3)))))) # label(fact_449_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 502 (all X_a (preorder(X_a) -> (all A_3 all B_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_3)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_3),A_3)))))) # label(fact_450_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 503 (all X_a (preorder(X_a) -> (all Pa 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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_2)) -> hBOOL(Pa)))))) # label(fact_451_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 504 (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_452_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 505 (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_453_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 506 (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_454_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 507 (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_455_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 508 (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_456_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 509 (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_457_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 510 (all X_a (linorder(X_a) -> (all Y_2 all X_2 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_2)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_2)) <-> ti(X_a,X_2) = ti(X_a,Y_2)))))) # label(fact_458_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 511 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(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_459_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 512 (all X_a (linorder(X_a) -> (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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_2)) | ti(X_a,X_2) = ti(X_a,Y_2))))) # label(fact_460_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 513 (all X_a (linorder(X_a) -> (all X_2 all Y_2 (ti(X_a,X_2) != ti(X_a,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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_2)))))) # label(fact_461_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 514 (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_462_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 515 (all X_a (linorder(X_a) -> (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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_2)))))) # label(fact_463_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 516 (all X_a (linorder(X_a) -> (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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_2)))))) # label(fact_464_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 517 (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_465_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 518 (all X_a (order(X_a) -> (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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) & ti(X_a,X_2) != ti(X_a,Y_2))))) # label(fact_466_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 519 (all X_a (preorder(X_a) -> (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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) & -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_2)))))) # label(fact_467_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 520 (all X_a (order(X_a) -> (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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_2)) | ti(X_a,X_2) = ti(X_a,Y_2))))) # label(fact_468_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 521 (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_469_leI) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 522 (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_470_not__leE) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 523 (all X_a (linorder(X_a) -> (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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) <-> ti(X_a,X_2) = ti(X_a,Y_2)))))) # label(fact_471_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 524 (all X_a (order(X_a) -> (all A_3 all B_3 (ti(X_a,A_3) != ti(X_a,B_3) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_3))))))) # label(fact_472_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 525 (all X_a (order(X_a) -> (all A_3 all B_3 (ti(X_a,A_3) != ti(X_a,B_3) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_3),A_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_3),A_3))))))) # label(fact_473_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 526 (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_474_leD) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 527 (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_475_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 528 (all X_a (linorder(X_a) -> (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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_2)) <-> ti(X_a,X_2) = ti(X_a,Y_2)))))) # label(fact_476_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 529 (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_477_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 530 (all X_a (order(X_a) -> (all A_3 all B_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_3)) -> (ti(X_a,A_3) != ti(X_a,B_3) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_3))))))) # label(fact_478_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 531 (all X_a (order(X_a) -> (all B_3 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_3),A_3)) -> (ti(X_a,A_3) != ti(X_a,B_3) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_3),A_3))))))) # label(fact_479_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.80 532 (all X_a (preorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))))))) # label(fact_480_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 533 (all X_a (order(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))))))) # label(fact_481_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 534 (all X_a (preorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))))))) # label(fact_482_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 535 (all X_a (order(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))))))) # label(fact_483_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 536 (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_484_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 537 (all X_a (ordered_ab_group_add(X_a) -> (all A_1 all B all Ca all D (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B) = 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),A_1),B)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),D))))))) # label(fact_485_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 538 (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_486_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 539 (all X_a (ordered_ring(X_a) -> (all A_1 all E all Ca all B all D (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),E)),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),E)),D))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),E)),Ca)),D)))))) # label(fact_487_less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 540 (all X_a (ordered_ring(X_a) -> (all A_1 all E all Ca all B all D (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),E)),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),E)),D))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1)),E)),D))))))) # label(fact_488_less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 541 (all X_a all A_2 all X_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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),B_1))) <-> (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(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_2),B_1)) -> (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(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(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),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))),B_1))) & (-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(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)))))) # label(fact_489_psubset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 542 (all X_a (linorder(X_a) -> (all X_2 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),ord_min(X_a)),A_2)),X_2)) <-> (exists 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)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),X_2)))))))))) # label(fact_490_fold1__strict__below__iff) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 543 (all X_a all X_b (comm_monoid_add(X_b) & ordere223160158up_add(X_b) -> (all F all G all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> ((all 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)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_2))))))))) # label(fact_491_setsum__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 544 (all X_a (dense_linorder(X_a) -> (all Z all Y ((all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z)))))) # label(fact_492_dense__le) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 545 (all X_a all C 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)) -> 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))))) # label(fact_493_psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 546 (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_494_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 547 (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_495_psubset__imp__ex__mem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 548 (all X_b all X_a (order(X_a) & ord(X_b) -> (all Ca all F all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,B)),A_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),B)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Y_1)),hAPP(X_b,X_a,F,X_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Ca)),A_1)))))))) # label(fact_496_xt6) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 549 (all X_a (dense_linorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ((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))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z))))))) # label(fact_497_dense__le__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 550 (all X_b all X_a (order(X_a) & order(X_b) -> (all Ca all F 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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),hAPP(X_a,X_b,F,B))) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Y_1)),hAPP(X_a,X_b,F,X_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),hAPP(X_a,X_b,F,A_1))))))))) # label(fact_498_xt5) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 551 (all X_b all X_a (order(X_a) & order(X_b) -> (all Ca all F all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,B)),A_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),B)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Y_1)),hAPP(X_b,X_a,F,X_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Ca)),A_1)))))))) # label(fact_499_xt4) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 552 (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].
% 1.48/1.81 553 (all T_2 all T_1 (finite_finite(T_1) & finite_finite(T_2) -> finite_finite(fun(T_2,T_1)))) # label(arity_fun___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 554 (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].
% 1.48/1.81 555 (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].
% 1.48/1.81 556 (all T_2 all T_1 (bot(T_1) -> bot(fun(T_2,T_1)))) # label(arity_fun___Orderings_Obot) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 557 (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].
% 1.48/1.81 558 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 559 (all P (-hBOOL(hAPP(bool,bool,fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 560 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 561 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R) = hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R))) # label(help_COMBB_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 562 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q)) # label(help_COMBC_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.81 563 (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].
% 1.48/1.83 564 (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].
% 1.48/1.83 565 (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].
% 1.48/1.83 566 (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].
% 1.48/1.83 567 (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].
% 1.48/1.83 568 (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].
% 1.48/1.83 569 (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].
% 1.48/1.83 570 (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].
% 1.48/1.83 571 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.83 572 (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].
% 1.48/1.83 573 (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].
% 1.48/1.83 574 (all Q all P (hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.83 575 (all P all Q (-hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.83 576 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)) | -hBOOL(P) | hBOOL(Q))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.48/1.83
% 1.48/1.83 ============================== end of process non-clausal formulas ===
% 1.48/1.83
% 1.48/1.83 ============================== PROCESS INITIAL CLAUSES ===============
% 1.48/1.83
% 1.48/1.83 ============================== PREDICATE ELIMINATION =================
% 1.48/1.83 577 comm_monoid_add(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.48/1.83 578 -comm_monoid_add(A) | ti(fun(fun(B,A),fun(fun(B,bool),A)),big_co1399186613setsum(B,A)) = big_co1399186613setsum(B,A) # label(tsy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_res) # label(axiom). [clausify(1)].
% 1.48/1.83 579 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f91(B,A,D,E,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C) # label(fact_328_setsum_Ocong) # label(axiom). [clausify(380)].
% 1.48/1.83 580 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(B,A,D,f91(B,A,E,D,C)) != hAPP(B,A,E,f91(B,A,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) # label(fact_328_setsum_Ocong) # label(axiom). [clausify(380)].
% 1.48/1.83 581 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),bot_bot(fun(B,bool)))))) # label(fact_345_setsum_Oremove) # label(axiom). [clausify(397)].
% 1.48/1.83 582 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),bot_bot(fun(B,bool)))))) # label(fact_346_setsum__diff1_H) # label(axiom). [clausify(398)].
% 1.48/1.83 583 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C)) # label(fact_364_setsum_Oinsert) # label(axiom). [clausify(416)].
% 1.48/1.83 584 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C)) # label(fact_365_setsum__insert) # label(axiom). [clausify(417)].
% 1.48/1.83 585 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),E),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(B,A,D,E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),E),bot_bot(fun(B,bool)))))) # label(fact_366_setsum_Oinsert__remove) # label(axiom). [clausify(418)].
% 1.48/1.83 586 -comm_monoid_add(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f96(B,A,C,D,E)),E)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E) # label(fact_367_setsum__cong2) # label(axiom). [clausify(419)].
% 1.48/1.83 587 -comm_monoid_add(A) | hAPP(B,A,C,f96(B,A,D,C,E)) != hAPP(B,A,D,f96(B,A,D,C,E)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E) # label(fact_367_setsum__cong2) # label(axiom). [clausify(419)].
% 1.48/1.83 588 -comm_monoid_add(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f97(B,A,E,F,D,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D) # label(fact_368_setsum__cong) # label(axiom). [clausify(420)].
% 1.48/1.83 589 -comm_monoid_add(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hAPP(B,A,E,f97(B,A,F,E,D,C)) != hAPP(B,A,F,f97(B,A,F,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),D) # label(fact_368_setsum__cong) # label(axiom). [clausify(420)].
% 1.48/1.83 590 -comm_monoid_add(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f98(B,A,E,F,D,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),C) # label(fact_369_setsum_OF__cong) # label(axiom). [clausify(421)].
% 1.48/1.83 591 -comm_monoid_add(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hAPP(B,A,E,f98(B,A,E,F,D,C)) != hAPP(B,A,F,f98(B,A,E,F,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),C) # label(fact_369_setsum_OF__cong) # label(axiom). [clausify(421)].
% 1.48/1.83 592 -comm_monoid_add(A) | -ordere223160158up_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | bot_bot(fun(B,bool)) = ti(fun(B,bool),C) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,A,D,E,C)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_491_setsum__strict__mono) # label(axiom). [clausify(543)].
% 1.48/1.83 593 -comm_monoid_add(A) | -ordere223160158up_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | bot_bot(fun(B,bool)) = ti(fun(B,bool),C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(B,A,D,f106(B,A,D,E,C))),hAPP(B,A,E,f106(B,A,D,E,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_491_setsum__strict__mono) # label(axiom). [clausify(543)].
% 1.48/1.83 Derived: ti(fun(fun(A,nat),fun(fun(A,bool),nat)),big_co1399186613setsum(A,nat)) = big_co1399186613setsum(A,nat). [resolve(577,a,578,a)].
% 1.48/1.83 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f91(A,nat,C,D,B)),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),B). [resolve(577,a,579,a)].
% 1.48/1.83 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,nat,C,f91(A,nat,D,C,B)) != hAPP(A,nat,D,f91(A,nat,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B). [resolve(577,a,580,a)].
% 1.48/1.83 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(A,nat,D,C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))). [resolve(577,a,581,a)].
% 1.48/1.83 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(A,nat,D,C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B)). [resolve(577,a,583,a)].
% 1.48/1.83 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(A,nat,C,D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),bot_bot(fun(A,bool)))))). [resolve(577,a,585,a)].
% 1.48/1.86 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f96(A,nat,B,C,D)),D)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D). [resolve(577,a,586,a)].
% 1.48/1.86 Derived: hAPP(A,nat,B,f96(A,nat,C,B,D)) != hAPP(A,nat,C,f96(A,nat,C,B,D)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D). [resolve(577,a,587,a)].
% 1.48/1.86 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f97(A,nat,D,E,C,B)),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),E),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C). [resolve(577,a,588,a)].
% 1.48/1.86 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,nat,D,f97(A,nat,E,D,C,B)) != hAPP(A,nat,E,f97(A,nat,E,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),E),C). [resolve(577,a,589,a)].
% 1.48/1.86 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f98(A,nat,D,E,C,B)),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),E),B). [resolve(577,a,590,a)].
% 1.48/1.86 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,nat,D,f98(A,nat,D,E,C,B)) != hAPP(A,nat,E,f98(A,nat,D,E,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),E),B). [resolve(577,a,591,a)].
% 1.48/1.86 Derived: -ordere223160158up_add(nat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f106(A,nat,C,D,B)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),B)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B))). [resolve(577,a,592,a)].
% 1.48/1.86 Derived: -ordere223160158up_add(nat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(A,nat,C,f106(A,nat,C,D,B))),hAPP(A,nat,D,f106(A,nat,C,D,B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),B)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B))). [resolve(577,a,593,a)].
% 1.48/1.86 594 comm_monoid_mult(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.48/1.86 595 -comm_monoid_mult(A) | big_co302546470etprod(B,A) = ti(fun(fun(B,A),fun(fun(B,bool),A)),big_co302546470etprod(B,A)) # label(tsy_c_Big__Operators_Ocomm__monoid__mult__class_Osetprod_res) # label(axiom). [clausify(2)].
% 1.48/1.86 596 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),bot_bot(fun(B,bool)))))) # label(fact_408_setprod_Oremove) # label(axiom). [clausify(460)].
% 1.48/1.86 597 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),E),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(B,A,D,E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),E),bot_bot(fun(B,bool)))))) # label(fact_409_setprod_Oinsert__remove) # label(axiom). [clausify(461)].
% 1.48/1.86 598 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C)) # label(fact_410_setprod_Oinsert) # label(axiom). [clausify(462)].
% 1.48/1.86 599 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C)) # label(fact_411_setprod__insert) # label(axiom). [clausify(463)].
% 1.48/1.86 600 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f101(B,A,D,E,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_412_setprod_Ocong) # label(axiom). [clausify(464)].
% 1.48/1.86 601 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(B,A,D,f101(B,A,E,D,C)) != hAPP(B,A,E,f101(B,A,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) # label(fact_412_setprod_Ocong) # label(axiom). [clausify(464)].
% 1.48/1.86 602 -comm_monoid_mult(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f102(B,A,E,F,D,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),F),C) # label(fact_413_setprod_OF__cong) # label(axiom). [clausify(465)].
% 1.48/1.86 603 -comm_monoid_mult(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hAPP(B,A,E,f102(B,A,E,F,D,C)) != hAPP(B,A,F,f102(B,A,E,F,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),F),C) # label(fact_413_setprod_OF__cong) # label(axiom). [clausify(465)].
% 1.48/1.86 604 -comm_monoid_mult(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f103(B,A,E,F,D,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),F),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) # label(fact_414_setprod__cong) # label(axiom). [clausify(466)].
% 1.48/1.86 605 -comm_monoid_mult(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hAPP(B,A,E,f103(B,A,F,E,D,C)) != hAPP(B,A,F,f103(B,A,F,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),F),D) # label(fact_414_setprod__cong) # label(axiom). [clausify(466)].
% 1.48/1.86 Derived: big_co302546470etprod(A,nat) = ti(fun(fun(A,nat),fun(fun(A,bool),nat)),big_co302546470etprod(A,nat)). [resolve(594,a,595,a)].
% 1.48/1.86 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(A,nat,D,C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))). [resolve(594,a,596,a)].
% 1.48/1.86 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(A,nat,C,D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),bot_bot(fun(A,bool)))))). [resolve(594,a,597,a)].
% 1.48/1.86 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(A,nat,D,C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B)). [resolve(594,a,598,a)].
% 1.48/1.86 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f101(A,nat,C,D,B)),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B). [resolve(594,a,600,a)].
% 1.48/1.86 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,nat,C,f101(A,nat,D,C,B)) != hAPP(A,nat,D,f101(A,nat,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B). [resolve(594,a,601,a)].
% 1.48/1.86 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f102(A,nat,D,E,C,B)),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),E),B). [resolve(594,a,602,a)].
% 1.48/1.86 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,nat,D,f102(A,nat,D,E,C,B)) != hAPP(A,nat,E,f102(A,nat,D,E,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),E),B). [resolve(594,a,603,a)].
% 1.48/1.86 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f103(A,nat,D,E,C,B)),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),E),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C). [resolve(594,a,604,a)].
% 1.48/1.86 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,nat,D,f103(A,nat,E,D,C,B)) != hAPP(A,nat,E,f103(A,nat,E,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),E),C). [resolve(594,a,605,a)].
% 1.48/1.89 606 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom). [assumption].
% 1.48/1.89 607 -linorder(A) | big_Inf_fin(A) = ti(fun(fun(A,fun(A,A)),fun(fun(A,bool),A)),big_Inf_fin(A)) # label(tsy_c_Big__Operators_Olattice_OInf__fin_res) # label(axiom). [clausify(3)].
% 1.48/1.89 608 -linorder(A) | big_Sup_fin(A) = ti(fun(fun(A,fun(A,A)),fun(fun(A,bool),A)),big_Sup_fin(A)) # label(tsy_c_Big__Operators_Olattice_OSup__fin_res) # label(axiom). [clausify(4)].
% 1.48/1.89 609 -linorder(A) | big_linorder_Max(A) = ti(fun(fun(A,bool),A),big_linorder_Max(A)) # label(tsy_c_Big__Operators_Olinorder__class_OMax_res) # label(axiom). [clausify(5)].
% 1.48/1.89 610 -linorder(A) | big_linorder_Min(A) = ti(fun(fun(A,bool),A),big_linorder_Min(A)) # label(tsy_c_Big__Operators_Olinorder__class_OMin_res) # label(axiom). [clausify(6)].
% 1.48/1.89 611 -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_90_linorder__linear) # label(axiom). [clausify(142)].
% 1.48/1.89 612 -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_106_linorder__le__cases) # label(axiom). [clausify(158)].
% 1.48/1.89 613 -linorder(A) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),B),C)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),C)),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) # label(fact_187_fold1__antimono) # label(axiom). [clausify(239)].
% 1.48/1.89 614 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),B) = ti(A,B) # label(fact_190_Min_Oidem) # label(axiom). [clausify(242)].
% 1.48/1.89 615 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),B) = ti(A,B) # label(fact_192_min__max_Oinf_Oidem) # label(axiom). [clausify(244)].
% 1.48/1.89 616 -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_193_min__max_Oinf_Ocommute) # label(axiom). [clausify(245)].
% 1.48/1.89 617 -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_194_min__max_Oinf__commute) # label(axiom). [clausify(246)].
% 1.48/1.89 618 -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_195_min__max_Oinf_Oleft__idem) # label(axiom). [clausify(247)].
% 1.48/1.89 619 -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_196_min__max_Oinf__left__idem) # label(axiom). [clausify(248)].
% 1.48/1.89 620 -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_197_min__max_Oinf_Oleft__commute) # label(axiom). [clausify(249)].
% 1.48/1.89 621 -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_198_min__max_Oinf__left__commute) # label(axiom). [clausify(250)].
% 1.48/1.89 622 -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_199_min__max_Oinf_Oassoc) # label(axiom). [clausify(251)].
% 1.48/1.89 623 -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_200_min__max_Oinf__assoc) # label(axiom). [clausify(252)].
% 1.48/1.89 624 -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_201_min__max_Oinf__le1) # label(axiom). [clausify(253)].
% 1.48/1.89 625 -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_202_min__max_Oinf__le2) # label(axiom). [clausify(254)].
% 1.48/1.89 626 -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_203_min__max_Ole__iff__inf) # label(axiom). [clausify(255)].
% 1.48/1.89 627 -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_203_min__max_Ole__iff__inf) # label(axiom). [clausify(255)].
% 1.48/1.89 628 -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_204_min__max_Ole__inf__iff) # label(axiom). [clausify(256)].
% 1.48/1.89 629 -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_204_min__max_Ole__inf__iff) # label(axiom). [clausify(256)].
% 1.48/1.89 630 -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_204_min__max_Ole__inf__iff) # label(axiom). [clausify(256)].
% 1.48/1.89 631 -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_205_min__max_Ole__infI1) # label(axiom). [clausify(257)].
% 1.48/1.89 632 -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_206_min__max_Ole__infI2) # label(axiom). [clausify(258)].
% 1.48/1.89 633 -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_207_min__max_Oinf__absorb1) # label(axiom). [clausify(259)].
% 1.48/1.89 634 -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_208_min__max_Oinf__absorb2) # label(axiom). [clausify(260)].
% 1.48/1.89 635 -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_209_min__max_Ole__infI) # label(axiom). [clausify(261)].
% 1.48/1.89 636 -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_210_min__max_Oinf__greatest) # label(axiom). [clausify(262)].
% 1.48/1.89 637 -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_211_min__max_Oinf__mono) # label(axiom). [clausify(263)].
% 1.48/1.89 638 -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_212_min__max_Ole__infE) # label(axiom). [clausify(264)].
% 1.48/1.89 639 -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_212_min__max_Ole__infE) # label(axiom). [clausify(264)].
% 1.48/1.89 640 -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_213_min__le__iff__disj) # label(axiom). [clausify(265)].
% 1.48/1.89 641 -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_213_min__le__iff__disj) # label(axiom). [clausify(265)].
% 1.48/1.89 642 -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_213_min__le__iff__disj) # label(axiom). [clausify(265)].
% 1.48/1.89 643 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),C)) # label(fact_215_min__max_Ofold1__belowI) # label(axiom). [clausify(267)].
% 1.48/1.89 644 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f70(A,C,B)),B)) # label(fact_217_fold1__below__iff) # label(axiom). [clausify(269)].
% 1.48/1.89 645 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f70(A,C,B)),C)) # label(fact_217_fold1__below__iff) # label(axiom). [clausify(269)].
% 1.48/1.89 646 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),C)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) # label(fact_217_fold1__below__iff) # label(axiom). [clausify(269)].
% 1.48/1.89 647 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_218_min__max_Obelow__fold1__iff) # label(axiom). [clausify(270)].
% 1.48/1.89 648 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f71(A,C,B)),B)) # label(fact_218_min__max_Obelow__fold1__iff) # label(axiom). [clausify(270)].
% 1.48/1.89 649 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),f71(A,C,B))) # label(fact_218_min__max_Obelow__fold1__iff) # label(axiom). [clausify(270)].
% 1.48/1.89 650 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) != bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Min(A),B) = ti(A,C) # label(fact_223_Min_Oremove) # label(axiom). [clausify(275)].
% 1.48/1.89 651 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Min(A),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_223_Min_Oremove) # label(axiom). [clausify(275)].
% 1.48/1.89 652 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,big_linorder_Min(A),B)),C)) # label(fact_224_Min__le) # label(axiom). [clausify(276)].
% 1.48/1.89 653 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,big_linorder_Min(A),B)),B)) # label(fact_225_Min__in) # label(axiom). [clausify(277)].
% 1.48/1.89 654 -linorder(A) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),bot_bot(fun(A,bool)))) = ti(A,B) # label(fact_226_Min_Osingleton) # label(axiom). [clausify(278)].
% 1.48/1.89 655 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,big_linorder_Min(A),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,big_linorder_Min(A),B)) # label(fact_227_Min_Oin__idem) # label(axiom). [clausify(279)].
% 1.48/1.89 656 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B) = hAPP(fun(A,bool),A,big_linorder_Min(A),B) # label(fact_228_Min_OF__eq) # label(axiom). [clausify(280)].
% 1.48/1.89 657 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),B),C)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,big_linorder_Min(A),C)),hAPP(fun(A,bool),A,big_linorder_Min(A),B))) # label(fact_229_Min__antimono) # label(axiom). [clausify(281)].
% 1.48/1.89 658 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,big_linorder_Min(A),B)) # label(fact_230_Min_Oinsert) # label(axiom). [clausify(282)].
% 1.48/1.89 659 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,big_linorder_Min(A),B)) # label(fact_231_Min__insert) # label(axiom). [clausify(283)].
% 1.48/1.89 660 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),C) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),A,big_linorder_Min(A),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(fun(A,bool),A,big_linorder_Min(A),C)),hAPP(fun(A,bool),A,big_linorder_Min(A),B)) # label(fact_232_Min_Osubset__idem) # label(axiom). [clausify(284)].
% 1.48/1.89 661 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) != bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = ti(A,C) # label(fact_233_Min_Oinsert__remove) # label(axiom). [clausify(285)].
% 1.48/1.89 662 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_233_Min_Oinsert__remove) # label(axiom). [clausify(285)].
% 1.48/1.89 663 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f75(A,B)),f76(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f75(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f76(A,B)),bot_bot(fun(A,bool)))))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,big_linorder_Min(A),B)),B)) # label(fact_234_Min_Oclosed) # label(axiom). [clausify(286)].
% 1.48/1.89 664 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f77(A,C,B)),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,big_linorder_Min(A),B) = ti(A,C) # label(fact_235_Min__eqI) # label(axiom). [clausify(287)].
% 1.48/1.89 665 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),f77(A,C,B))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,big_linorder_Min(A),B) = ti(A,C) # label(fact_235_Min__eqI) # label(axiom). [clausify(287)].
% 1.48/1.89 666 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) != bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = ti(A,C) # label(fact_236_min__max_OInf__fin_Oinsert__remove) # label(axiom). [clausify(288)].
% 1.48/1.89 667 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_236_min__max_OInf__fin_Oinsert__remove) # label(axiom). [clausify(288)].
% 1.48/1.89 668 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) != bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B) = ti(A,C) # label(fact_237_min__max_OInf__fin_Oremove) # label(axiom). [clausify(289)].
% 1.48/1.89 669 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_237_min__max_OInf__fin_Oremove) # label(axiom). [clausify(289)].
% 1.48/1.89 670 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)) # label(fact_238_min__max_OInf__fin_Oin__idem) # label(axiom). [clausify(290)].
% 1.48/1.89 671 -linorder(A) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),bot_bot(fun(A,bool)))) = ti(A,B) # label(fact_239_min__max_OInf__fin_Osingleton) # label(axiom). [clausify(291)].
% 1.48/1.89 672 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B) # label(fact_240_min__max_OInf__fin_OF__eq) # label(axiom). [clausify(292)].
% 1.48/1.89 673 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)) # label(fact_241_min__max_OInf__fin_Oinsert) # label(axiom). [clausify(293)].
% 1.48/1.89 674 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)) # label(fact_242_min__max_OInf__fin_Oinsert__idem) # label(axiom). [clausify(294)].
% 1.48/1.89 675 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),C) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),C)),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)) # label(fact_243_min__max_OInf__fin_Osubset__idem) # label(axiom). [clausify(295)].
% 1.48/1.89 676 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f78(A,B)),f79(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f78(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f79(A,B)),bot_bot(fun(A,bool)))))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)),B)) # label(fact_244_min__max_OInf__fin_Oclosed) # label(axiom). [clausify(296)].
% 1.48/1.89 677 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),B),C)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,big_linorder_Max(A),B)),hAPP(fun(A,bool),A,big_linorder_Max(A),C))) # label(fact_247_Max__mono) # label(axiom). [clausify(299)].
% 1.48/1.89 678 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),B))) # label(fact_250_Max__ge) # label(axiom). [clausify(302)].
% 1.48/1.89 679 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,big_linorder_Max(A),B)),B)) # label(fact_251_Max__in) # label(axiom). [clausify(303)].
% 1.48/1.89 680 -linorder(A) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),bot_bot(fun(A,bool)))) = ti(A,B) # label(fact_252_Max_Osingleton) # label(axiom). [clausify(304)].
% 1.48/1.89 681 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),D),B)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) # label(fact_254_min__max_Ofold__inf__le__inf) # label(axiom). [clausify(306)].
% 1.48/1.89 682 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),B)) # label(fact_255_min__max_Ofold__inf__insert) # label(axiom). [clausify(307)].
% 1.48/1.89 683 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),B) = hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) # label(fact_261_Min_Oeq__fold__idem_H) # label(axiom). [clausify(313)].
% 1.48/1.89 684 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),B) = hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) # label(fact_262_Min_Oeq__fold_H) # label(axiom). [clausify(314)].
% 1.48/1.89 685 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),B) # label(fact_263_min__max_OInf__fin_Oeq__fold__idem_H) # label(axiom). [clausify(315)].
% 1.48/1.89 686 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),B) # label(fact_264_min__max_OInf__fin_Oeq__fold_H) # label(axiom). [clausify(316)].
% 1.48/1.89 687 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f80(A,C,D,B)),B)) | 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),C)),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),B))) # label(fact_265_min__max_Oinf__le__fold__inf) # label(axiom). [clausify(317)].
% 1.48/1.89 688 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),f80(A,D,C,B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),D),B))) # label(fact_265_min__max_Oinf__le__fold__inf) # label(axiom). [clausify(317)].
% 1.48/1.89 689 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f81(A,C,B)),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,big_linorder_Max(A),B) = ti(A,C) # label(fact_266_Max__eqI) # label(axiom). [clausify(318)].
% 1.48/1.89 690 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f81(A,C,B)),C)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,big_linorder_Max(A),B) = ti(A,C) # label(fact_266_Max__eqI) # label(axiom). [clausify(318)].
% 1.48/1.89 691 -linorder(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite_comp_fun_idem(A,A),ord_min(A))) # label(fact_271_min__max_Ocomp__fun__idem__inf) # label(axiom). [clausify(323)].
% 1.48/1.89 692 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) != bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Max(A),B) = ti(A,C) # label(fact_272_Max_Oremove) # label(axiom). [clausify(324)].
% 1.48/1.89 693 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Max(A),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_272_Max_Oremove) # label(axiom). [clausify(324)].
% 1.48/1.89 694 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) != bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = ti(A,C) # label(fact_273_Max_Oinsert__remove) # label(axiom). [clausify(325)].
% 1.48/1.89 695 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_273_Max_Oinsert__remove) # label(axiom). [clausify(325)].
% 1.48/1.89 696 -linorder(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite_comp_fun_idem(A,A),ord_max(A))) # label(fact_276_min__max_Ocomp__fun__idem__sup) # label(axiom). [clausify(328)].
% 1.48/1.89 697 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),B) = ti(A,B) # label(fact_279_min__max_Osup_Oidem) # label(axiom). [clausify(331)].
% 1.48/1.89 698 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) # label(fact_280_min__max_Osup_Ocommute) # label(axiom). [clausify(332)].
% 1.48/1.89 699 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) # label(fact_281_min__max_Osup__commute) # label(axiom). [clausify(333)].
% 1.48/1.89 700 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) = ti(A,B) # label(fact_282_min__max_Osup__inf__absorb) # label(axiom). [clausify(334)].
% 1.48/1.89 701 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) = ti(A,B) # label(fact_283_min__max_Oinf__sup__absorb) # label(axiom). [clausify(335)].
% 1.48/1.89 702 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) # label(fact_284_min__max_Osup_Oleft__idem) # label(axiom). [clausify(336)].
% 1.48/1.89 703 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) # label(fact_285_min__max_Osup__left__idem) # label(axiom). [clausify(337)].
% 1.48/1.89 704 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) # label(fact_286_min__max_Osup_Oleft__commute) # label(axiom). [clausify(338)].
% 1.48/1.89 705 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) # label(fact_287_min__max_Osup__left__commute) # label(axiom). [clausify(339)].
% 1.48/1.89 706 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_288_min__max_Osup__inf__distrib1) # label(axiom). [clausify(340)].
% 1.48/1.89 707 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_289_min__max_Oinf__sup__distrib1) # label(axiom). [clausify(341)].
% 1.48/1.89 708 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) # label(fact_290_min__max_Osup_Oassoc) # label(axiom). [clausify(342)].
% 1.48/1.89 709 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) # label(fact_291_min__max_Osup__assoc) # label(axiom). [clausify(343)].
% 1.48/1.89 710 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C) # label(fact_292_min__max_Osup__inf__distrib2) # label(axiom). [clausify(344)].
% 1.48/1.89 711 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_293_min__max_Oinf__sup__distrib2) # label(axiom). [clausify(345)].
% 1.48/1.89 712 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C))) # label(fact_294_le__maxI1) # label(axiom). [clausify(346)].
% 1.48/1.89 713 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B))) # label(fact_295_le__maxI2) # label(axiom). [clausify(347)].
% 1.48/1.89 714 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) = ti(A,C) # label(fact_296_min__max_Ole__iff__sup) # label(axiom). [clausify(348)].
% 1.48/1.89 715 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) != ti(A,C) # label(fact_296_min__max_Ole__iff__sup) # label(axiom). [clausify(348)].
% 1.48/1.89 716 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_297_min__max_Ole__sup__iff) # label(axiom). [clausify(349)].
% 1.48/1.89 717 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_297_min__max_Ole__sup__iff) # label(axiom). [clausify(349)].
% 1.48/1.89 718 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_297_min__max_Ole__sup__iff) # label(axiom). [clausify(349)].
% 1.48/1.89 719 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) # label(fact_298_min__max_Ole__supI1) # label(axiom). [clausify(350)].
% 1.48/1.89 720 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_299_min__max_Ole__supI2) # label(axiom). [clausify(351)].
% 1.48/1.89 721 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) = ti(A,C) # label(fact_300_min__max_Osup__absorb2) # label(axiom). [clausify(352)].
% 1.48/1.89 722 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) = ti(A,C) # label(fact_301_min__max_Osup__absorb1) # label(axiom). [clausify(353)].
% 1.48/1.89 723 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C)) # label(fact_302_min__max_Ole__supI) # label(axiom). [clausify(354)].
% 1.48/1.89 724 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C)) # label(fact_303_min__max_Osup__least) # label(axiom). [clausify(355)].
% 1.48/1.89 725 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),E))) # label(fact_304_min__max_Osup__mono) # label(axiom). [clausify(356)].
% 1.48/1.89 726 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_305_min__max_Ole__supE) # label(axiom). [clausify(357)].
% 1.48/1.89 727 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_305_min__max_Ole__supE) # label(axiom). [clausify(357)].
% 1.48/1.89 728 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_306_le__max__iff__disj) # label(axiom). [clausify(358)].
% 1.48/1.89 729 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_306_le__max__iff__disj) # label(axiom). [clausify(358)].
% 1.48/1.89 730 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_306_le__max__iff__disj) # label(axiom). [clausify(358)].
% 1.48/1.89 731 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),B) = ti(A,B) # label(fact_307_Max_Oidem) # label(axiom). [clausify(359)].
% 1.48/1.89 732 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D))),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)))) # label(fact_308_min__max_Odistrib__inf__le) # label(axiom). [clausify(360)].
% 1.48/1.89 733 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)))) # label(fact_309_min__max_Odistrib__sup__le) # label(axiom). [clausify(361)].
% 1.48/1.89 734 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,big_linorder_Max(A),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),B)) # label(fact_310_Max_Oin__idem) # label(axiom). [clausify(362)].
% 1.48/1.89 735 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),D),B))) # label(fact_313_min__max_Osup__le__fold__sup) # label(axiom). [clausify(365)].
% 1.48/1.89 736 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B)) # label(fact_314_min__max_Ofold__sup__insert) # label(axiom). [clausify(366)].
% 1.48/1.89 737 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)) = ti(A,C) # label(fact_315_min__max_Osup__Inf__absorb) # label(axiom). [clausify(367)].
% 1.48/1.89 738 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_max(A)),B) = hAPP(fun(A,bool),A,big_linorder_Max(A),B) # label(fact_316_Max_OF__eq) # label(axiom). [clausify(368)].
% 1.48/1.90 739 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),B)) # label(fact_318_Max_Oinsert) # label(axiom). [clausify(370)].
% 1.48/1.90 740 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),B)) # label(fact_319_Max__insert) # label(axiom). [clausify(371)].
% 1.48/1.90 741 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),C) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),A,big_linorder_Max(A),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(fun(A,bool),A,big_linorder_Max(A),C)),hAPP(fun(A,bool),A,big_linorder_Max(A),B)) # label(fact_320_Max_Osubset__idem) # label(axiom). [clausify(372)].
% 1.48/1.90 742 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B) = hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) # label(fact_321_Max_Oeq__fold__idem_H) # label(axiom). [clausify(373)].
% 1.48/1.90 743 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B) = hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) # label(fact_322_Max_Oeq__fold_H) # label(axiom). [clausify(374)].
% 1.48/1.90 744 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f82(A,B)),f83(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f82(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f83(A,B)),bot_bot(fun(A,bool)))))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,big_linorder_Max(A),B)),B)) # label(fact_324_Max_Oclosed) # label(axiom). [clausify(376)].
% 1.48/1.90 745 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f84(A,C,D,B)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_325_min__max_Ofold__sup__le__sup) # label(axiom). [clausify(377)].
% 1.48/1.90 746 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f84(A,C,D,B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_325_min__max_Ofold__sup__le__sup) # label(axiom). [clausify(377)].
% 1.48/1.90 747 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f85(A,B,C,D)),f86(A,B,C,D))),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f85(A,B,C,D)),f87(A,B,C,D))) != hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f85(A,B,C,D)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f86(A,B,C,D)),f87(A,B,C,D))) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_326_min__max_Odistrib__imp2) # label(axiom). [clausify(378)].
% 1.48/1.90 748 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f88(A,B,C,D)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f89(A,B,C,D)),f90(A,B,C,D))) != hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f88(A,B,C,D)),f89(A,B,C,D))),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f88(A,B,C,D)),f90(A,B,C,D))) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_327_min__max_Odistrib__imp1) # label(axiom). [clausify(379)].
% 1.48/1.90 749 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B))) # label(fact_332_min__max_OInf__le__Sup) # label(axiom). [clausify(384)].
% 1.48/1.90 750 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) != bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = ti(A,C) # label(fact_333_min__max_OSup__fin_Oinsert__remove) # label(axiom). [clausify(385)].
% 1.48/1.90 751 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_333_min__max_OSup__fin_Oinsert__remove) # label(axiom). [clausify(385)].
% 1.48/1.90 752 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)) # label(fact_334_min__max_OSup__fin_Oin__idem) # label(axiom). [clausify(386)].
% 1.48/1.90 753 -linorder(A) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),bot_bot(fun(A,bool)))) = ti(A,B) # label(fact_335_min__max_OSup__fin_Osingleton) # label(axiom). [clausify(387)].
% 1.48/1.90 754 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)) = ti(A,C) # label(fact_336_min__max_Oinf__Sup__absorb) # label(axiom). [clausify(388)].
% 1.48/1.90 755 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_max(A)),B) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B) # label(fact_337_min__max_OSup__fin_OF__eq) # label(axiom). [clausify(389)].
% 1.48/1.90 756 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)) # label(fact_338_min__max_OSup__fin_Oinsert__idem) # label(axiom). [clausify(390)].
% 1.48/1.90 757 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)) # label(fact_339_min__max_OSup__fin_Oinsert) # label(axiom). [clausify(391)].
% 1.48/1.90 758 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),C) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),C)),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)) # label(fact_340_min__max_OSup__fin_Osubset__idem) # label(axiom). [clausify(392)].
% 1.48/1.90 759 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B) # label(fact_341_min__max_OSup__fin_Oeq__fold__idem_H) # label(axiom). [clausify(393)].
% 1.48/1.90 760 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B) # label(fact_342_min__max_OSup__fin_Oeq__fold_H) # label(axiom). [clausify(394)].
% 1.48/1.90 761 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) != bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B) = ti(A,C) # label(fact_343_min__max_OSup__fin_Oremove) # label(axiom). [clausify(395)].
% 1.48/1.90 762 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_343_min__max_OSup__fin_Oremove) # label(axiom). [clausify(395)].
% 1.48/1.90 763 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f94(A,B)),f95(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f94(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f95(A,B)),bot_bot(fun(A,bool)))))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)),B)) # label(fact_344_min__max_OSup__fin_Oclosed) # label(axiom). [clausify(396)].
% 1.48/1.90 764 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_415_strict__below__fold1__iff) # label(axiom). [clausify(467)].
% 1.48/1.90 765 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f104(A,C,B)),B)) # label(fact_415_strict__below__fold1__iff) # label(axiom). [clausify(467)].
% 1.48/1.90 766 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),f104(A,C,B))) # label(fact_415_strict__below__fold1__iff) # label(axiom). [clausify(467)].
% 1.48/1.90 767 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) # label(fact_425_min__max_Oless__supI1) # label(axiom). [clausify(477)].
% 1.48/1.90 768 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_426_min__max_Oless__supI2) # label(axiom). [clausify(478)].
% 1.48/1.90 769 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_427_less__max__iff__disj) # label(axiom). [clausify(479)].
% 1.48/1.90 770 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_427_less__max__iff__disj) # label(axiom). [clausify(479)].
% 1.48/1.90 771 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_427_less__max__iff__disj) # label(axiom). [clausify(479)].
% 1.48/1.90 772 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_428_max__less__iff__conj) # label(axiom). [clausify(480)].
% 1.48/1.90 773 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_428_max__less__iff__conj) # label(axiom). [clausify(480)].
% 1.48/1.90 774 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_428_max__less__iff__conj) # label(axiom). [clausify(480)].
% 1.48/1.90 775 -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_437_min__max_Oless__infI2) # label(axiom). [clausify(489)].
% 1.48/1.90 776 -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_438_min__max_Oless__infI1) # label(axiom). [clausify(490)].
% 1.48/1.90 777 -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_439_min__less__iff__conj) # label(axiom). [clausify(491)].
% 1.48/1.90 778 -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_439_min__less__iff__conj) # label(axiom). [clausify(491)].
% 1.48/1.90 779 -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_439_min__less__iff__conj) # label(axiom). [clausify(491)].
% 1.48/1.90 780 -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_440_min__less__iff__disj) # label(axiom). [clausify(492)].
% 1.48/1.90 781 -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_440_min__less__iff__disj) # label(axiom). [clausify(492)].
% 1.48/1.90 782 -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_440_min__less__iff__disj) # label(axiom). [clausify(492)].
% 1.48/1.90 783 -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_441_linorder__cases) # label(axiom). [clausify(493)].
% 1.48/1.90 784 -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_457_linorder__neqE) # label(axiom). [clausify(509)].
% 1.48/1.90 785 -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_458_linorder__antisym__conv3) # label(axiom). [clausify(510)].
% 1.48/1.90 786 -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_458_linorder__antisym__conv3) # label(axiom). [clausify(510)].
% 1.48/1.90 787 -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_459_linorder__less__linear) # label(axiom). [clausify(511)].
% 1.48/1.90 788 -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_460_not__less__iff__gr__or__eq) # label(axiom). [clausify(512)].
% 1.48/1.90 789 -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_460_not__less__iff__gr__or__eq) # label(axiom). [clausify(512)].
% 1.48/1.90 790 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_460_not__less__iff__gr__or__eq) # label(axiom). [clausify(512)].
% 1.48/1.90 791 -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_461_linorder__neq__iff) # label(axiom). [clausify(513)].
% 1.48/1.90 792 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_461_linorder__neq__iff) # label(axiom). [clausify(513)].
% 1.48/1.90 793 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_461_linorder__neq__iff) # label(axiom). [clausify(513)].
% 1.48/1.90 794 -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_463_linorder__not__less) # label(axiom). [clausify(515)].
% 1.48/1.90 795 -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_463_linorder__not__less) # label(axiom). [clausify(515)].
% 1.48/1.90 796 -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_464_linorder__not__le) # label(axiom). [clausify(516)].
% 1.48/1.90 797 -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_464_linorder__not__le) # label(axiom). [clausify(516)].
% 1.48/1.90 798 -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_465_linorder__le__less__linear) # label(axiom). [clausify(517)].
% 1.48/1.90 799 -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_469_leI) # label(axiom). [clausify(521)].
% 1.48/1.90 800 -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_470_not__leE) # label(axiom). [clausify(522)].
% 1.48/1.90 801 -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_471_linorder__antisym__conv1) # label(axiom). [clausify(523)].
% 1.48/1.90 802 -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_471_linorder__antisym__conv1) # label(axiom). [clausify(523)].
% 1.48/1.90 803 -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_474_leD) # label(axiom). [clausify(526)].
% 1.48/1.90 804 -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_476_linorder__antisym__conv2) # label(axiom). [clausify(528)].
% 1.48/1.90 805 -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_476_linorder__antisym__conv2) # label(axiom). [clausify(528)].
% 1.48/1.90 806 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f105(A,C,B)),B)) # label(fact_490_fold1__strict__below__iff) # label(axiom). [clausify(542)].
% 1.48/1.90 807 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f105(A,C,B)),C)) # label(fact_490_fold1__strict__below__iff) # label(axiom). [clausify(542)].
% 1.48/1.90 808 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),C)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) # label(fact_490_fold1__strict__below__iff) # label(axiom). [clausify(542)].
% 1.48/1.90 Derived: big_Inf_fin(nat) = ti(fun(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat)),big_Inf_fin(nat)). [resolve(606,a,607,a)].
% 1.48/1.90 Derived: big_Sup_fin(nat) = ti(fun(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat)),big_Sup_fin(nat)). [resolve(606,a,608,a)].
% 1.48/1.90 Derived: big_linorder_Max(nat) = ti(fun(fun(nat,bool),nat),big_linorder_Max(nat)). [resolve(606,a,609,a)].
% 1.48/1.90 Derived: big_linorder_Min(nat) = ti(fun(fun(nat,bool),nat),big_linorder_Min(nat)). [resolve(606,a,610,a)].
% 1.48/1.90 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(606,a,611,a)].
% 1.48/1.90 Derived: bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A),B)) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),B)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))). [resolve(606,a,613,a)].
% 1.48/1.90 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),A) = ti(nat,A). [resolve(606,a,614,a)].
% 1.48/1.90 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(606,a,616,a)].
% 1.48/1.90 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(606,a,618,a)].
% 1.48/1.90 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(606,a,620,a)].
% 1.48/1.90 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(606,a,622,a)].
% 1.48/1.90 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(606,a,624,a)].
% 1.48/1.90 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(606,a,625,a)].
% 1.48/1.90 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(606,a,626,a)].
% 1.48/1.90 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(606,a,627,a)].
% 1.48/1.90 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(606,a,628,a)].
% 1.48/1.90 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(606,a,629,a)].
% 1.48/1.90 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(606,a,630,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),B)). [resolve(606,a,631,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),C),A)),B)). [resolve(606,a,632,a)].
% 1.48/1.90 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(606,a,634,a)].
% 1.48/1.90 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(606,a,637,a)].
% 1.48/1.90 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(606,a,640,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),B)). [resolve(606,a,643,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),B)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f70(nat,B,A)),A)). [resolve(606,a,644,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f70(nat,B,A)),B)). [resolve(606,a,645,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),B)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),C),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),B)). [resolve(606,a,646,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),C),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(606,a,647,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f71(nat,B,A)),A)). [resolve(606,a,648,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f71(nat,B,A))). [resolve(606,a,649,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) != bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A) = ti(nat,B). [resolve(606,a,650,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))). [resolve(606,a,651,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)),B)). [resolve(606,a,652,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)),A)). [resolve(606,a,653,a)].
% 1.48/1.90 Derived: hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),A),bot_bot(fun(nat,bool)))) = ti(nat,A). [resolve(606,a,654,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)). [resolve(606,a,655,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A) = hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A). [resolve(606,a,656,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A),B)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),B)),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A))). [resolve(606,a,657,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)). [resolve(606,a,658,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)). [resolve(606,a,659,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),B) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),B),A)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),B)),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)). [resolve(606,a,660,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) != bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = ti(nat,B). [resolve(606,a,661,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))). [resolve(606,a,662,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f77(nat,B,A)),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A) = ti(nat,B). [resolve(606,a,664,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f77(nat,B,A))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A) = ti(nat,B). [resolve(606,a,665,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) != bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = ti(nat,B). [resolve(606,a,666,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))). [resolve(606,a,667,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) != bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A) = ti(nat,B). [resolve(606,a,668,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))). [resolve(606,a,669,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)). [resolve(606,a,670,a)].
% 1.48/1.90 Derived: hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),A),bot_bot(fun(nat,bool)))) = ti(nat,A). [resolve(606,a,671,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A). [resolve(606,a,672,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)). [resolve(606,a,673,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)). [resolve(606,a,674,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),B) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),B)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)). [resolve(606,a,675,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),f78(nat,A)),f79(nat,A))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f78(nat,A)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f79(nat,A)),bot_bot(fun(nat,bool)))))) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)),A)). [resolve(606,a,676,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A),B)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),B))). [resolve(606,a,677,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A))). [resolve(606,a,678,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)),A)). [resolve(606,a,679,a)].
% 1.48/1.90 Derived: hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),A),bot_bot(fun(nat,bool)))) = ti(nat,A). [resolve(606,a,680,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))). [resolve(606,a,681,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),B),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),C),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),C),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),B),A)). [resolve(606,a,682,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),B),A) = hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)). [resolve(606,a,683,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),B),A). [resolve(606,a,685,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f80(nat,B,C,A)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),C),B)),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),B),A))). [resolve(606,a,687,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f80(nat,C,B,A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),C),A))). [resolve(606,a,688,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f81(nat,B,A)),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A) = ti(nat,B). [resolve(606,a,689,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f81(nat,B,A)),B)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A) = ti(nat,B). [resolve(606,a,690,a)].
% 1.48/1.90 Derived: hBOOL(hAPP(fun(nat,fun(nat,nat)),bool,finite_comp_fun_idem(nat,nat),ord_min(nat))). [resolve(606,a,691,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) != bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A) = ti(nat,B). [resolve(606,a,692,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))). [resolve(606,a,693,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) != bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = ti(nat,B). [resolve(606,a,694,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))). [resolve(606,a,695,a)].
% 1.48/1.90 Derived: hBOOL(hAPP(fun(nat,fun(nat,nat)),bool,finite_comp_fun_idem(nat,nat),ord_max(nat))). [resolve(606,a,696,a)].
% 1.48/1.90 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),A) = ti(nat,A). [resolve(606,a,697,a)].
% 1.48/1.90 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A). [resolve(606,a,698,a)].
% 1.48/1.90 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)) = ti(nat,A). [resolve(606,a,700,a)].
% 1.48/1.90 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)) = ti(nat,A). [resolve(606,a,701,a)].
% 1.48/1.90 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B). [resolve(606,a,702,a)].
% 1.48/1.90 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)). [resolve(606,a,704,a)].
% 1.48/1.90 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)). [resolve(606,a,706,a)].
% 1.48/1.90 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)). [resolve(606,a,707,a)].
% 1.48/1.90 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)). [resolve(606,a,708,a)].
% 1.48/1.90 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),B). [resolve(606,a,710,a)].
% 1.48/1.90 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)). [resolve(606,a,711,a)].
% 1.48/1.90 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B))). [resolve(606,a,712,a)].
% 1.48/1.90 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A))). [resolve(606,a,713,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B) = ti(nat,B). [resolve(606,a,714,a)].
% 1.48/1.90 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B) != ti(nat,B). [resolve(606,a,715,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(606,a,716,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(606,a,717,a)].
% 1.48/1.90 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(606,a,718,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))). [resolve(606,a,719,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B))). [resolve(606,a,720,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A) = ti(nat,B). [resolve(606,a,722,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),D))). [resolve(606,a,725,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(606,a,728,a)].
% 1.48/1.90 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)))). [resolve(606,a,732,a)].
% 1.48/1.90 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)))). [resolve(606,a,733,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)). [resolve(606,a,734,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),C),A))). [resolve(606,a,735,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),B),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),C),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),B),A)). [resolve(606,a,736,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)) = ti(nat,B). [resolve(606,a,737,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_max(nat)),A) = hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A). [resolve(606,a,738,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)). [resolve(606,a,739,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)). [resolve(606,a,740,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),B) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),B),A)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),B)),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)). [resolve(606,a,741,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),B),A) = hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)). [resolve(606,a,742,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f84(nat,B,C,A)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B))). [resolve(606,a,745,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f84(nat,B,C,A)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B))). [resolve(606,a,746,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A))). [resolve(606,a,749,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) != bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = ti(nat,B). [resolve(606,a,750,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))). [resolve(606,a,751,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A)). [resolve(606,a,752,a)].
% 1.48/1.90 Derived: hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),A),bot_bot(fun(nat,bool)))) = ti(nat,A). [resolve(606,a,753,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A)) = ti(nat,B). [resolve(606,a,754,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_max(nat)),A) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A). [resolve(606,a,755,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A)). [resolve(606,a,756,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),B) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),B)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A)). [resolve(606,a,758,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),B),A). [resolve(606,a,759,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) != bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A) = ti(nat,B). [resolve(606,a,761,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))). [resolve(606,a,762,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),f94(nat,A)),f95(nat,A))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f94(nat,A)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f95(nat,A)),bot_bot(fun(nat,bool)))))) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A)),A)). [resolve(606,a,763,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),C),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(606,a,764,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f104(nat,B,A)),A)). [resolve(606,a,765,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),f104(nat,B,A))). [resolve(606,a,766,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))). [resolve(606,a,767,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B))). [resolve(606,a,768,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(606,a,769,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(606,a,772,a)].
% 1.48/1.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(606,a,773,a)].
% 1.48/1.90 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(606,a,774,a)].
% 1.48/1.91 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),ord_min(nat),C),A)),B)). [resolve(606,a,775,a)].
% 1.48/1.91 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),ord_min(nat),A),C)),B)). [resolve(606,a,776,a)].
% 1.48/1.91 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(606,a,777,a)].
% 1.48/1.91 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(606,a,778,a)].
% 1.48/1.91 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(606,a,779,a)].
% 1.48/1.93 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(606,a,780,a)].
% 1.48/1.93 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) = ti(nat,A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(606,a,783,a)].
% 1.48/1.93 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)) | ti(nat,A) != ti(nat,B). [resolve(606,a,786,a)].
% 1.48/1.93 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(606,a,789,a)].
% 1.48/1.93 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) != ti(nat,A). [resolve(606,a,790,a)].
% 1.48/1.93 Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(606,a,793,a)].
% 1.48/1.93 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(606,a,794,a)].
% 1.48/1.93 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(606,a,795,a)].
% 1.48/1.93 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(606,a,801,a)].
% 1.48/1.93 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(606,a,802,a)].
% 1.48/1.93 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),B)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f105(nat,B,A)),A)). [resolve(606,a,806,a)].
% 1.48/1.93 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f105(nat,B,A)),B)). [resolve(606,a,807,a)].
% 1.48/1.93 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),B)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),C),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),B)). [resolve(606,a,808,a)].
% 1.48/1.93 809 cancel_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.48/1.93 810 -cancel_semigroup_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(25)].
% 1.48/1.93 811 -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_350_add__left__cancel) # label(axiom). [clausify(402)].
% 1.48/1.93 812 -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_350_add__left__cancel) # label(axiom). [clausify(402)].
% 1.48/1.93 813 -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_351_add__right__cancel) # label(axiom). [clausify(403)].
% 1.48/2.00 814 -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_351_add__right__cancel) # label(axiom). [clausify(403)].
% 1.48/2.00 815 -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_352_add__left__imp__eq) # label(axiom). [clausify(404)].
% 1.48/2.00 816 -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_354_add__right__imp__eq) # label(axiom). [clausify(406)].
% 1.48/2.00 Derived: plus_plus(nat) = ti(fun(nat,fun(nat,nat)),plus_plus(nat)). [resolve(809,a,810,a)].
% 1.48/2.00 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(809,a,811,a)].
% 1.48/2.00 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(809,a,812,a)].
% 1.48/2.00 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(809,a,813,a)].
% 1.48/2.00 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(809,a,814,a)].
% 1.48/2.00 817 ab_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 1.48/2.00 818 -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(26)].
% 1.48/2.00 819 -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_349_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom). [clausify(401)].
% 1.48/2.00 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(817,a,819,a)].
% 1.48/2.00 820 semiring(nat) # label(arity_Nat_Onat___Rings_Osemiring) # label(axiom). [assumption].
% 1.48/2.00 821 -semiring(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_0_res) # label(axiom). [clausify(27)].
% 1.48/2.00 822 -semiring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),E)) # label(fact_384_combine__common__factor) # label(axiom). [clausify(436)].
% 1.48/2.00 Derived: times_times(nat) = ti(fun(nat,fun(nat,nat)),times_times(nat)). [resolve(820,a,821,a)].
% 1.48/2.00 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C)),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)),D)). [resolve(820,a,822,a)].
% 1.48/2.00 823 ab_semigroup_mult(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.48/2.00 824 -ab_semigroup_mult(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_1_res) # label(axiom). [clausify(28)].
% 1.48/2.00 825 -ab_semigroup_mult(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),times_times(A)),C),B) # label(fact_371_fold1__eq__fold) # label(axiom). [clausify(423)].
% 1.48/2.00 826 -ab_semigroup_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_375_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom). [clausify(427)].
% 1.48/2.00 827 -ab_semigroup_mult(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite100568337ommute(A,A),times_times(A))) # label(fact_376_comp__fun__commute) # label(axiom). [clausify(428)].
% 1.48/2.00 828 -ab_semigroup_mult(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),fun(A,bool))),finite_fold_graph(A,A),times_times(A)),B),C),D)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),fun(A,bool))),finite_fold_graph(A,A),times_times(A)),E),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),D))) # label(fact_378_fold__graph__insert__swap) # label(axiom). [clausify(430)].
% 1.48/2.00 829 -ab_semigroup_mult(A) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),B)) # label(fact_380_fold1__insert) # label(axiom). [clausify(432)].
% 1.48/2.00 830 -ab_semigroup_mult(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),fun(A,bool))),finite_fold_graph(A,A),times_times(A)),B),C),D)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),E),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),fun(A,bool))),finite_fold_graph(A,A),times_times(A)),E),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),E),bot_bot(fun(A,bool)))))),D)) # label(fact_381_fold__graph__permute__diff) # label(axiom). [clausify(433)].
% 1.48/2.00 831 -ab_semigroup_mult(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f99(A,B)),f100(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f99(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f100(A,B)),bot_bot(fun(A,bool)))))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),B)),B)) # label(fact_382_fold1__in) # label(axiom). [clausify(434)].
% 1.48/2.00 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),times_times(nat)),B),A). [resolve(823,a,825,a)].
% 1.48/2.00 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(823,a,826,a)].
% 1.48/2.14 Derived: hBOOL(hAPP(fun(nat,fun(nat,nat)),bool,finite100568337ommute(nat,nat),times_times(nat))). [resolve(823,a,827,a)].
% 1.48/2.14 Derived: -hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),finite_fold_graph(nat,nat),times_times(nat)),A),B),C)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),finite_fold_graph(nat,nat),times_times(nat)),D),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D),C))). [resolve(823,a,828,a)].
% 1.48/2.14 Derived: bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),A)). [resolve(823,a,829,a)].
% 1.48/2.14 Derived: -hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),finite_fold_graph(nat,nat),times_times(nat)),A),B),C)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),D),B)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),finite_fold_graph(nat,nat),times_times(nat)),D),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),B),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),D),bot_bot(fun(nat,bool)))))),C)). [resolve(823,a,830,a)].
% 1.48/2.14 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),A) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f99(nat,A)),f100(nat,A))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f99(nat,A)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f100(nat,A)),bot_bot(fun(nat,bool)))))) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),A)),A)). [resolve(823,a,831,a)].
% 1.48/2.14 832 cancel146912293up_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.48/2.14 833 -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_353_add__imp__eq) # label(axiom). [clausify(405)].
% 1.48/2.14 834 ordere236663937imp_le(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.48/2.14 835 -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_355_add__le__cancel__right) # label(axiom). [clausify(407)].
% 1.48/2.14 836 -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_355_add__le__cancel__right) # label(axiom). [clausify(407)].
% 1.48/2.14 837 -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_356_add__le__cancel__left) # label(axiom). [clausify(408)].
% 1.48/2.14 838 -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_356_add__le__cancel__left) # label(axiom). [clausify(408)].
% 1.48/2.14 839 -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_360_add__le__imp__le__right) # label(axiom). [clausify(412)].
% 1.48/2.14 840 -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_361_add__le__imp__le__left) # label(axiom). [clausify(413)].
% 1.48/2.14 841 -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_362_min__add__distrib__left) # label(axiom). [clausify(414)].
% 1.48/2.14 842 -ordere236663937imp_le(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C) # label(fact_363_max__add__distrib__left) # label(axiom). [clausify(415)].
% 1.48/2.14 843 -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_416_add__less__cancel__right) # label(axiom). [clausify(468)].
% 1.48/2.14 844 -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_416_add__less__cancel__right) # label(axiom). [clausify(468)].
% 1.48/2.14 845 -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_417_add__less__cancel__left) # label(axiom). [clausify(469)].
% 1.48/2.14 846 -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_417_add__less__cancel__left) # label(axiom). [clausify(469)].
% 1.48/2.14 847 -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_421_add__less__imp__less__right) # label(axiom). [clausify(473)].
% 1.48/2.14 848 -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_422_add__less__imp__less__left) # label(axiom). [clausify(474)].
% 1.48/2.14 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(834,a,835,a)].
% 1.92/2.16 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(834,a,836,a)].
% 1.92/2.16 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(834,a,837,a)].
% 1.92/2.16 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(834,a,838,a)].
% 1.92/2.16 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(834,a,841,a)].
% 1.92/2.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)),B). [resolve(834,a,842,a)].
% 1.92/2.16 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(834,a,843,a)].
% 1.92/2.16 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(834,a,844,a)].
% 1.92/2.16 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(834,a,845,a)].
% 1.92/2.16 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(834,a,846,a)].
% 1.92/2.16 849 ordere779506340up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 1.92/2.16 850 -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_357_add__right__mono) # label(axiom). [clausify(409)].
% 1.92/2.16 851 -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_358_add__left__mono) # label(axiom). [clausify(410)].
% 1.92/2.16 852 -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_359_add__mono) # label(axiom). [clausify(411)].
% 1.92/2.16 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(849,a,852,a)].
% 2.00/2.24 853 comm_semiring(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring) # label(axiom). [assumption].
% 2.00/2.24 854 -comm_semiring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_385_comm__semiring__class_Odistrib) # label(axiom). [clausify(437)].
% 2.00/2.24 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(853,a,854,a)].
% 2.00/2.24 855 semiri456707255roduct(nat) # label(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption].
% 2.00/2.24 856 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,B) = ti(A,D) | ti(A,C) = ti(A,E) # label(fact_389_crossproduct__eq) # label(axiom). [clausify(441)].
% 2.00/2.24 857 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,B) != ti(A,D) # label(fact_389_crossproduct__eq) # label(axiom). [clausify(441)].
% 2.00/2.24 858 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,C) != ti(A,E) # label(fact_389_crossproduct__eq) # label(axiom). [clausify(441)].
% 2.00/2.24 859 -semiri456707255roduct(A) | ti(A,B) = ti(A,C) | ti(A,D) = ti(A,E) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_406_crossproduct__noteq) # label(axiom). [clausify(458)].
% 2.00/2.24 860 -semiri456707255roduct(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_406_crossproduct__noteq) # label(axiom). [clausify(458)].
% 2.00/2.24 861 -semiri456707255roduct(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),B)) # label(fact_406_crossproduct__noteq) # label(axiom). [clausify(458)].
% 2.00/2.24 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)) | ti(nat,A) = ti(nat,C) | ti(nat,B) = ti(nat,D). [resolve(855,a,856,a)].
% 2.00/2.24 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)) | ti(nat,A) != ti(nat,C). [resolve(855,a,857,a)].
% 2.00/2.26 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)) | ti(nat,B) != ti(nat,D). [resolve(855,a,858,a)].
% 2.00/2.26 Derived: ti(nat,A) = ti(nat,B) | ti(nat,C) = ti(nat,D) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)). [resolve(855,a,859,a)].
% 2.00/2.26 Derived: ti(nat,A) != ti(nat,B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)). [resolve(855,a,860,a)].
% 2.00/2.26 862 comm_semiring_1(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 2.00/2.26 863 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_390_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom). [clausify(442)].
% 2.00/2.26 864 -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_391_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom). [clausify(443)].
% 2.00/2.26 865 -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_392_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom). [clausify(444)].
% 2.00/2.26 866 -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_393_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom). [clausify(445)].
% 2.00/2.26 867 -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_394_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom). [clausify(446)].
% 2.00/2.26 868 -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_395_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom). [clausify(447)].
% 2.00/2.26 869 -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_396_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom). [clausify(448)].
% 2.00/2.26 870 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)) # label(fact_397_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom). [clausify(449)].
% 2.00/2.26 871 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),E)) # label(fact_398_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom). [clausify(450)].
% 2.00/2.26 872 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E))) # label(fact_399_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom). [clausify(451)].
% 2.00/2.26 873 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_400_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom). [clausify(452)].
% 2.00/2.26 874 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_401_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom). [clausify(453)].
% 2.00/2.26 875 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_402_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom). [clausify(454)].
% 2.00/2.26 876 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_403_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom). [clausify(455)].
% 2.00/2.26 877 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B) # label(fact_404_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom). [clausify(456)].
% 2.00/2.26 878 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_405_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom). [clausify(457)].
% 2.00/2.26 879 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_407_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom). [clausify(459)].
% 2.00/2.26 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(862,a,864,a)].
% 2.00/2.26 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(862,a,865,a)].
% 2.00/2.26 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(862,a,868,a)].
% 2.00/2.26 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),B),A). [resolve(862,a,869,a)].
% 2.00/2.26 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D)). [resolve(862,a,870,a)].
% 3.61/3.85 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),D)). [resolve(862,a,871,a)].
% 3.61/3.85 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),B). [resolve(862,a,873,a)].
% 3.61/3.85 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)). [resolve(862,a,876,a)].
% 3.61/3.85 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A). [resolve(862,a,877,a)].
% 3.61/3.85 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)). [resolve(862,a,878,a)].
% 3.61/3.85
% 3.61/3.85 ============================== end predicate elimination =============
% 3.61/3.85
% 3.61/3.85 Auto_denials: (non-Horn, no changes).
% 3.61/3.85
% 3.61/3.85 Term ordering decisions:
% 3.61/3.85 Function symbol KB weights: bool=1. nat=1. state=1. com=1. pname=1. vname=1. semi=1. loc=1. fconj=1. fdisj=1. fimplies=1. fNot=1. c=1. fFalse=1. skip=1. fTrue=1. hoare_Mirabelle_MGT=1. p=1. q=1. fun=1. ti=1. finite_fold_graph=1. finite_fold=1. big_co1399186613setsum=1. big_co302546470etprod=1. finite100568337ommute=1. finite1357897459simple=1. finite_comp_fun_idem=1. finite908156982e_idem=1. fold_graph=1. combk=1. hoare_1312322281e_case=1. hoare_1632998903le_rec=1. f8=1. f9=1. f10=1. f11=1. f12=1. f13=1. f14=1. f17=1. f21=1. f22=1. f33=1. f34=1. f78=1. f79=1. f94=1. f95=1. f99=1. f100=1. hoare_1656922687triple=1. ord_less_eq=1. insert=1. bot_bot=1. member=1. finite_finite_1=1. ord_less=1. ord_min=1. ord_max=1. minus_minus=1. plus_plus=1. times_times=1. hoare_279057269derivs=1. hoare_246368825triple=1. finite_fold1=1. big_linorder_Max=1. big_linorder_Min=1. big_Inf_fin=1. big_Sup_fin=1. collect=1. finite_fold1Set=1. finite_folding_one=1. finite2073411215e_idem=1. fequal=1. com_case=1. hoare_2027193591valids=1. big_semilattice_big=1. max=1. min=1. the_elem=1. undefined=1. combb=1. combc=1. combs=1. f15=1. f16=1. f31=1. f32=1. f35=1. f36=1. f46=1. f47=1. f48=1. f49=1. f50=1. f67=1. f68=1. f70=1. f71=1. f73=1. f74=1. f77=1. f81=1. f92=1. f93=1. f104=1. f105=1. f108=1. hAPP=1. f23=1. f24=1. f27=1. f28=1. f29=1. f30=1. f39=1. f40=1. f41=1. f42=1. f80=1. f84=1. f18=1. f19=1. f25=1. f26=1. f38=1. f53=1. f54=1. f63=1. f64=1. f91=1. f96=1. f101=1. f106=1. f1=1. f2=1. f3=1. f4=1. f43=1. f44=1. f45=1. f51=1. f52=1. f55=1. f56=1. f57=1. f58=1. f59=1. f60=1. f61=1. f62=1. f65=1. f66=1. f97=1. f98=1. f102=1. f103=1. f109=1. f110=1. f112=1. f113=1. f114=1. f115=1. f5=1. f6=1. f7=1. f20=1. f37=1. f69=1. f72=1.
% 3.61/3.85
% 3.61/3.85 ============================== end of process initial clauses ========
% 3.61/3.85
% 3.61/3.85 ============================== CLAUSES FOR SEARCH ====================
% 3.61/3.85
% 3.61/3.85 ============================== end of clauses for search =============
% 3.61/3.85
% 3.61/3.85 ============================== SEARCH ================================
% 3.61/3.85
% 3.61/3.85 % Starting search at 0.78 seconds.
% 3.61/3.85
% 3.61/3.85 Low Water (keep): wt=168.000, iters=3422
% 3.61/3.85
% 3.61/3.85 Low Water (keep): wt=158.000, iters=3442
% 3.61/3.85
% 3.61/3.85 Low Water (keep): wt=154.000, iters=3366
% 3.61/3.85
% 3.61/3.85 Low Water (keep): wt=153.000, iters=3346
% 3.61/3.85
% 3.61/3.85 Low Water (keep): wt=151.000, iters=3345
% 129.14/129.43
% 129.14/129.43 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 105 (0.00 of 2.13 sec).
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=146.000, iters=3578
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=129.000, iters=3333
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=128.000, iters=3364
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=126.000, iters=3354
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=125.000, iters=3344
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=121.000, iters=3348
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=120.000, iters=3376
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=119.000, iters=3355
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=112.000, iters=3341
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=111.000, iters=3341
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=110.000, iters=3407
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=109.000, iters=3383
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=108.000, iters=3359
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=107.000, iters=3347
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=105.000, iters=3419
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=103.000, iters=3441
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=102.000, iters=3402
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=101.000, iters=3343
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=100.000, iters=3400
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=98.000, iters=3336
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=95.000, iters=3408
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=90.000, iters=3353
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=87.000, iters=3395
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=86.000, iters=3787
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=84.000, iters=3804
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=75.000, iters=3355
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=74.000, iters=3431
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=70.000, iters=3339
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=68.000, iters=3339
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=65.000, iters=3352
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=62.000, iters=3432
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=60.000, iters=3408
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=59.000, iters=3390
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=58.000, iters=3357
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=57.000, iters=3395
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=54.000, iters=3353
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=49.000, iters=3442
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=46.000, iters=3368
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=44.000, iters=3461
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=42.000, iters=3366
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=39.000, iters=3445
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=37.000, iters=3548
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=35.000, iters=3418
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=33.000, iters=3511
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=29.000, iters=3341
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=28.000, iters=3460
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=24.000, iters=3344
% 129.14/129.43
% 129.14/129.43 Low Water (keep): wt=22.000, iters=3339
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=3639, wt=200.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=4151, wt=199.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=3630, wt=198.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=5175, wt=197.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=3620, wt=196.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=4105, wt=195.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=5151, wt=194.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=6468, wt=192.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=9224, wt=189.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=9230, wt=186.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=8018, wt=177.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=10023, wt=175.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=9532, wt=170.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=2733, wt=165.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=10024, wt=162.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=3542, wt=156.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=14105, wt=145.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=7949, wt=143.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=14135, wt=142.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=9360, wt=141.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=11565, wt=138.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=14290, wt=20.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=14314, wt=18.000
% 129.14/129.43
% 129.14/129.43 Low Water (displace): id=14498, wt=16.000
% 129.14/129.43
% 129.14/129.43 ============================== STATISTICS ============================
% 129.14/129.43
% 129.14/129.43 Given=12217. Generated=3618207. Kept=123477. proofs=0.
% 129.14/129.43 Usable=11574. Sos=10000. Demods=614. Limbo=12286, Disabled=90663. Hints=0.
% 129.14/129.43 Kept_by_rule=0, Deleted_by_rule=95659.
% 129.14/129.43 Forward_subsumed=188785. Back_subsumed=41.
% 129.14/129.43 Sos_limit_deleted=3210286. Sos_displaced=86956. Sos_removed=0.
% 129.14/129.43 New_demodulators=862 (0 lex), Back_demodulated=2323. Back_unit_deleted=297.
% 129.14/129.43 Demod_attempts=168844966. Demod_rewrites=320207.
% 129.14/129.43 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
% 129.14/129.43 Nonunit_fsub_feature_tests=2068495. Nonunit_bsub_feature_tests=10237.
% 129.14/129.43 Megabytes=419.43.
% 129.14/129.43 User_CPU=125.56, System_CPU=2.12, Wall_clock=127.
% 129.14/129.43
% 129.14/129.43 Megs malloced by palloc(): 400.
% 129.14/129.43 type (bytes each) gets frees in use bytes
% 129.14/129.43 chunk ( 104) 53717 53717 0 0.0 K
% 129.14/129.43 string_buf ( 8) 47254 47254 0 0.0 K
% 129.14/129.43 token ( 20) 120301 120301 0 0.0 K
% 129.14/129.43 pterm ( 16) 83661 83661 0 0.0 K
% 129.14/129.43 hashtab ( 8) 576 576 0 0.0 K
% 129.14/129.43 hashnode ( 8) 2842 2842 0 0.0 K
% 129.14/129.43 term ( 20) 197598109 187205737 10392372 202976.0 K
% 129.14/129.43 term arg arrays: 47149.6 K
% 129.14/129.43 attribute ( 12) 3996 76 3920 45.9 K
% 129.14/129.43 ilist ( 8) 444190582 443455037 735545 5746.4 K
% 129.14/129.43 plist ( 8) 6237297 6067709 169588 1324.9 K
% 129.14/129.43 i2list ( 12) 5021596 5021596 0 0.0 K
% 129.14/129.43 just ( 12) 3862329 3721793 140536 1646.9 K
% 129.14/129.43 parajust ( 16) 377102 277542 99560 1555.6 K
% 129.14/129.43 instancejust ( 8) 0 0 0 0.0 K
% 129.14/129.43 ivyjust ( 24) 0 0 0 0.0 K
% 129.14/129.43 formula ( 28) 30325 19887 10438 285.4 K
% 129.14/129.43 formula arg arrays: 36.3 K
% 129.14/129.43 topform ( 52) 3619903 3494730 125173 6356.4 K
% 129.14/129.43 clist_pos ( 20) 339945 214808 125137 2444.1 K
% 129.14/129.43 clist ( 16) 8 1 7 0.1 K
% 129.14/129.43 context ( 808) 13489524 13489524 0 0.0 K
% 129.14/129.43 trail ( 12) 16110250 16110250 0 0.0 K
% 129.14/129.43 ac_match_pos (70044) 0 0 0 0.0 K
% 129.14/129.43 ac_match_free_vars_pos (20020)
% 129.14/129.43 0 0 0 0.0 K
% 129.14/129.43 btm_state ( 60) 0 0 0 0.0 K
% 129.14/129.43 btu_state ( 60) 0 0 0 0.0 K
% 129.14/129.43 ac_position (285432) 0 0 0 0.0 K
% 129.14/129.43 fpa_trie ( 20) 2690753 2387367 303386 5925.5 K
% 129.14/129.43 fpa_state ( 28) 6213350 6213350 0 0.0 K
% 129.14/129.43 fpa_index ( 12) 10 0 10 0.1 K
% 129.14/129.43 fpa_chunk ( 20) 4018095 3812416 205679 4017.2 K
% 129.14/129.43 fpa_list ( 16) 2470474 0 2470474 38601.2 K
% 129.14/129.43 fpa_list chunks: 22475.5 K
% 129.14/129.43 discrim ( 12) 3517136 2757733 759403 8899.3 K
% 129.14/129.43 discrim_pos ( 16) 460323 460323 0 0.0 K
% 129.14/129.43 flat2 ( 32) 41121073 41121073 0 0.0 K
% 129.14/129.43 flat ( 48) 0 0 0 0.0 K
% 129.14/129.43 flatterm ( 32) 192009260 192009260 0 0.0 K
% 129.14/129.43 mindex ( 28) 13 0 13 0.4 K
% 129.14/129.43 mindex_pos ( 56) 5575354 5575354 0 0.0 K
% 129.14/129.43 lindex ( 12) 5 0 5 0.1 K
% 129.14/129.43 clash ( 40) 0 0 0 0.0 K
% 129.14/129.43 di_tree ( 12) 21075948 16015695 5060253 59299.8 K
% 129.14/129.43 avl_node ( 20) 221593 201593 20000 390.6 K
% 129.14/129.43
% 129.14/129.43 Memory report, 20 @ 20 = 400 megs (400.00 megs used).
% 129.14/129.43 List 1, length 8, 0.0 K
% 129.14/129.43 List 2, length 944, 7.4 K
% 129.14/129.43 List 3, length 74322, 871.0 K
% 129.14/129.43 List 5, length 366, 7.1 K
% 129.14/129.43 List 7, length 450, 12.3 K
% 129.14/129.43 List 8, length 418, 13.1 K
% 129.14/129.43 List 9, length 54, 1.9 K
% 129.14/129.43 List 10, length 6, 0.2 K
% 129.14/129.43 List 11, length 18, 0.8 K
% 129.14/129.43 List 12, length 18, 0.8 K
% 129.14/129.43 List 13, length 1, 0.1 K
% 129.14/129.43 List 14, length 2, 0.1 K
% 129.14/129.43 List 16, length 50, 3.1 K
% 129.14/129.43 List 26, length 385, 39.1 K
% 129.14/129.43 List 32, length 27, 3.4 K
% 129.14/129.43 List 64, length 1152, 288.0 K
% 129.14/129.43 List 128, length 328, 164.0 K
% 129.14/129.43 List 202, length 4, 3.2 K
% 129.14/129.43 List 256, length 679, 679.0 K
% 129.14/129.43
% 129.14/129.43 ============================== SELECTOR REPORT =======================
% 129.14/129.43 Sos_deleted=3210286, Sos_displaced=86956, Sos_size=10000
% 129.14/129.43 SELECTOR PART PRIORITY ORDER SIZE SELECTED
% 129.14/129.43 I 2147483647 high age 0 669
% 129.14/129.43 H 1 high weight 0 0
% 129.14/129.43 A 1 low age 10000 1284
% 129.14/129.43 F 4 low weight 2593 5132
% 129.14/129.43 T 4 low weight 7407 5132
% 129.14/129.43 ============================== end of selector report ================
% 129.14/129.43
% 129.14/129.43 ============================== end of statistics =====================
% 129.14/129.43
% 129.14/129.43 Exiting with failure.
% 129.14/129.43
% 129.14/129.43 Process 16557 exit (max_megs) Sat Jun 4 10:57:16 2022
% 129.14/129.43 Prover9 interrupted
%------------------------------------------------------------------------------