TSTP Solution File: SWW470+7 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW470+7 : 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 01:17:06 EDT 2022
% Result : Theorem 10.64s 10.82s
% Output : Refutation 10.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWW470+7 : TPTP v8.1.0. Released v5.3.0.
% 0.13/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jun 4 18:20:52 EDT 2022
% 0.21/0.35 % CPUTime :
% 2.13/2.55 ============================== Prover9 ===============================
% 2.13/2.55 Prover9 (32) version 2009-11A, November 2009.
% 2.13/2.55 Process 29149 was started by sandbox on n020.cluster.edu,
% 2.13/2.55 Sat Jun 4 18:20:54 2022
% 2.13/2.55 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_28996_n020.cluster.edu".
% 2.13/2.55 ============================== end of head ===========================
% 2.13/2.55
% 2.13/2.55 ============================== INPUT =================================
% 2.13/2.55
% 2.13/2.55 % Reading from file /tmp/Prover9_28996_n020.cluster.edu
% 2.13/2.55
% 2.13/2.55 set(prolog_style_variables).
% 2.13/2.55 set(auto2).
% 2.13/2.55 % set(auto2) -> set(auto).
% 2.13/2.55 % set(auto) -> set(auto_inference).
% 2.13/2.55 % set(auto) -> set(auto_setup).
% 2.13/2.55 % set(auto_setup) -> set(predicate_elim).
% 2.13/2.55 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.13/2.55 % set(auto) -> set(auto_limits).
% 2.13/2.55 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.13/2.55 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.13/2.55 % set(auto) -> set(auto_denials).
% 2.13/2.55 % set(auto) -> set(auto_process).
% 2.13/2.55 % set(auto2) -> assign(new_constants, 1).
% 2.13/2.55 % set(auto2) -> assign(fold_denial_max, 3).
% 2.13/2.55 % set(auto2) -> assign(max_weight, "200.000").
% 2.13/2.55 % set(auto2) -> assign(max_hours, 1).
% 2.13/2.55 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.13/2.55 % set(auto2) -> assign(max_seconds, 0).
% 2.13/2.55 % set(auto2) -> assign(max_minutes, 5).
% 2.13/2.55 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.13/2.55 % set(auto2) -> set(sort_initial_sos).
% 2.13/2.55 % set(auto2) -> assign(sos_limit, -1).
% 2.13/2.55 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.13/2.55 % set(auto2) -> assign(max_megs, 400).
% 2.13/2.55 % set(auto2) -> assign(stats, some).
% 2.13/2.55 % set(auto2) -> clear(echo_input).
% 2.13/2.55 % set(auto2) -> set(quiet).
% 2.13/2.55 % set(auto2) -> clear(print_initial_clauses).
% 2.13/2.55 % set(auto2) -> clear(print_given).
% 2.13/2.55 assign(lrs_ticks,-1).
% 2.13/2.55 assign(sos_limit,10000).
% 2.13/2.55 assign(order,kbo).
% 2.13/2.55 set(lex_order_vars).
% 2.13/2.55 clear(print_given).
% 2.13/2.55
% 2.13/2.55 % formulas(sos). % not echoed (1194 formulas)
% 2.13/2.55
% 2.13/2.55 ============================== end of input ==========================
% 2.13/2.55
% 2.13/2.55 % From the command line: assign(max_seconds, 300).
% 2.13/2.55
% 2.13/2.55 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.13/2.55
% 2.13/2.55 % Formulas that are not ordinary clauses:
% 2.13/2.55 1 (all X_c all X_b (comm_monoid_add(X_b) -> ti(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),big_co1399186613setsum(X_c,X_b)) = big_co1399186613setsum(X_c,X_b))) # label(tsy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 2 (all X_b all X_c (comm_monoid_mult(X_c) -> ti(fun(fun(X_b,X_c),fun(fun(X_b,bool),X_c)),big_co302546470etprod(X_b,X_c)) = big_co302546470etprod(X_b,X_c))) # label(tsy_c_Big__Operators_Ocomm__monoid__mult__class_Osetprod_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 3 (all X_b (linorder(X_b) -> ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b)),big_Inf_fin(X_b)) = big_Inf_fin(X_b))) # label(tsy_c_Big__Operators_Olattice_OInf__fin_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 4 (all X_b (linorder(X_b) -> ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b)),big_Sup_fin(X_b)) = big_Sup_fin(X_b))) # label(tsy_c_Big__Operators_Olattice_OSup__fin_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 5 (all X_b (linorder(X_b) -> ti(fun(fun(X_b,bool),X_b),big_linorder_Max(X_b)) = big_linorder_Max(X_b))) # label(tsy_c_Big__Operators_Olinorder__class_OMax_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 6 (all X_b (linorder(X_b) -> ti(fun(fun(X_b,bool),X_b),big_linorder_Min(X_b)) = big_linorder_Min(X_b))) # label(tsy_c_Big__Operators_Olinorder__class_OMin_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 7 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),big_semilattice_big(X_b)) = big_semilattice_big(X_b)) # label(tsy_c_Big__Operators_Osemilattice__big_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 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].
% 2.13/2.55 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].
% 2.13/2.55 10 (all X_a ti(fun(X_a,X_a),combi(X_a)) = combi(X_a)) # label(tsy_c_COMBI_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 11 (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].
% 2.13/2.55 12 (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].
% 2.13/2.55 13 (all X_b ti(fun(fun(X_b,bool),nat),finite_card(X_b)) = finite_card(X_b)) # label(tsy_c_Finite__Set_Ocard_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 14 (all X_b all X_c ti(fun(fun(X_b,fun(X_c,X_c)),bool),finite100568337ommute(X_b,X_c)) = finite100568337ommute(X_b,X_c)) # label(tsy_c_Finite__Set_Ocomp__fun__commute_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 15 (all X_b all X_c ti(fun(fun(X_b,fun(X_c,X_c)),bool),finite_comp_fun_idem(X_b,X_c)) = finite_comp_fun_idem(X_b,X_c)) # label(tsy_c_Finite__Set_Ocomp__fun__idem_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 16 (all X_b ti(fun(fun(X_b,bool),bool),finite_finite_1(X_b)) = finite_finite_1(X_b)) # label(tsy_c_Finite__Set_Ofinite_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 17 (all X_b all X_c ti(fun(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold(X_b,X_c)) = finite_fold(X_b,X_c)) # label(tsy_c_Finite__Set_Ofold_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 18 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b)),finite_fold1(X_b)) = finite_fold1(X_b)) # label(tsy_c_Finite__Set_Ofold1_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 19 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool))),finite_fold1Set(X_b)) = finite_fold1Set(X_b)) # label(tsy_c_Finite__Set_Ofold1Set_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 20 (all X_b all X_c ti(fun(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool)))),finite_fold_graph(X_b,X_c)) = finite_fold_graph(X_b,X_c)) # label(tsy_c_Finite__Set_Ofold__graph_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 21 (all X_b all X_c ti(fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)))),finite1357897459simple(X_b,X_c)) = finite1357897459simple(X_b,X_c)) # label(tsy_c_Finite__Set_Ofolding__image__simple_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 22 (all X_b all X_c ti(fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)))),finite908156982e_idem(X_b,X_c)) = finite908156982e_idem(X_b,X_c)) # label(tsy_c_Finite__Set_Ofolding__image__simple__idem_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 23 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),finite_folding_one(X_b)) = finite_folding_one(X_b)) # label(tsy_c_Finite__Set_Ofolding__one_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 24 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),finite2073411215e_idem(X_b)) = finite2073411215e_idem(X_b)) # label(tsy_c_Finite__Set_Ofolding__one__idem_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 25 (all X_b (minus(X_b) -> ti(fun(X_b,fun(X_b,X_b)),minus_minus(X_b)) = minus_minus(X_b))) # label(tsy_c_Groups_Ominus__class_Ominus_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 26 (all X_b (one(X_b) -> ti(X_b,one_one(X_b)) = one_one(X_b))) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 27 (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_0_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 28 (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_1_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 29 (all X_b (power(X_b) -> ti(fun(X_b,fun(X_b,X_b)),times_times(X_b)) = times_times(X_b))) # label(tsy_c_Groups_Otimes__class_Otimes_0_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 30 (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_1_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 31 (all X_b (ab_semigroup_mult(X_b) -> ti(fun(X_b,fun(X_b,X_b)),times_times(X_b)) = times_times(X_b))) # label(tsy_c_Groups_Otimes__class_Otimes_2_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 32 (all X_c (uminus(X_c) -> ti(fun(X_c,X_c),uminus_uminus(X_c)) = uminus_uminus(X_c))) # label(tsy_c_Groups_Ouminus__class_Ouminus_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 33 (all X_a (ordere216010020id_add(X_a) -> ti(X_a,zero_zero(X_a)) = zero_zero(X_a))) # label(tsy_c_Groups_Ozero__class_Ozero_0_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 34 (all X_b (ab_group_add(X_b) -> ti(X_b,zero_zero(X_b)) = zero_zero(X_b))) # label(tsy_c_Groups_Ozero__class_Ozero_1_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 35 (all X_b ti(fun(fun(X_b,bool),X_b),the(X_b)) = the(X_b)) # label(tsy_c_HOL_OThe_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 36 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 37 (all X_b ti(fun(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool)),hoare_1301688828derivs(X_b)) = hoare_1301688828derivs(X_b)) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Ohoare__derivs_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 38 (all X_b ti(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hoare_759811442triple(X_b)) = hoare_759811442triple(X_b)) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Otriple_Otriple_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 39 (all X_c all X_b ti(fun(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b)),hoare_225284258e_case(X_c,X_b)) = hoare_225284258e_case(X_c,X_b)) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Otriple_Otriple__case_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 40 (all X_c all X_b ti(fun(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b)),hoare_1759541758le_rec(X_c,X_b)) = hoare_1759541758le_rec(X_c,X_b)) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Otriple_Otriple__rec_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 41 (all X_a ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a)) = if(X_a)) # label(tsy_c_If_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 42 (all X_a (semiring_1(X_a) -> ti(fun(nat,X_a),semiring_1_of_nat(X_a)) = semiring_1_of_nat(X_a))) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 43 (all X_b all X_c ti(fun(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool)))),fold_graph(X_b,X_c)) = fold_graph(X_b,X_c)) # label(tsy_c_Nitpick_Ofold__graph_H_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 44 (all X_b (bot(X_b) -> ti(X_b,bot_bot(X_b)) = bot_bot(X_b))) # label(tsy_c_Orderings_Obot__class_Obot_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 45 (all X_b (ord(X_b) -> ti(fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,X_b))),max(X_b)) = max(X_b))) # label(tsy_c_Orderings_Oord_Omax_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 46 (all X_b (ord(X_b) -> ti(fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,X_b))),min(X_b)) = min(X_b))) # label(tsy_c_Orderings_Oord_Omin_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 47 (all X_b (ord(X_b) -> ti(fun(X_b,fun(X_b,bool)),ord_less(X_b)) = ord_less(X_b))) # label(tsy_c_Orderings_Oord__class_Oless_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 48 (all X_c (ord(X_c) -> ti(fun(X_c,fun(X_c,bool)),ord_less_eq(X_c)) = ord_less_eq(X_c))) # label(tsy_c_Orderings_Oord__class_Oless__eq_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 49 (all X_b (ord(X_b) -> ti(fun(X_b,fun(X_b,X_b)),ord_max(X_b)) = ord_max(X_b))) # label(tsy_c_Orderings_Oord__class_Omax_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 50 (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].
% 2.13/2.55 51 (all X_b ti(fun(X_b,fun(fun(X_b,bool),X_b)),partial_flat_lub(X_b)) = partial_flat_lub(X_b)) # label(tsy_c_Partial__Function_Oflat__lub_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 52 (all X_b ti(fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(nat,X_b)))),power_1(X_b)) = power_1(X_b)) # label(tsy_c_Power_Opower_Opower_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 53 (all X_b (power(X_b) -> ti(fun(X_b,fun(nat,X_b)),power_power(X_b)) = power_power(X_b))) # label(tsy_c_Power_Opower__class_Opower_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 54 (all X_b (order(X_b) -> ti(fun(X_b,fun(X_b,fun(X_b,bool))),ord_atLeastAtMost(X_b)) = ord_atLeastAtMost(X_b))) # label(tsy_c_SetInterval_Oord__class_OatLeastAtMost_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 55 (all X_b (ord(X_b) -> ti(fun(X_b,fun(X_b,bool)),ord_greaterThan(X_b)) = ord_greaterThan(X_b))) # label(tsy_c_SetInterval_Oord__class_OgreaterThan_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 56 (all X_b (ord(X_b) -> ti(fun(X_b,fun(X_b,bool)),ord_lessThan(X_b)) = ord_lessThan(X_b))) # label(tsy_c_SetInterval_Oord__class_OlessThan_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 57 (all X_b ti(fun(fun(X_b,bool),fun(X_b,bool)),collect(X_b)) = collect(X_b)) # label(tsy_c_Set_OCollect_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 58 (all X_b all X_c ti(fun(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool))),image(X_b,X_c)) = image(X_b,X_c)) # label(tsy_c_Set_Oimage_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 59 (all X_b ti(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),insert(X_b)) = insert(X_b)) # label(tsy_c_Set_Oinsert_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 60 (all X_b ti(fun(fun(X_b,bool),X_b),the_elem(X_b)) = the_elem(X_b)) # label(tsy_c_Set_Othe__elem_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 61 (all X_a ti(fun(fun(X_a,bool),bool),fEx(X_a)) = fEx(X_a)) # label(tsy_c_fEx_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 62 (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].
% 2.13/2.55 63 (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].
% 2.13/2.55 64 (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].
% 2.13/2.55 65 (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].
% 2.13/2.55 66 (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].
% 2.13/2.55 67 (all X_b ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b)) = member(X_b)) # label(tsy_c_member_res) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 68 (all X_b all Ga hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) # label(fact_0_empty) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 69 (all X_b all Fun1_1 all Com_1 all Fun2_1 all Fun1_2 all Com_2 all Fun2_2 (hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1_1),Com_1),Fun2_1) = hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),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].
% 2.13/2.55 70 (all X_b all Ga all G_1 all Ts (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),G_1),Ts)) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),G_1)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts))))) # label(fact_2_cut) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 71 (all X_b all Ts all Ga all T_5 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),T_5),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),T_5),Ts)))))) # label(fact_3_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 72 (all X_b all Ga all Pa all Ca all Q_3 all C_1 ((hBOOL(C_1) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(bool,fun(X_b,fun(state,bool)),hAPP(fun(X_b,fun(bool,fun(state,bool))),fun(bool,fun(X_b,fun(state,bool))),combc(X_b,bool,fun(state,bool)),hAPP(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(bool,fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(bool,fun(state,bool))),fun(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(bool,fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X_b),combc(state,bool,bool)),hAPP(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),Pa))),C_1)),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))) # label(fact_4_constant) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 73 (all X_b all Ga all Ca all Q_3 all Pa ((all Z_4 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_4),S_3)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(fun(state,bool),fun(X_b,fun(state,bool)),combk(fun(state,bool),X_b),hAPP(state,fun(state,bool),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),S_3))),Ca),hAPP(fun(state,bool),fun(X_b,fun(state,bool)),combk(fun(state,bool),X_b),hAPP(X_b,fun(state,bool),Q_3,Z_4)))),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))) # label(fact_5_escape) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 74 (all X_b all Q_3 all Ga all Pa all Ca all Q_5 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_5)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> ((all Z_4 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_5,Z_4),S_3)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_3,Z_4),S_3)))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))))) # label(fact_6_conseq2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 75 (all X_b all Pa all Ga all P_4 all Ca all Q_3 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),P_4),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> ((all Z_4 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_4),S_3)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_4,Z_4),S_3)))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))))) # label(fact_7_conseq1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 76 (all X_b all Q_3 all Pa all Ga all P_4 all Ca all Q_5 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),P_4),Ca),Q_5)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> ((all Z_4 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_4),S_3)) -> (all S_4 ((all Z_5 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_4,Z_5),S_3)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_5,Z_5),S_4)))) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_3,Z_4),S_4)))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))))) # label(fact_8_conseq12) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 77 (all X_b all A_2 all Ba all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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),Ba),A_3))) -> (ti(X_b,A_2) != ti(X_b,Ba) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))))) # label(fact_9_insertE) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 78 (all X_b all Ba all A_2 all B_2 ((-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2)) -> ti(X_b,A_2) = ti(X_b,Ba)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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),Ba),B_2))))) # label(fact_10_insertCI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 79 (all X_b all A_2 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),bot_bot(fun(X_b,bool))))) # label(fact_11_emptyE) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 80 (all X_b all A_2 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),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),A_2),bot_bot(fun(X_b,bool)))) # label(fact_12_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.55 81 (all X_b all A_2 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),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),A_2),bot_bot(fun(X_b,bool)))) # label(fact_13_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 82 (all X_b all Pa all A_2 ((hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) & (-hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Pa)) = bot_bot(fun(X_b,bool))))) # label(fact_14_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 83 (all X_b all Pa all A_2 ((hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) & (-hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Pa)) = bot_bot(fun(X_b,bool))))) # label(fact_15_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 84 (all X_c all X_b all F1 all Fun1_1 all Com_1 all Fun2_1 hAPP(hoare_2118899576triple(X_c),X_b,hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b),hoare_1759541758le_rec(X_c,X_b),F1),hAPP(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hoare_759811442triple(X_c),Fun1_1),Com_1),Fun2_1)) = hAPP(fun(X_c,fun(state,bool)),X_b,hAPP(com,fun(fun(X_c,fun(state,bool)),X_b),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b)),F1,Fun1_1),Com_1),Fun2_1)) # label(fact_16_triple_Orecs) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 85 (all X_b all A_2 all A_3 (ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)))) # label(fact_17_equals0D) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 86 (all X_b all Pa (hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = bot_bot(fun(X_b,bool)) <-> (all X_2 -hBOOL(hAPP(X_b,bool,Pa,X_2))))) # label(fact_18_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 87 (all X_b all Ca -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),bot_bot(fun(X_b,bool))))) # label(fact_19_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 88 (all X_b all Pa (bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) <-> (all X_2 -hBOOL(hAPP(X_b,bool,Pa,X_2))))) # label(fact_20_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 89 (all X_b all A_3 ((exists X_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))) <-> ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)))) # label(fact_21_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 90 (all X_b all A_3 ((all X_2 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))) <-> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)))) # label(fact_22_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 91 (all X_b bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse))) # label(fact_23_empty__def) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 92 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3) = ti(fun(X_b,bool),A_3))) # label(fact_24_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 93 (all X_b all Ba all A_2 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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),Ba),B_2))))) # label(fact_25_insertI2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 94 (all X_b all B_2 all X_1 all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_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_1),A_3) = 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_1),B_2) <-> ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2))))) # label(fact_26_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 95 (all X_b all Y_2 all A_3 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),A_3),X_1)) <-> ti(X_b,Y_2) = ti(X_b,X_1) | hBOOL(hAPP(X_b,bool,A_3,X_1)))) # label(fact_27_insert__code) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 96 (all X_b all A_2 all Ba all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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),Ba),A_3))) <-> ti(X_b,A_2) = ti(X_b,Ba) | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)))) # label(fact_28_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 97 (all X_b all X_1 all Y_2 all A_3 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_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),Y_2),A_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_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_1),A_3))) # label(fact_29_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 98 (all X_b all X_1 all A_3 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_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_1),A_3)) = 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_1),A_3)) # label(fact_30_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 99 (all X_b all A_2 all Pa hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fimplies),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)))),Pa))) # label(fact_31_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 100 (all X_b all A_2 all B_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),A_2),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2)))) # label(fact_32_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 101 (all X_b all A_2 all B_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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),A_2),B_2)))) # label(fact_33_insertI1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 102 (all X_b all X_2 all Xa 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),Xa) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),Xa)))) # label(fact_34_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 103 (all X_b all A_2 all Ba (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),bot_bot(fun(X_b,bool))) -> ti(X_b,A_2) = ti(X_b,Ba))) # label(fact_35_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 104 (all X_b all Ba all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) -> ti(X_b,Ba) = ti(X_b,A_2))) # label(fact_36_singletonE) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 105 (all X_b all A_2 all Ba all Ca all D (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),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),Ba),bot_bot(fun(X_b,bool)))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),D),bot_bot(fun(X_b,bool)))) <-> ti(X_b,A_2) = ti(X_b,Ca) & ti(X_b,Ba) = ti(X_b,D) | ti(X_b,A_2) = ti(X_b,D) & ti(X_b,Ba) = ti(X_b,Ca))) # label(fact_37_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 106 (all X_b all Ba all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) <-> ti(X_b,Ba) = ti(X_b,A_2))) # label(fact_38_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 107 (all X_b all A_2 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3) != bot_bot(fun(X_b,bool))) # label(fact_39_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 108 (all X_b all A_2 all A_3 bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) # label(fact_40_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 109 (all X_b all X_1 hAPP(fun(X_b,bool),X_b,the_elem(X_b),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_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1)) # label(fact_41_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 110 (all X_c all X_b all F1 all Fun1_1 all Com_1 all Fun2_1 hAPP(hoare_2118899576triple(X_c),X_b,hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b),hoare_225284258e_case(X_c,X_b),F1),hAPP(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hoare_759811442triple(X_c),Fun1_1),Com_1),Fun2_1)) = hAPP(fun(X_c,fun(state,bool)),X_b,hAPP(com,fun(fun(X_c,fun(state,bool)),X_b),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b)),F1,Fun1_1),Com_1),Fun2_1)) # label(fact_42_triple_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 111 (all X_c all X_b (bot(X_b) -> (all X_1 hAPP(X_c,X_b,bot_bot(fun(X_c,X_b)),X_1) = bot_bot(X_b)))) # label(fact_43_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 112 (all X_b all X_c (bot(X_c) -> (all X_2 hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c)))) # label(fact_44_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 113 (all X_b all Ga all Pa hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),skip),Pa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))) # label(fact_45_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 114 (all X_b all D all R_1 all Ga all Pa all Ca all Q_3 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Q_3),D),R_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(com,com,hAPP(com,fun(com,com),semi,Ca),D)),R_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))))) # label(fact_46_Comp) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 115 (all X_b all Y_2 -(all Fun1 all Com all Fun2 Y_2 != hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1),Com),Fun2))) # label(fact_47_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 116 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> -(all B_3 (ti(fun(X_b,bool),A_3) = 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_1),B_3) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_3)))))) # label(fact_48_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 117 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> (exists B_3 (ti(fun(X_b,bool),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_3) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_3)))))) # label(fact_49_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 118 (all X_b all A_3 ((all Y_1 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_3))) -> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)))) # label(fact_50_equals0I) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 119 (all X_b all Q_3 all Ga all Ca all Pa ((all Z_4 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_4),S_3)) -> (exists P_3 exists Q_4 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),P_3),Ca),Q_4)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) & (all S_4 ((all Z_5 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_3,Z_5),S_3)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_4,Z_5),S_4)))) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_3,Z_4),S_4)))))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))) # label(fact_51_conseq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 120 (all X_b all A_3 (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) <-> (exists X_2 exists B_3 (ti(fun(X_b,bool),A_3) = 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),B_3) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_3)))))) # label(fact_52_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 121 (all Com1_2 all Com2_2 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2) != skip) # label(fact_53_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 122 (all Com1_2 all Com2_2 skip != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2)) # label(fact_54_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 123 (all X_b all X_3 hAPP(fun(X_b,bool),X_b,the_elem(X_b),X_3) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),fequal(fun(X_b,bool)),X_3)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool)))))) # label(fact_55_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 124 (all Com1_1 all Com2_1 all Com1 all Com2 (hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1) = hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2) <-> Com1_1 = Com1 & Com2_1 = Com2)) # label(fact_56_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 125 (all X_b all F all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))),Ba)) <-> ti(X_b,A_2) = ti(X_b,Ba))) # label(fact_57_fold1Set__sing) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 126 (all X_b all X_1 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> hAPP(fun(X_b,bool),X_b,F_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_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1))) # label(fact_58_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 127 (all X_b all X_2 (hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),bot_bot(fun(X_b,bool)))))) # label(fact_59_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 128 (all X_b all Ga all Pa all X_3 all A_2 hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(fun(state,state),fun(X_b,fun(state,bool)),hAPP(fun(X_b,fun(fun(state,state),fun(state,bool))),fun(fun(state,state),fun(X_b,fun(state,bool))),combc(X_b,fun(state,state),fun(state,bool)),hAPP(fun(X_b,fun(state,bool)),fun(X_b,fun(fun(state,state),fun(state,bool))),hAPP(fun(fun(state,bool),fun(fun(state,state),fun(state,bool))),fun(fun(X_b,fun(state,bool)),fun(X_b,fun(fun(state,state),fun(state,bool)))),combb(fun(state,bool),fun(fun(state,state),fun(state,bool)),X_b),combb(state,bool,state)),Pa)),hAPP(fun(state,nat),fun(state,state),hAPP(fun(state,fun(nat,state)),fun(fun(state,nat),fun(state,state)),combs(state,nat,state),hAPP(vname,fun(state,fun(nat,state)),hAPP(fun(state,fun(vname,fun(nat,state))),fun(vname,fun(state,fun(nat,state))),combc(state,vname,fun(nat,state)),update),X_3)),A_2))),hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,X_3),A_2)),Pa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))) # label(fact_60_Ass) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 129 (all X_b all F all A_2 hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) = ti(X_b,A_2)) # label(fact_61_fold1__singleton) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 130 (all X_b all A_2 all G all F (G = hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F) -> hAPP(fun(X_b,bool),X_b,G,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) = ti(X_b,A_2))) # label(fact_62_fold1__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 131 (all X_c all X_b all Ca all A_3 ((ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),Ca)),A_3) = bot_bot(fun(X_c,bool))) & (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),Ca)),A_3) = hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),Ca),bot_bot(fun(X_c,bool)))))) # label(fact_63_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 132 (all X_b all X_c all A_3 all Ba all F all X_1 (ti(X_b,Ba) = hAPP(X_c,X_b,F,X_1) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))))) # label(fact_64_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 133 (all X_b all F all A_3 hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_3) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_3))) # label(fact_65_fold1__def) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 134 (all Vname_1 all Fun_1 all Vname all Fun (hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname_1),Fun_1) = hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname),Fun) <-> ti(vname,Vname_1) = ti(vname,Vname) & Fun_1 = Fun)) # label(fact_66_com_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 135 (all X_c all X_b all Ba all F all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (ti(X_c,Ba) = hAPP(X_b,X_c,F,X_1) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Ba),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))))) # label(fact_67_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 136 (all X_c all X_b all F all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))))) # label(fact_68_imageI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 137 (all X_b all X_c all Z_2 all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) <-> (exists X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)) & ti(X_b,Z_2) = hAPP(X_c,X_b,F,X_2))))) # label(fact_69_image__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 138 (all X_c all X_b all X_d all F all G all A_3 hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_d,bool),fun(X_c,bool),hAPP(fun(X_d,X_c),fun(fun(X_d,bool),fun(X_c,bool)),image(X_d,X_c),G),A_3)) = hAPP(fun(X_d,bool),fun(X_b,bool),hAPP(fun(X_d,X_b),fun(fun(X_d,bool),fun(X_b,bool)),image(X_d,X_b),hAPP(fun(X_d,X_c),fun(X_d,X_b),hAPP(fun(X_c,X_b),fun(fun(X_d,X_c),fun(X_d,X_b)),combb(X_c,X_b,X_d),F),G)),A_3)) # label(fact_70_image__image) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 139 (all X_b all Y_4 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),combi(X_b)),Y_4) = ti(fun(X_b,bool),Y_4)) # label(fact_71_image__ident) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 140 (all Vname_1 all Fun_1 all Com1 all Com2 hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname_1),Fun_1) != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2)) # label(fact_72_com_Osimps_I24_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 141 (all Com1 all Com2 all Vname_1 all Fun_1 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2) != hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname_1),Fun_1)) # label(fact_73_com_Osimps_I25_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 142 (all Vname all Fun skip != hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname),Fun)) # label(fact_74_com_Osimps_I8_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 143 (all X_b all X_c all F all G ((all X_2 hAPP(X_b,X_c,F,X_2) = hAPP(X_b,X_c,G,X_2)) -> ti(fun(X_b,X_c),F) = ti(fun(X_b,X_c),G))) # label(fact_75_ext) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 144 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) <-> hBOOL(hAPP(X_b,bool,A_3,X_1)))) # label(fact_76_mem__def) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 145 (all X_b all Pa hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa)) # label(fact_77_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 146 (all Vname all Fun hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname),Fun) != skip) # label(fact_78_com_Osimps_I9_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 147 (all X_c all X_b all F all A_3 (hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3) = bot_bot(fun(X_b,bool)) <-> ti(fun(X_c,bool),A_3) = bot_bot(fun(X_c,bool)))) # label(fact_79_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 148 (all X_c all X_b all F hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),bot_bot(fun(X_c,bool))) = bot_bot(fun(X_b,bool))) # label(fact_80_image__empty) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 149 (all X_b all X_c all F all A_3 (bot_bot(fun(X_b,bool)) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3) <-> ti(fun(X_c,bool),A_3) = bot_bot(fun(X_c,bool)))) # label(fact_81_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 150 (all X_c all X_b all F all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)) = hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) # label(fact_82_insert__image) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 151 (all X_c all X_b all F all A_2 all B_2 hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),A_2),B_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),hAPP(X_c,X_b,F,A_2)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B_2))) # label(fact_83_image__insert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 152 (all X_b all F all A_3 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_3),X_1)) -> ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)))) # label(fact_84_fold1Set__nonempty) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 153 (all X_b all F all X_1 -hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),bot_bot(fun(X_b,bool))),X_1))) # label(fact_85_empty__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 154 (all X_c all X_b all Ca all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),Ca)),A_3) = hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),Ca),bot_bot(fun(X_c,bool))))) # label(fact_86_image__constant) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 155 (all X_b all X_c all Ba all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) -> -(all X_2 (ti(X_b,Ba) = hAPP(X_c,X_b,F,X_2) -> -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)))))) # label(fact_87_imageE) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 156 (all X_b all X_1 hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),X_1)) = ti(X_b,X_1)) # label(fact_88_the__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 157 (all X_b all A_2 hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)) = ti(X_b,A_2)) # label(fact_89_the__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 158 (all X_b all X_1 all Y_2 all Pa ((hBOOL(Pa) -> ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_1)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),Y_2))))) & (-hBOOL(Pa) -> ti(X_b,Y_2) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_1)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),Y_2))))))) # label(fact_90_If__def) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 159 (all X_c all X_b all F all G all M_3 all N_3 (ti(fun(X_b,bool),M_3) = ti(fun(X_b,bool),N_3) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),N_3)) -> hAPP(X_b,X_c,F,X_2) = hAPP(X_b,X_c,G,X_2))) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),M_3) = hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),G),N_3)))) # label(fact_91_image__cong) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 160 (all X_b all F all A_2 all A_3 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),F),A_2),A_3),X_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)),X_1))))) # label(fact_92_fold1Set_Ointros) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 161 (all X_b all Pa all A_2 (hBOOL(hAPP(X_b,bool,Pa,A_2)) -> ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> ti(X_b,X_2) = ti(X_b,A_2))) -> hAPP(fun(X_b,bool),X_b,the(X_b),Pa) = ti(X_b,A_2)))) # label(fact_93_the__equality) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 162 (all X_b all X_1 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,A_3))))))) # label(fact_94_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 163 (all X_b all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,F_2,A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_3)))) # label(fact_95_folding__one_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 164 (all X_b all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),Y_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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,F_2,A_3)),A_3))))))) # label(fact_96_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 165 (all X_b all Q_3 all Pa (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) | hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),Pa)),Q_3)))))) # label(fact_97_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 166 (all X_b hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),bot_bot(fun(X_b,bool))))) # label(fact_98_finite_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 167 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3))))) # label(fact_99_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 168 (all X_c all X_b all H all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),H),F_2))))) # label(fact_100_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 169 (all X_b (finite_finite(X_b) -> (all A_3 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))))) # label(fact_101_finite) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 170 (all X_b (finite_finite(X_b) -> (all A_3 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))))) # label(fact_102_finite__code) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 171 (all X_b all Pa all Q_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),Pa)),Q_3)))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3))))) # label(fact_103_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 172 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)))) # label(fact_104_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 173 (all X_c all X_b all F all Z_2 hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),bot_bot(fun(X_b,bool))),Z_2))) # label(fact_105_fold__graph_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 174 (all X_c all X_b all F all Z_2 all X_1 (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),bot_bot(fun(X_b,bool))),X_1)) -> ti(X_c,X_1) = ti(X_c,Z_2))) # label(fact_106_empty__fold__graphE) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 175 (all X_c all X_b all F all Z_2 all Y_2 all X_1 all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),Y_2)) -> hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_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_1),A_3)),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Y_2)))))) # label(fact_107_fold__graph_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 176 (all X_b all F all A_2 all X_3 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),X_3)),X_1)) -> -(all A_5 all A_4 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),X_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_5),A_4) -> (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),F),A_5),A_4),X_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),A_4))))))) # label(fact_108_insert__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 177 (all X_b all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (exists X1 hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_3),X1)))))) # label(fact_109_finite__nonempty__imp__fold1Set) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 178 (all X_b all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_2)) <-> ti(fun(X_b,bool),A_2) = bot_bot(fun(X_b,bool)) | (exists A_4 exists A_5 (ti(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),A_5),A_4) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_4)))))) # label(fact_110_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 179 (all X_b all Pa all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))) -> ((all X_2 all F_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,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),F_3))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2)))))) # label(fact_111_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 180 (all X_c all X_b all F all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) -> (exists X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) & -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))),hAPP(X_c,fun(X_b,bool),hAPP(fun(X_b,fun(X_c,bool)),fun(X_c,fun(X_b,bool)),combc(X_b,X_c,bool),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,bool)),hAPP(fun(X_c,fun(X_c,bool)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,bool))),combb(X_c,fun(X_c,bool),X_b),fequal(X_c)),F)),hAPP(X_b,X_c,F,X_2))))))))))) # label(fact_112_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 181 (all X_c all X_b all F all Z_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (exists X1 hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),X1))))) # label(fact_113_finite__imp__fold__graph) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 182 (all X_b all F all A1 all A2 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A1),A2)) <-> (exists A_5 exists A_4 exists X_2 (ti(fun(X_b,bool),A1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_5),A_4) & ti(X_b,A2) = ti(X_b,X_2) & hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),F),A_5),A_4),X_2)) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),A_4)))))) # label(fact_114_fold1Set_Osimps) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 183 (all X_b all Pa all A_2 (hBOOL(hAPP(X_b,bool,Pa,A_2)) -> ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> ti(X_b,X_2) = ti(X_b,A_2))) -> hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa)))))) # label(fact_115_theI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 184 (all X_b all A_2 all Pa ((exists X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) & (all Y_1 (hBOOL(hAPP(X_b,bool,Pa,Y_1)) -> ti(X_b,Y_1) = ti(X_b,X_2))))) -> (hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),X_b,the(X_b),Pa) = ti(X_b,A_2)))) # label(fact_116_the1__equality) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 185 (all X_b all Pa ((exists X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) & (all Y_1 (hBOOL(hAPP(X_b,bool,Pa,Y_1)) -> ti(X_b,Y_1) = ti(X_b,X_2))))) -> hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa))))) # label(fact_117_theI_H) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 186 (all X_c all X_b all F all Z_2 all A1 all A2 (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A1),A2)) <-> ti(fun(X_b,bool),A1) = bot_bot(fun(X_b,bool)) & ti(X_c,A2) = ti(X_c,Z_2) | (exists X_2 exists A_4 exists Y_1 (ti(fun(X_b,bool),A1) = 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_4) & ti(X_c,A2) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_2),Y_1) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_4)) & hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_4),Y_1)))))) # label(fact_118_fold__graph_Osimps) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 187 (all X_b all X_1 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,A_3)))))) # label(fact_119_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 188 (all X_b all Pa all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> (ti(fun(X_b,bool),F_2) != bot_bot(fun(X_b,bool)) -> ((all X_2 hBOOL(hAPP(fun(X_b,bool),bool,Pa,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)))))) -> ((all X_2 all F_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_3)) -> (ti(fun(X_b,bool),F_3) != bot_bot(fun(X_b,bool)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,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),F_3)))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2))))))) # label(fact_120_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 189 (all X_c all X_b all X_1 all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,A_3))))) # label(fact_121_folding__image__simple__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 190 (all X_b all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),big_semilattice_big(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,F_2,A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_3)))) # label(fact_122_semilattice__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 191 (all X_b all X_1 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (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_3),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_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_2,A_3) = ti(X_b,X_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_3),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_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_2,A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,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_3),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_1),bot_bot(fun(X_b,bool))))))))))) # label(fact_123_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.56 192 (all X_b all X_1 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (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_3),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_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_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_1),A_3)) = ti(X_b,X_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_3),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_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,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_3),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_1),bot_bot(fun(X_b,bool)))))))))) # label(fact_124_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 193 (all X_b (ab_semigroup_mult(X_b) -> (all X_1 all A_3 (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3)))))))) # label(fact_125_fold1__insert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 194 (all X_b (ab_sem1668676832m_mult(X_b) -> (all X_1 all A_3 (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3))))))) # label(fact_126_fold1__insert__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 195 (all X_b all B_2 all Ca all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),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_3),B_2)))))) # label(fact_127_DiffI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 196 (all X_b all Ca all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),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_3),B_2))) -> -(hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B_2))))) # label(fact_128_DiffE) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 197 (all X_b all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),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_3),B_2))))) # label(fact_129_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 198 (all X_b all X_1 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),X_1) = ti(X_b,X_1))) # label(fact_130_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 199 (all X_b all A_3 all B_2 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_3),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2))))) # label(fact_131_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 200 (all X_b all Ca all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),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_3),B_2))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B_2)))) # label(fact_132_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 201 (all X_b all A_3 all B_2 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)),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_3),B_2)),B_2) = 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_3),B_2)) # label(fact_133_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 202 (all X_b all Ca all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),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_3),B_2))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)))) # label(fact_134_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 203 (all X_b all Ca all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),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_3),B_2))) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B_2)))) # label(fact_135_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 204 (all X_c all X_b all X_1 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_2)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),X_1) = ti(X_b,X_1))) # label(fact_136_folding__image__simple__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 205 (all X_b all A_3 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)),bot_bot(fun(X_b,bool))),A_3) = bot_bot(fun(X_b,bool))) # label(fact_137_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 206 (all X_b all A_3 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_3),bot_bot(fun(X_b,bool))) = ti(fun(X_b,bool),A_3)) # label(fact_138_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 207 (all X_b all A_3 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_3),A_3) = bot_bot(fun(X_b,bool))) # label(fact_139_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 208 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),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_3),B_2))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))))) # label(fact_140_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 209 (all X_b all A_3 all X_1 all B_2 ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) -> 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)),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_1),A_3)),B_2) = 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_3),B_2)) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) -> 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)),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_1),A_3)),B_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_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_3),B_2))))) # label(fact_141_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 210 (all X_b all A_3 all X_1 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) -> 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)),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_1),A_3)),B_2) = 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_3),B_2))) # label(fact_142_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 211 (all X_b (ab_semigroup_mult(X_b) -> (all A_2 all Ba all A_3 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),times_times(X_b)),Ba),A_3),X_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),times_times(X_b)),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),Ba),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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))),X_1)))))))) # label(fact_143_fold__graph__permute__diff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 212 (all X_b all A_3 all A_2 all B_2 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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)) = 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)),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_3),B_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),A_2),bot_bot(fun(X_b,bool))))) # label(fact_144_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 213 (all X_b all A_3 all A_2 all B_2 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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)) = 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)),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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))),B_2)) # label(fact_145_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 214 (all X_b all A_2 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) # label(fact_146_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 215 (all X_b all X_1 all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> 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)),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_1),A_3)),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_1),bot_bot(fun(X_b,bool)))) = ti(fun(X_b,bool),A_3))) # label(fact_147_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 216 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = ti(fun(X_b,bool),A_3))) # label(fact_148_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 217 (all X_b all A_3 all A_2 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),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_3),B_2))))) # label(fact_149_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 218 (all X_b (ab_semigroup_mult(X_b) -> (all Z_2 all Ba all A_3 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),times_times(X_b)),Ba),A_3),Y_2)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),times_times(X_b)),Z_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),Ba),A_3)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Z_2),Y_2)))))))) # label(fact_150_fold__graph__insert__swap) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 219 (all X_b all X_1 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,A_3)) = hAPP(fun(X_b,bool),X_b,F_2,A_3))))) # label(fact_151_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 220 (all X_c all X_b all X_1 all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,A_3)) = hAPP(fun(X_c,bool),X_b,F_2,A_3))))) # label(fact_152_folding__image__simple__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 221 (all X_b (ab_sem1668676832m_mult(X_b) -> (all N_3 all H ((all X_2 all Y_1 hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),Y_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (ti(fun(X_b,bool),N_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),N_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_3)))))))) # label(fact_153_hom__fold1__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 222 (all X_b (ab_semigroup_mult(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),Y_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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3)),A_3)))))))) # label(fact_154_fold1__in) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 223 (all X_b all N_3 all H all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) -> ((all X_2 all Y_1 hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),Y_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (ti(fun(X_b,bool),N_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,F_2,N_3)) = hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_3))))))) # label(fact_155_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 224 (all X_b all Pa all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3)) -> ((all A_5 all A_4 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_4)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),A_4)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_4)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,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_4),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_5),bot_bot(fun(X_b,bool)))))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))))))) # label(fact_156_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 225 (all X_c all X_b all X_1 all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),bot_bot(fun(X_c,bool))))))))) # label(fact_157_folding__image__simple_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 226 (all X_c all X_b all X_1 all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3)) -> hAPP(fun(X_c,bool),X_b,F_2,A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),bot_bot(fun(X_c,bool)))))))))) # label(fact_158_folding__image__simple_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 227 (all X_c all X_b (minus(X_b) -> (all A_3 all B_2 all X_1 hAPP(X_c,X_b,hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),minus_minus(fun(X_c,X_b)),A_3),B_2),X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_c,X_b,A_3,X_1)),hAPP(X_c,X_b,B_2,X_1))))) # label(fact_159_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 228 (all X_b all X_c (minus(X_c) -> (all A_3 all B_2 all X_2 hAPP(X_b,X_c,hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),fun(X_b,X_c)),minus_minus(fun(X_b,X_c)),A_3),B_2),X_2) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(X_b,X_c,A_3,X_2)),hAPP(X_b,X_c,B_2,X_2))))) # label(fact_160_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 229 (all X_b hBOOL(hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),bool,finite_comp_fun_idem(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_b),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),combc(fun(X_b,bool),fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)))),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool))))))) # label(fact_161_comp__fun__idem__remove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 230 (all X_b all X_c all X_1 all Z_2 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite_comp_fun_idem(X_b,X_c),F)) -> hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2))) # label(fact_162_comp__fun__idem_Ofun__left__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 231 (all X_b hBOOL(hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),bool,finite_comp_fun_idem(X_b,fun(X_b,bool)),insert(X_b)))) # label(fact_163_comp__fun__idem__insert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 232 (all X_b (ab_sem1668676832m_mult(X_b) -> hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),times_times(X_b))))) # label(fact_164_comp__fun__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 233 (all X_c all X_b all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_2)) -> hAPP(fun(X_c,bool),X_b,F_2,bot_bot(fun(X_c,bool))) = ti(X_b,Z_2))) # label(fact_165_folding__image__simple_Oempty) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 234 (all X_a (ab_sem1668676832m_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1) = ti(X_a,A_1)))) # label(fact_166_times_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 235 (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_167_mult__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 236 (all X_a (ab_sem1668676832m_mult(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))) # label(fact_168_mult__left__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 237 (all X_c all X_b all X_1 all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> (-hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3)) -> hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,A_3)))))) # label(fact_169_folding__image__simple_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 238 (all X_c all X_b all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)) -> hAPP(X_c,X_b,G,X_2) = ti(X_b,Z_2))) -> hAPP(fun(X_c,bool),X_b,F_2,A_3) = ti(X_b,Z_2))))) # label(fact_170_folding__image__simple_Oneutral) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 239 (all X_b all X_c all A_2 all Z_2 all A_3 all Y_2 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),Y_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> (exists Y_3 (ti(X_c,Y_2) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,A_2),Y_3) & hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))),Y_3)))))))) # label(fact_171_comp__fun__commute_Ofold__graph__insertE__aux) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 240 (all X_c all X_b all F all Z_2 all Y_2 all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),fold_graph(X_b,X_c),F),Z_2),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_3),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_1),bot_bot(fun(X_b,bool))))),Y_2)) -> hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),fold_graph(X_b,X_c),F),Z_2),A_3),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Y_2)))))) # label(fact_172_fold__graph_H_Ointros_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 241 (all X_b all X_c (ab_group_add(X_c) -> (all F all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3)),hAPP(X_b,X_c,F,A_2))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3)))))) # label(fact_173_setsum__diff1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 242 (all X_b all X_c (ring(X_c) -> (all F all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3)),hAPP(X_b,X_c,F,A_2))))))) # label(fact_174_setsum__diff1__ring) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 243 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),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_1),A_3)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,G,X_1)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),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_3),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_1),bot_bot(fun(X_b,bool)))))))))) # label(fact_175_setprod_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 244 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),A_3) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,G,X_1)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),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_3),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_1),bot_bot(fun(X_b,bool))))))))))) # label(fact_176_setprod_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 245 (all X_b all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> 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)),B_2),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),finite_fold(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_b),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),combc(fun(X_b,bool),fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)))),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool))))),B_2),A_3))) # label(fact_177_minus__fold__remove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 246 (all X_b all X_c all X_1 all Z_2 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),A_3)) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2)),A_3)))) # label(fact_178_comp__fun__commute_Ofold__fun__comm) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 247 (all X_b all X_c all X_1 all Y_2 all Z_2 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,Y_2),Z_2)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,Y_2),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2)))) # label(fact_179_comp__fun__commute_Ofun__left__comm) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 248 (all X_c all X_d all X_b (comm_monoid_add(X_b) -> (all F all B_2 all A_3 hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_d,bool),fun(X_c,X_b),hAPP(fun(X_c,fun(fun(X_d,bool),X_b)),fun(fun(X_d,bool),fun(X_c,X_b)),combc(X_c,fun(X_d,bool),X_b),hAPP(fun(X_c,fun(X_d,X_b)),fun(X_c,fun(fun(X_d,bool),X_b)),hAPP(fun(fun(X_d,X_b),fun(fun(X_d,bool),X_b)),fun(fun(X_c,fun(X_d,X_b)),fun(X_c,fun(fun(X_d,bool),X_b))),combb(fun(X_d,X_b),fun(fun(X_d,bool),X_b),X_c),big_co1399186613setsum(X_d,X_b)),F)),B_2)),A_3) = hAPP(fun(X_d,bool),X_b,hAPP(fun(X_d,X_b),fun(fun(X_d,bool),X_b),big_co1399186613setsum(X_d,X_b),hAPP(fun(X_c,bool),fun(X_d,X_b),hAPP(fun(X_d,fun(fun(X_c,bool),X_b)),fun(fun(X_c,bool),fun(X_d,X_b)),combc(X_d,fun(X_c,bool),X_b),hAPP(fun(X_d,fun(X_c,X_b)),fun(X_d,fun(fun(X_c,bool),X_b)),hAPP(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),fun(fun(X_d,fun(X_c,X_b)),fun(X_d,fun(fun(X_c,bool),X_b))),combb(fun(X_c,X_b),fun(fun(X_c,bool),X_b),X_d),big_co1399186613setsum(X_c,X_b)),hAPP(fun(X_c,fun(X_d,X_b)),fun(X_d,fun(X_c,X_b)),combc(X_c,X_d,X_b),F))),A_3)),B_2)))) # label(fact_180_setsum__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 249 (all X_b all X_c all Z_2 all A_3 all Y_2 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),Y_2)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),A_3) = ti(X_c,Y_2)))) # label(fact_181_comp__fun__commute_Ofold__equality) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 250 (all X_c all X_b all F all Z_2 hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,bool),X_b)),finite_fold(X_c,X_b),F),Z_2),bot_bot(fun(X_c,bool))) = ti(X_b,Z_2)) # label(fact_182_fold__empty) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 251 (all X_b all X_c all Z_2 all X_1 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_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_1),A_3)) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2)),A_3))))) # label(fact_183_comp__fun__commute_Ofold__insert2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 252 (all X_b all X_c all Z_2 all X_1 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_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_1),A_3)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),A_3)))))) # label(fact_184_comp__fun__commute_Ofold__insert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 253 (all X_b all X_c all Z_2 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),A_3)))))) # label(fact_185_comp__fun__commute_Ofold__graph__fold) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 254 (all X_c all X_b (comm_monoid_mult(X_b) -> (all F all G all A_3 hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,X_b)),combs(X_c,X_b,X_b),hAPP(fun(X_c,X_b),fun(X_c,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_c),times_times(X_b)),F)),G)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),F),A_3)),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),G),A_3))))) # label(fact_186_setprod__timesf) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 255 (all X_c all X_d all X_b (semiring_0(X_b) -> (all F all A_3 all G all B_2 hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),F),A_3)),hAPP(fun(X_d,bool),X_b,hAPP(fun(X_d,X_b),fun(fun(X_d,bool),X_b),big_co1399186613setsum(X_d,X_b),G),B_2)) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_d,bool),fun(X_c,X_b),hAPP(fun(X_c,fun(fun(X_d,bool),X_b)),fun(fun(X_d,bool),fun(X_c,X_b)),combc(X_c,fun(X_d,bool),X_b),hAPP(fun(X_c,fun(X_d,X_b)),fun(X_c,fun(fun(X_d,bool),X_b)),hAPP(fun(fun(X_d,X_b),fun(fun(X_d,bool),X_b)),fun(fun(X_c,fun(X_d,X_b)),fun(X_c,fun(fun(X_d,bool),X_b))),combb(fun(X_d,X_b),fun(fun(X_d,bool),X_b),X_c),big_co1399186613setsum(X_d,X_b)),hAPP(fun(X_d,X_b),fun(X_c,fun(X_d,X_b)),hAPP(fun(X_c,fun(fun(X_d,X_b),fun(X_d,X_b))),fun(fun(X_d,X_b),fun(X_c,fun(X_d,X_b))),combc(X_c,fun(X_d,X_b),fun(X_d,X_b)),hAPP(fun(X_c,fun(X_b,X_b)),fun(X_c,fun(fun(X_d,X_b),fun(X_d,X_b))),hAPP(fun(fun(X_b,X_b),fun(fun(X_d,X_b),fun(X_d,X_b))),fun(fun(X_c,fun(X_b,X_b)),fun(X_c,fun(fun(X_d,X_b),fun(X_d,X_b)))),combb(fun(X_b,X_b),fun(fun(X_d,X_b),fun(X_d,X_b)),X_c),combb(X_b,X_b,X_d)),hAPP(fun(X_c,X_b),fun(X_c,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_c),times_times(X_b)),F))),G))),B_2)),A_3)))) # label(fact_187_setsum__product) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 256 (all X_c all X_b (semiring_0(X_b) -> (all F all A_3 all R_2 hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),F),A_3)),R_2) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(X_b,fun(X_c,X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(X_b,fun(X_c,X_b)),combc(X_c,X_b,X_b),hAPP(fun(X_c,X_b),fun(X_c,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_c),times_times(X_b)),F)),R_2)),A_3)))) # label(fact_188_setsum__left__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 257 (all X_c all X_b (semiring_0(X_b) -> (all R_2 all F all A_3 hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),R_2),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),F),A_3)) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_b,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),combb(X_b,X_b,X_c),hAPP(X_b,fun(X_b,X_b),times_times(X_b),R_2)),F)),A_3)))) # label(fact_189_setsum__right__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 258 (all X_c all X_b (ab_group_add(X_b) -> (all F all G all A_3 hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,X_b)),combs(X_c,X_b,X_b),hAPP(fun(X_c,X_b),fun(X_c,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_c),minus_minus(X_b)),F)),G)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),F),A_3)),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),G),A_3))))) # label(fact_190_setsum__subtractf) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 259 (all X_c all X_b all F all Z_2 hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),fold_graph(X_b,X_c),F),Z_2),bot_bot(fun(X_b,bool))),Z_2))) # label(fact_191_fold__graph_H_Ointros_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 260 (all X_b (ab_semigroup_mult(X_b) -> hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite100568337ommute(X_b,X_b),times_times(X_b))))) # label(fact_192_comp__fun__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 261 (all X_b all X_c all Y_2 all Z_2 all A_3 all X_1 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),X_1)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),Y_2)) -> ti(X_c,Y_2) = ti(X_c,X_1))))) # label(fact_193_comp__fun__commute_Ofold__graph__determ) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 262 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,X_c)),combs(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combb(X_c,fun(X_c,X_c),X_b),times_times(X_c)),G)),H)),A_3) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),A_3)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),H),A_3)))))) # label(fact_194_setprod_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 263 (all X_b all X_c all Z_2 all X_1 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),A_3) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),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_3),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_1),bot_bot(fun(X_b,bool)))))))))) # label(fact_195_comp__fun__commute_Ofold__rec) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 264 (all X_b all X_c all Z_2 all X_1 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_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_1),A_3)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),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_3),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_1),bot_bot(fun(X_b,bool))))))))) # label(fact_196_comp__fun__commute_Ofold__insert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 265 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,F,A_2)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),A_3))))))) # label(fact_197_setprod__insert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 266 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),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_1),A_3)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,G,X_1)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),A_3))))))) # label(fact_198_setprod_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 267 (all X_b all F all A_2 all A_3 ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),A_3)),hAPP(X_b,nat,F,A_2))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),A_3)))) # label(fact_199_setsum__diff1__nat) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 268 (all X_c all X_b all F all Z_2 all A_3 hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,bool),X_b)),finite_fold(X_c,X_b),F),Z_2),A_3) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_c,bool),fun(X_b,bool)),hAPP(fun(X_c,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,bool),fun(X_b,bool))),finite_fold_graph(X_c,X_b),F),Z_2),A_3))) # label(fact_200_fold__def) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 269 (all X_b all X_c all Z_2 all X_1 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite_comp_fun_idem(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_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_1),A_3)) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2)),A_3)))) # label(fact_201_comp__fun__idem_Ofold__insert__idem2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 270 (all X_b all X_c all Z_2 all X_1 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite_comp_fun_idem(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_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_1),A_3)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),A_3))))) # label(fact_202_comp__fun__idem_Ofold__insert__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 271 (all X_b all X_1 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,F_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_1),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),F),X_1),A_3))))) # label(fact_203_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 272 (all X_b all A_2 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,F_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),A_2),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),F),A_2),A_3)))) # label(fact_204_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 273 (all X_b (ab_semigroup_mult(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),times_times(X_b)),A_2),A_3)))))) # label(fact_205_fold1__eq__fold) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 274 (all X_b (ab_sem1668676832m_mult(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),times_times(X_b)),A_2),A_3))))) # label(fact_206_fold1__eq__fold__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 275 (all X_b all X_c all Z_2 all X_1 all A_3 all V all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_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_1),A_3)),V)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> -(all Y_1 (ti(X_c,V) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Y_1) -> -hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),Y_1)))))))) # label(fact_207_comp__fun__commute_Ofold__graph__insertE) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 276 (all X_d all X_b all X_c (comm_monoid_add(X_c) -> (all G all F all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),S_1) = hAPP(fun(X_d,bool),X_c,hAPP(fun(X_d,X_c),fun(fun(X_d,bool),X_c),big_co1399186613setsum(X_d,X_c),hAPP(fun(X_d,fun(X_b,bool)),fun(X_d,X_c),hAPP(fun(fun(X_b,bool),X_c),fun(fun(X_d,fun(X_b,bool)),fun(X_d,X_c)),combb(fun(X_b,bool),X_c,X_d),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G)),hAPP(fun(X_d,fun(X_b,bool)),fun(X_d,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_d,fun(X_b,bool)),fun(X_d,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_d),collect(X_b)),hAPP(fun(X_d,fun(X_b,bool)),fun(X_d,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_d,fun(X_b,bool)),fun(X_d,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_d),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S_1)))),hAPP(fun(X_b,fun(X_d,bool)),fun(X_d,fun(X_b,bool)),combc(X_b,X_d,bool),hAPP(fun(X_b,X_d),fun(X_b,fun(X_d,bool)),hAPP(fun(X_d,fun(X_d,bool)),fun(fun(X_b,X_d),fun(X_b,fun(X_d,bool))),combb(X_d,fun(X_d,bool),X_b),fequal(X_d)),F)))))),hAPP(fun(X_b,bool),fun(X_d,bool),hAPP(fun(X_b,X_d),fun(fun(X_b,bool),fun(X_d,bool)),image(X_b,X_d),F),S_1)))))) # label(fact_208_setsum__image__gen) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 277 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(X_b,X_c,G,X_2) = hAPP(X_b,X_c,H,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),H),A_3)))))) # label(fact_209_setprod_Ocong) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 278 (all X_b all X_c (comm_monoid_add(X_c) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(X_b,X_c,G,X_2) = hAPP(X_b,X_c,H,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),H),A_3)))))) # label(fact_210_setsum_Ocong) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.57 279 (all X_c all X_b all X_d (comm_monoid_add(X_d) -> (all F all R_1 all T_4 all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),T_4)) -> hAPP(fun(X_b,bool),X_d,hAPP(fun(X_b,X_d),fun(fun(X_b,bool),X_d),big_co1399186613setsum(X_b,X_d),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,X_d),hAPP(fun(X_b,fun(fun(X_c,bool),X_d)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,X_d)),combs(X_b,fun(X_c,bool),X_d),hAPP(fun(X_b,fun(X_c,X_d)),fun(X_b,fun(fun(X_c,bool),X_d)),hAPP(fun(fun(X_c,X_d),fun(fun(X_c,bool),X_d)),fun(fun(X_b,fun(X_c,X_d)),fun(X_b,fun(fun(X_c,bool),X_d))),combb(fun(X_c,X_d),fun(fun(X_c,bool),X_d),X_b),big_co1399186613setsum(X_c,X_d)),F)),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool)),hAPP(fun(fun(X_c,bool),fun(X_c,bool)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool))),combb(fun(X_c,bool),fun(X_c,bool),X_b),collect(X_c)),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool)),hAPP(fun(fun(X_c,bool),fun(X_c,bool)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool))),combb(fun(X_c,bool),fun(X_c,bool),X_b),hAPP(fun(X_c,fun(bool,bool)),fun(fun(X_c,bool),fun(X_c,bool)),combs(X_c,bool,bool),hAPP(fun(X_c,bool),fun(X_c,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_c,bool),fun(X_c,fun(bool,bool))),combb(bool,fun(bool,bool),X_c),fconj),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,fun(fun(X_c,bool),bool)),fun(fun(X_c,bool),fun(X_c,bool)),combc(X_c,fun(X_c,bool),bool),member(X_c)),T_4)))),R_1)))),S_1) = hAPP(fun(X_c,bool),X_d,hAPP(fun(X_c,X_d),fun(fun(X_c,bool),X_d),big_co1399186613setsum(X_c,X_d),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,X_d),hAPP(fun(X_c,fun(fun(X_b,bool),X_d)),fun(fun(X_c,fun(X_b,bool)),fun(X_c,X_d)),combs(X_c,fun(X_b,bool),X_d),hAPP(fun(X_c,fun(X_b,X_d)),fun(X_c,fun(fun(X_b,bool),X_d)),hAPP(fun(fun(X_b,X_d),fun(fun(X_b,bool),X_d)),fun(fun(X_c,fun(X_b,X_d)),fun(X_c,fun(fun(X_b,bool),X_d))),combb(fun(X_b,X_d),fun(fun(X_b,bool),X_d),X_c),big_co1399186613setsum(X_b,X_d)),hAPP(fun(X_b,fun(X_c,X_d)),fun(X_c,fun(X_b,X_d)),combc(X_b,X_c,X_d),F))),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_c),collect(X_b)),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_c),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S_1)))),hAPP(fun(X_b,fun(X_c,bool)),fun(X_c,fun(X_b,bool)),combc(X_b,X_c,bool),R_1))))),T_4)))))) # label(fact_211_setsum__setsum__restrict) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 280 (all X_b all X_c (comm_monoid_add(X_c) -> (all G all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),A_3) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(X_b,X_c,G,X_1)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),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_3),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_1),bot_bot(fun(X_b,bool))))))))))) # label(fact_212_setsum_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 281 (all X_b all X_c (comm_monoid_add(X_c) -> (all F all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(X_b,X_c,F,A_2)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))))))))) # label(fact_213_setsum__diff1_H) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 282 (all X_b all X_c (comm_monoid_add(X_c) -> (all G all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),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_1),A_3)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(X_b,X_c,G,X_1)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),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_3),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_1),bot_bot(fun(X_b,bool)))))))))) # label(fact_214_setsum_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 283 (all X_c all X_b (comm_monoid_add(X_b) -> (all F all G all A_3 hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,X_b)),combs(X_c,X_b,X_b),hAPP(fun(X_c,X_b),fun(X_c,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_c),plus_plus(X_b)),F)),G)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),F),A_3)),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),G),A_3))))) # label(fact_215_setsum__addf) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 284 (all X_b all X_c (comm_monoid_add(X_c) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,X_c)),combs(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combb(X_c,fun(X_c,X_c),X_b),plus_plus(X_c)),G)),H)),A_3) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),A_3)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),H),A_3)))))) # label(fact_216_setsum_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 285 (all X_b all X_c (comm_monoid_add(X_c) -> (all F all A_2 all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),F_2)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),F_2)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(X_b,X_c,F,A_2)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),F_2))))))) # label(fact_217_setsum__insert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 286 (all X_b all X_c (comm_monoid_add(X_c) -> (all G all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),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_1),A_3)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(X_b,X_c,G,X_1)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),A_3))))))) # label(fact_218_setsum_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 287 (all X_b (ring(X_b) -> (all A_2 all E all Ca all Ba all D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),Ca) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),E)),D) <-> ti(X_b,Ca) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ba),A_2)),E)),D))))) # label(fact_219_eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 288 (all X_b (ring(X_b) -> (all A_2 all E all Ca all Ba all D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),Ca) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),E)),D) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),Ba)),E)),Ca) = ti(X_b,D))))) # label(fact_220_eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 289 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),B) = ti(X_a,A_1)))) # label(fact_221_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 290 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),B) = ti(X_a,A_1)))) # label(fact_222_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 291 (all X_b (semiri456707255roduct(X_b) -> (all W_1 all Y_2 all X_1 all Z_2 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Y_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Z_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Z_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Y_2)) <-> ti(X_b,W_1) = ti(X_b,X_1) | ti(X_b,Y_2) = ti(X_b,Z_2))))) # label(fact_223_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 292 (all X_a (semiring(X_a) -> (all A_1 all E_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),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),E_1)),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),E_1)),C)))) # label(fact_224_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 293 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),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_1),B)),M)))) # label(fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 294 (all X_a (cancel_semigroup_add(X_a) -> (all B all A_1 all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1) -> ti(X_a,B) = ti(X_a,C))))) # label(fact_226_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 295 (all X_a (cancel146912293up_add(X_a) -> (all A_1 all B all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) -> ti(X_a,B) = ti(X_a,C))))) # label(fact_227_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 296 (all X_a (cancel_semigroup_add(X_a) -> (all A_1 all B all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) -> ti(X_a,B) = ti(X_a,C))))) # label(fact_228_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 297 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))))) # label(fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 298 (all X_b (cancel_semigroup_add(X_b) -> (all Ba all A_2 all Ca (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ba),A_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ca),A_2) <-> ti(X_b,Ba) = ti(X_b,Ca))))) # label(fact_230_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 299 (all X_b (cancel_semigroup_add(X_b) -> (all A_2 all Ba all Ca (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),Ba) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),Ca) <-> ti(X_b,Ba) = ti(X_b,Ca))))) # label(fact_231_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 300 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),B)))) # label(fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 301 (all X_a (ab_semigroup_add(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))) # label(fact_233_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 302 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))) # label(fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 303 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),D_1)))) # label(fact_235_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 304 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),D_1))))) # label(fact_236_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 305 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)))) # label(fact_237_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 306 (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_238_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 307 (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_239_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 308 (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_240_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 309 (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_241_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 310 (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_242_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 311 (all X_a (ab_semigroup_mult(X_a) -> (all A_1 all B all C 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_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))) # label(fact_243_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 312 (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_244_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 313 (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_245_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 314 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)))) # label(fact_246_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 315 (all X_b (ab_group_add(X_b) -> (all A_2 all Ba all Ca all D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),Ba) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ca),D) -> (ti(X_b,A_2) = ti(X_b,Ba) <-> ti(X_b,Ca) = ti(X_b,D)))))) # label(fact_247_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 316 (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_248_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 317 (all X_b (semiri456707255roduct(X_b) -> (all Ca all D all A_2 all Ba (ti(X_b,A_2) != ti(X_b,Ba) & ti(X_b,Ca) != ti(X_b,D) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),D)) != hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),D)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),Ca)))))) # label(fact_249_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 318 (all X_a (comm_semiring(X_a) -> (all A_1 all B all C 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_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))) # label(fact_250_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 319 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))) # label(fact_251_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 320 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all G all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)) -> hAPP(X_b,X_c,F,X_2) = hAPP(X_b,X_c,G,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),B_2)))))) # label(fact_252_setprod__cong) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 321 (all X_b all X_c (comm_monoid_mult(X_c) -> (all H all G all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)) -> hAPP(X_b,X_c,H,X_2) = hAPP(X_b,X_c,G,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),H),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),B_2)))))) # label(fact_253_setprod_OF__cong) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 322 (all X_b all X_c (comm_monoid_add(X_c) -> (all F all G all A_3 ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(X_b,X_c,F,X_2) = hAPP(X_b,X_c,G,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),A_3))))) # label(fact_254_setsum__cong2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 323 (all X_b all X_c (comm_monoid_add(X_c) -> (all F all G all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)) -> hAPP(X_b,X_c,F,X_2) = hAPP(X_b,X_c,G,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),B_2)))))) # label(fact_255_setsum__cong) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 324 (all X_b all X_c (comm_monoid_add(X_c) -> (all H all G all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)) -> hAPP(X_b,X_c,H,X_2) = hAPP(X_b,X_c,G,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),H),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),B_2)))))) # label(fact_256_setsum_OF__cong) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 325 (all X_b (order(X_b) -> (all K_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)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),K_1),bot_bot(fun(X_b,bool)))),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),K_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),K_1),bot_bot(fun(X_b,bool)))))) # label(fact_257_single__Diff__lessThan) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 326 (all X_b all F all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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_2),A_3)) -> hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),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_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),A_3)),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),B_2))))) # label(fact_258_setsum__diff__nat) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 327 (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_259_order__refl) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 328 (all X_b all A_3 all B_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)),A_3),B_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_2),A_3)) -> ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2)))) # label(fact_260_equalityI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 329 (all X_b all Ca all A_3 all B_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)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B_2))))) # label(fact_261_subsetD) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 330 (all X_b all A_3 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)),bot_bot(fun(X_b,bool))),A_3))) # label(fact_262_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 331 (all X_b all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(fun(fun(X_b,bool),bool),bool,finite_finite_1(fun(X_b,bool)),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,bool),bool),collect(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),combc(fun(X_b,bool),fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool))),A_3)))))) # label(fact_263_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 332 (all X_b all R_1 all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),R_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S_1))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),R_1),S_1)))) # label(fact_264_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 333 (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_265_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 334 (all X_b all X_c (ord(X_c) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(X_b,X_c,G,X_1))))))) # label(fact_266_le__funE) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 335 (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_267_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 336 (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_268_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 337 (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_269_order__trans) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 338 (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_270_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 339 (all X_a (order(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1))))))) # label(fact_271_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 340 (all X_a (ord(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_272_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 341 (all X_a (order(X_a) -> (all C all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1))))))) # label(fact_273_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 342 (all X_a (ord(X_a) -> (all C all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_274_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 343 (all X_b (order(X_b) -> (all Y_2 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) <-> ti(X_b,X_1) = ti(X_b,Y_2)))))) # label(fact_275_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 344 (all X_b all X_c (ord(X_c) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(X_b,X_c,G,X_1))))))) # label(fact_276_le__funD) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 345 (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_277_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 346 (all X_b (order(X_b) -> (all X_1 all Y_2 (ti(X_b,X_1) = ti(X_b,Y_2) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)))))) # label(fact_278_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 347 (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_279_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 348 (all X_b all X_c (ord(X_c) -> (all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) <-> (all X_2 hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2)))))))) # label(fact_280_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 349 (all X_b all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_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)),A_3),B_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_2),A_3))))) # label(fact_281_equalityE) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 350 (all X_b all C_1 all A_3 all B_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)),A_3),B_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_2),C_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),C_1))))) # label(fact_282_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 351 (all X_b all X_1 all A_3 all B_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)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))))) # label(fact_283_set__mp) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 352 (all X_b all B_2 all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (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)),A_3),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))))) # label(fact_284_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 353 (all X_b all X_1 all A_3 all B_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)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))))) # label(fact_285_in__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 354 (all X_b all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_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_2),A_3)))) # label(fact_286_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 355 (all X_b all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_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)),A_3),B_2)))) # label(fact_287_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 356 (all X_b all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_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)),A_3),B_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_2),A_3)))) # label(fact_288_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 357 (all X_b all A_3 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)),A_3),A_3))) # label(fact_289_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 358 (all X_b all X_1 all Pa all Q_3 (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)),Pa),Q_3)) -> (hBOOL(hAPP(X_b,bool,Pa,X_1)) -> hBOOL(hAPP(X_b,bool,Q_3,X_1))))) # label(fact_290_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 359 (all X_b all Q_3 all Pa all X_1 (hBOOL(hAPP(X_b,bool,Pa,X_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),Pa),Q_3)) -> hBOOL(hAPP(X_b,bool,Q_3,X_1))))) # label(fact_291_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 360 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),X_1)),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),Y_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)))))) # label(fact_292_lessThan__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 361 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),X_1) = hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),Y_2) <-> ti(X_b,X_1) = ti(X_b,Y_2))))) # label(fact_293_lessThan__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 362 (all X_a (ordere236663937imp_le(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_294_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 363 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_295_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 364 (all X_a (ordere779506340up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_296_add__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 365 (all X_a (ordere779506340up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))))))) # label(fact_297_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 366 (all X_a (ordere779506340up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))))) # label(fact_298_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 367 (all X_b (ordere236663937imp_le(X_b) -> (all Ca all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ca),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ca),Ba))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)))))) # label(fact_299_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 368 (all X_b (ordere236663937imp_le(X_b) -> (all A_2 all Ca all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ba),Ca))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)))))) # label(fact_300_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 369 (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_301_le__bot) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 370 (all X_b (bot(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),bot_bot(X_b))) <-> ti(X_b,A_2) = bot_bot(X_b))))) # label(fact_302_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 371 (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),bot_bot(X_a)),A_1))))) # label(fact_303_bot__least) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 372 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all Ba all Ca all D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),Ba) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ca),D) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),D))))))) # label(fact_304_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 373 (all X_b all A_3 (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)),A_3),bot_bot(fun(X_b,bool)))) <-> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)))) # label(fact_305_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 374 (all X_b all A_3 all B_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)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))))) # label(fact_306_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 375 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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)),A_3),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))))) # label(fact_307_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 376 (all X_b all A_2 all C_1 all D_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)),C_1),D_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),C_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),A_2),D_2))))) # label(fact_308_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 377 (all X_b all Ba all A_3 all B_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)),A_3),B_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)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),B_2))))) # label(fact_309_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 378 (all X_b all B_2 all X_1 all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (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)),A_3),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_1),B_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)),A_3),B_2))))) # label(fact_310_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 379 (all X_b all X_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_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)),A_3),B_2)))) # label(fact_311_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 380 (all X_b all B_2 all 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_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),A_2),B_2)))) # label(fact_312_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 381 (all X_c all X_b all F all A_3 all B_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)),A_3),B_2)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),B_2))))) # label(fact_313_image__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 382 (all X_b all X_c all B_2 all F all A_3 (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_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) <-> (exists AA (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),AA),A_3)) & ti(fun(X_b,bool),B_2) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),AA))))) # label(fact_314_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 383 (all X_b all C_1 all A_3 all B_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)),A_3),B_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_2),C_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)),B_2),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)),C_1),A_3)) = ti(fun(X_b,bool),A_3)))) # label(fact_315_double__diff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 384 (all X_b all D_2 all B_2 all A_3 all C_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),C_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),D_2),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(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_3),B_2)),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)),C_1),D_2)))))) # label(fact_316_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 385 (all X_b all A_3 all B_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(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_3),B_2)),A_3))) # label(fact_317_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 386 (all X_b all Ts all Ga all Ts_1 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts_1)) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),ord_less_eq(fun(hoare_2118899576triple(X_b),bool)),Ts),Ts_1)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts))))) # label(fact_318_weaken) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 387 (all X_b all Ts all Ga (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),ord_less_eq(fun(hoare_2118899576triple(X_b),bool)),Ts),Ga)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts)))) # label(fact_319_asm) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 388 (all X_b all A_3 all X_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),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_1),bot_bot(fun(X_b,bool))))) -> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) | ti(fun(X_b,bool),A_3) = 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_1),bot_bot(fun(X_b,bool))))) # label(fact_320_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 389 (all X_c all X_b all B_2 all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),B_2),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))))) # label(fact_321_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 390 (all X_b all X_c all F all A_3 all B_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(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)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B_2))),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),B_2))))) # label(fact_322_image__diff__subset) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 391 (all X_c all X_b all B_2 all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),B_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_2,B_2)),hAPP(fun(X_c,bool),X_b,F_2,A_3)) = hAPP(fun(X_c,bool),X_b,F_2,A_3))))) # label(fact_323_folding__image__simple__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 392 (all X_b (ordered_ring(X_b) -> (all A_2 all E all Ca all Ba all D (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),E)),D))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),Ba)),E)),Ca)),D)))))) # label(fact_324_le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 393 (all X_b (ordered_ring(X_b) -> (all A_2 all E all Ca all Ba all D (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),E)),D))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ba),A_2)),E)),D))))))) # label(fact_325_le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 394 (all X_b all A_3 all X_1 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(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_3),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_1),bot_bot(fun(X_b,bool))))),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> 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)),A_3),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_1),B_2)))))) # label(fact_326_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 395 (all X_b all A_3 all X_1 all B_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)),A_3),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_1),B_2))) <-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(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_3),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_1),bot_bot(fun(X_b,bool))))),B_2))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> 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)),A_3),B_2))))) # label(fact_327_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 396 (all X_b all B_2 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),B_2) != bot_bot(fun(X_b,bool)) -> (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_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_2,B_2)),hAPP(fun(X_b,bool),X_b,F_2,A_3)) = hAPP(fun(X_b,bool),X_b,F_2,A_3)))))) # label(fact_328_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 397 (all X_b all X_c (ab_group_add(X_c) -> (all F all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (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_2),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),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_3),B_2)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),B_2))))))) # label(fact_329_setsum__diff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 398 (all X_b all Pa all A_3 all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_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)),F_2),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))) -> ((all A_5 all F_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),F_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_5),F_3)))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2))))))) # label(fact_330_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 399 (all X_b all B_2 all A_3 ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_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)),A_3),B_2)))) # label(fact_331_subsetI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 400 (all X_c all X_b all F all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) -> (exists C_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),C_2),A_3)) & hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),C_2)) & ti(fun(X_b,bool),B_2) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),C_2)))))) # label(fact_332_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 401 (all X_b all X_c (comm_monoid_add(X_c) & ordere779506340up_add(X_c) -> (all F all G all K_2 ((all I_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),I_2),K_2)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,I_2)),hAPP(X_b,X_c,G,I_2))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),K_2)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),K_2))))))) # label(fact_333_setsum__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 402 (all X_c all X_b all F all B_2 all A_3 ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,X_2)),B_2)))) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)),B_2)))) # label(fact_334_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 403 (all X_b all X_c (ord(X_c) -> (all F all G ((all X_2 hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2)))) -> hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)))))) # label(fact_335_le__funI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 404 (all X_b all A_3 all Ba ((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)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),bot_bot(fun(X_b,bool))))) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),Ba),A_3) = ti(X_b,Ba)) & (-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)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),bot_bot(fun(X_b,bool))))) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),Ba),A_3) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),bot_bot(fun(X_b,bool))))))))) # label(fact_336_flat__lub__def) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 405 (all N all Q_3 all Pa ((all X_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,Q_3,X_2)),hAPP(nat,nat,Pa,X_2)))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),Pa),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),Q_3),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N))) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),minus_minus(nat)),Pa)),Q_3)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N)))) # label(fact_337_sum__diff__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 406 (all X_b (linorder(X_b) -> (all B_2 all A_3 (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (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)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),B_2)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3))))))))) # label(fact_338_fold1__antimono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 407 (all X_b all Q_3 all Pa ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> hBOOL(hAPP(X_b,bool,Q_3,X_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)),Pa),Q_3)))) # label(fact_339_predicate1I) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.58 408 (all X_b all Q_3 all Pa ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> hBOOL(hAPP(X_b,bool,Q_3,X_2)))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3))))) # label(fact_340_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 409 (all X_b (linorder(X_b) -> (all M_3 all N_3 (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)),M_3),N_3)) -> (ti(fun(X_b,bool),M_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),N_3)),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),M_3))))))))) # label(fact_341_Min__antimono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 410 (all X_b (linorder(X_b) -> (all M_3 all N_3 (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)),M_3),N_3)) -> (ti(fun(X_b,bool),M_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),M_3)),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),N_3))))))))) # label(fact_342_Max__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 411 (all K_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),ord_lessThan(nat),K_1)))) # label(fact_343_finite__lessThan) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 412 (all K_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),K_1))))) # label(fact_344_finite__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 413 (all N_3 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3)) <-> (exists M_2 all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_2),M_2)))))) # label(fact_345_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 414 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)))))) # label(fact_346_Min_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 415 (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_347_Min_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 416 (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_348_min__max_Oinf__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 417 (all X_a (linorder(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),C))))) # label(fact_349_min__max_Oinf_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 418 (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_350_min__max_Oinf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 419 (all X_a (linorder(X_a) -> (all B all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),C))))) # label(fact_351_min__max_Oinf_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 420 (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_352_min__max_Oinf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 421 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)))) # label(fact_353_min__max_Oinf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 422 (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_354_min__max_Oinf__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 423 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),A_1)))) # label(fact_355_min__max_Oinf_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 424 (all X_a (linorder(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),A_1) = ti(X_a,A_1)))) # label(fact_356_min__max_Oinf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 425 (all X_b (linorder(X_b) -> (all X_1 all Y_2 all Z_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),Y_2)),Z_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Z_2)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),Z_2)))))) # label(fact_357_min__le__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 426 (all X_a (linorder(X_a) -> (all X all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B))) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B))))))) # label(fact_358_min__max_Ole__infE) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 427 (all X_a (linorder(X_a) -> (all B all D_1 all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),C),D_1)))))))) # label(fact_359_min__max_Oinf__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 428 (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_360_min__max_Oinf__greatest) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 429 (all X_a (linorder(X_a) -> (all B all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)))))))) # label(fact_361_min__max_Ole__infI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 430 (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_362_min__max_Oinf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 431 (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_363_min__max_Oinf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 432 (all X_a (linorder(X_a) -> (all A_1 all B all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_364_min__max_Ole__infI2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 433 (all X_a (linorder(X_a) -> (all B all A_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_365_min__max_Ole__infI1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 434 (all X_b (linorder(X_b) -> (all X_1 all Y_2 all Z_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),Y_2),Z_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Z_2)))))) # label(fact_366_min__max_Ole__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 435 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),Y_2) = ti(X_b,X_1))))) # label(fact_367_min__max_Ole__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 436 (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_368_min__max_Oinf__le2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 437 (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_369_min__max_Oinf__le1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 438 (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_370_min__add__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 439 (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_371_min__diff__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 440 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3))))) # label(fact_372_Min_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 441 (all X_b (linorder(X_b) -> hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),ord_min(X_b))))) # label(fact_373_min__max_Ocomp__fun__idem__inf) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 442 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3))))))) # label(fact_374_Min__insert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 443 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)))))))) # label(fact_375_Min_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 444 (all X_b (linorder(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),B_2) != bot_bot(fun(X_b,bool)) -> (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_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),B_2)),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3))))))) # label(fact_376_Min_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 445 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),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_1),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),X_1),A_3)))))) # label(fact_377_Min_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 446 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),A_2),A_3))))) # label(fact_378_Min_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 447 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (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_3),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_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),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_1),A_3)) = ti(X_b,X_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_3),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_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),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_3),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_1),bot_bot(fun(X_b,bool))))))))))) # label(fact_379_Min_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 448 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (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_3),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_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3) = ti(X_b,X_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_3),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_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),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_3),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_1),bot_bot(fun(X_b,bool)))))))))))) # label(fact_380_Min_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 449 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)))))))) # label(fact_381_Max__ge) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 450 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)),X_1))))))) # label(fact_382_Min__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 451 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)),A_3))))))) # label(fact_383_Max__in) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 452 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)),A_3))))))) # label(fact_384_Min__in) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 453 (all X_b (linorder(X_b) -> (all X_1 hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),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_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1)))) # label(fact_385_Min_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 454 (all X_b (linorder(X_b) -> (all X_1 hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),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_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1)))) # label(fact_386_Max_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 455 (all X_b (linorder(X_b) -> (all Ba all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),Ba),A_3)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),A_2),Ba)))))))) # label(fact_387_min__max_Ofold__inf__le__inf) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 456 (all X_b (linorder(X_b) -> (all Ba all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),Ba),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),A_2),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),Ba),A_3)))))) # label(fact_388_min__max_Ofold__inf__insert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 457 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3)),A_2))))))) # label(fact_389_min__max_Ofold1__belowI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 458 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3)),X_1)) <-> (exists X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),X_1)))))))))) # label(fact_390_fold1__below__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 459 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3))) <-> (all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),X_2)))))))))) # label(fact_391_min__max_Obelow__fold1__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 460 (all X_b (linorder(X_b) -> (all N_3 all H ((all X_2 all Y_1 hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_2),Y_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (ti(fun(X_b,bool),N_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),N_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_3)))))))) # label(fact_392_Min_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 461 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_2),Y_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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)),A_3)))))))) # label(fact_393_Min_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 462 (all X_b (linorder(X_b) -> (all Ca all Ba all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),X_2)))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),Ba),Ca)),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),Ca),A_3)))))))) # label(fact_394_min__max_Oinf__le__fold__inf) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 463 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all Y_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)))) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3) = ti(X_b,X_1))))))) # label(fact_395_Min__eqI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 464 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all Y_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1)))) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3) = ti(X_b,X_1))))))) # label(fact_396_Max__eqI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 465 (all X_b (linorder(X_b) -> hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,X_b)),max(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),ord_less_eq(X_b))) = ord_min(X_b))) # label(fact_397_dual__max) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 466 (all U all F ((all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),hAPP(nat,nat,F,N_2)))) -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),F)),U)))))) # label(fact_398_finite__less__ub) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 467 (all X_a (order(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Least) = ti(X_a,Least))))) # label(fact_399_min__leastR) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 468 (all X_a (ord(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Least),X) = ti(X_a,Least))))) # label(fact_400_min__leastL) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 469 (all X_b (ord(X_b) -> ord_min(X_b) = hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,X_b)),min(X_b),ord_less_eq(X_b)))) # label(fact_401_min__ord__min) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 470 (all N all K_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))))) # label(fact_402_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 471 (all K all L_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),L_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),L_1)))))) # label(fact_403_mult__le__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 472 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),I)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),J))))) # label(fact_404_mult__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 473 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),K))))) # label(fact_405_mult__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 474 (all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M))))) # label(fact_406_le__cube) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 475 (all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M)))) # label(fact_407_le__square) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 476 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_1))) # label(fact_408_le__refl) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 477 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)))) # label(fact_409_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 478 (all M all N_1 (M = N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)))) # label(fact_410_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 479 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),K))))) # label(fact_411_le__trans) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 480 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> M = N_1))) # label(fact_412_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 481 (all M all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N_1)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1))))) # label(fact_413_add__leE) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 482 (all M all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)))) # label(fact_414_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 483 (all M all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)))) # label(fact_415_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 484 (all K all L_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),L_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1)))))) # label(fact_416_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 485 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))))) # label(fact_417_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 486 (all M all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J))))) # label(fact_418_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 487 (all M all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M))))) # label(fact_419_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 488 (all K_1 all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))) # label(fact_420_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 489 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) <-> (exists K_3 N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_3)))) # label(fact_421_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 490 (all N_1 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M)))) # label(fact_422_le__add1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 491 (all N_1 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)))) # label(fact_423_le__add2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 492 (all M all I all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),I)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),I)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),M),N_1)),I)) # label(fact_424_min__diff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 493 (all K all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))) # label(fact_425_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 494 (all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)),N_1) = M) # label(fact_426_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 495 (all N_1 all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M)),N_1) = M) # label(fact_427_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 496 (all I all J all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))) # label(fact_428_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 497 (all I all J all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),K)),J)) # label(fact_429_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 498 (all M all N_1 all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))) # label(fact_430_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 499 (all K all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)) # label(fact_431_diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 500 (all M all K all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)) # label(fact_432_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 501 (all M all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),M))) # label(fact_433_diff__le__self) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 502 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),J))) # label(fact_434_diff__diff__right) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 503 (all J_1 all K_1 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_1)),I_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1))))) # label(fact_435_le__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 504 (all M all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M)),K))))) # label(fact_436_le__add__diff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 505 (all L_1 all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M))))) # label(fact_437_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 506 (all L_1 all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),L_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),L_1))))) # label(fact_438_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 507 (all I all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),I)) = I)) # label(fact_439_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 508 (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)) = M)) # label(fact_440_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 509 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),K))) # label(fact_441_add__diff__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 510 (all I_1 all K_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_1))))) # label(fact_442_le__diff__conv2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 511 (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),N_1) = M)) # label(fact_443_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 512 (all K_1 all I_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1) = K_1 <-> J_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),I_1)))) # label(fact_444_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 513 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)))) # label(fact_445_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 514 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)),I) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I)),K))) # label(fact_446_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 515 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)),I))) # label(fact_447_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 516 (all N all K_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K_1) <-> M_1 = N)))) # label(fact_448_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 517 (all N_1 all K all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)))) # label(fact_449_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 518 (all U all M_1 all N all I_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),N) <-> M_1 = 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),minus_minus(nat),J_1),I_1)),U)),N)))) # label(fact_450_nat__eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 519 (all U_1 all M all N_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),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),minus_minus(nat),J),I)),U_1)),N_1)))) # label(fact_451_nat__diff__add__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 520 (all U all M_1 all N all I_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),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),minus_minus(nat),J_1),I_1)),U)),N)))))) # label(fact_452_nat__le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 521 (all U all M_1 all N all J_1 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),I_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),N) <-> 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),minus_minus(nat),I_1),J_1)),U)),M_1) = N))) # label(fact_453_nat__eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 522 (all U_1 all M all N_1 all J all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),I)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),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),minus_minus(nat),I),J)),U_1)),M)),N_1))) # label(fact_454_nat__diff__add__eq1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 523 (all M all N_1 all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))) # label(fact_455_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 524 (all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),M)) # label(fact_456_nat__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 525 (all M_1 all K_1 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_1) <-> M_1 = N)) # label(fact_457_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 526 (all K_1 all M_1 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N) <-> M_1 = N)) # label(fact_458_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 527 (all M all N_1 all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K))) # label(fact_459_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 528 (all X all Y all Z hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Z))) # label(fact_460_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 529 (all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M)) # label(fact_461_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 530 (all K all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))) # label(fact_462_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 531 (all M all N_1 all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))) # label(fact_463_add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 532 (all I all U_1 all J all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),K)) = 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),I),J)),U_1)),K)) # label(fact_464_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 533 (all U all M_1 all N all J_1 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),I_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M_1)),N))))) # label(fact_465_nat__le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 534 (all Z all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))))) # label(fact_466_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 535 (all Y all X all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Z)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))))) # label(fact_467_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 536 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (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_3),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_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3) = ti(X_b,X_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_3),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_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),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_3),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_1),bot_bot(fun(X_b,bool)))))))))))) # label(fact_468_min__max_OInf__fin_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 537 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (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_3),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_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),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_1),A_3)) = ti(X_b,X_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_3),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_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),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_3),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_1),bot_bot(fun(X_b,bool))))))))))) # label(fact_469_min__max_OInf__fin_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 538 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)))))) # label(fact_470_min__max_OInf__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 539 (all X_b (linorder(X_b) -> (all X_1 hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),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_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1)))) # label(fact_471_min__max_OInf__fin_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 540 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3))))) # label(fact_472_min__max_OInf__fin_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 541 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3))))))) # label(fact_473_min__max_OInf__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 542 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)))))))) # label(fact_474_min__max_OInf__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 543 (all X_b (linorder(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),B_2) != bot_bot(fun(X_b,bool)) -> (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_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),B_2)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3))))))) # label(fact_475_min__max_OInf__fin_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 544 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),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_1),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),X_1),A_3)))))) # label(fact_476_min__max_OInf__fin_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 545 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),A_2),A_3))))) # label(fact_477_min__max_OInf__fin_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 546 (all X_b (linorder(X_b) -> (all N_3 all H ((all X_2 all Y_1 hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_2),Y_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (ti(fun(X_b,bool),N_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),N_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_3)))))))) # label(fact_478_min__max_OInf__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 547 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_2),Y_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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)),A_3)))))))) # label(fact_479_min__max_OInf__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 548 (all X_b (linord219039673up_add(X_b) -> (all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (ti(fun(X_b,bool),S_1) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,uminus_uminus(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),S_1)) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),uminus_uminus(X_b)),S_1))))))) # label(fact_480_minus__Max__eq__Min) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.59 549 (all X_b (linord219039673up_add(X_b) -> (all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (ti(fun(X_b,bool),S_1) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,uminus_uminus(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),S_1)) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),uminus_uminus(X_b)),S_1))))))) # label(fact_481_minus__Min__eq__Max) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 550 (all X_b all X_c (uminus(X_c) -> (all A_3 all X_2 hAPP(X_b,X_c,hAPP(fun(X_b,X_c),fun(X_b,X_c),uminus_uminus(fun(X_b,X_c)),A_3),X_2) = hAPP(X_c,X_c,uminus_uminus(X_c),hAPP(X_b,X_c,A_3,X_2))))) # label(fact_482_fun__Compl__def) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 551 (all X_a (boolean_algebra(X_a) -> (all X hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = ti(X_a,X)))) # label(fact_483_double__compl) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 552 (all X_c all X_b (uminus(X_b) -> (all A_3 all X_1 hAPP(X_c,X_b,hAPP(fun(X_c,X_b),fun(X_c,X_b),uminus_uminus(fun(X_c,X_b)),A_3),X_1) = hAPP(X_b,X_b,uminus_uminus(X_b),hAPP(X_c,X_b,A_3,X_1))))) # label(fact_484_uminus__apply) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 553 (all X_b (boolean_algebra(X_b) -> (all X_1 all Y_2 (hAPP(X_b,X_b,uminus_uminus(X_b),X_1) = hAPP(X_b,X_b,uminus_uminus(X_b),Y_2) <-> ti(X_b,X_1) = ti(X_b,Y_2))))) # label(fact_485_compl__eq__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 554 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)) = ti(X_a,A_1)))) # label(fact_486_minus__minus) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 555 (all X_b (group_add(X_b) -> (all A_2 all Ba (ti(X_b,A_2) = hAPP(X_b,X_b,uminus_uminus(X_b),Ba) <-> ti(X_b,Ba) = hAPP(X_b,X_b,uminus_uminus(X_b),A_2))))) # label(fact_487_equation__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 556 (all X_b (group_add(X_b) -> (all A_2 all Ba (hAPP(X_b,X_b,uminus_uminus(X_b),A_2) = ti(X_b,Ba) <-> hAPP(X_b,X_b,uminus_uminus(X_b),Ba) = ti(X_b,A_2))))) # label(fact_488_minus__equation__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 557 (all X_b (group_add(X_b) -> (all A_2 all Ba (hAPP(X_b,X_b,uminus_uminus(X_b),A_2) = hAPP(X_b,X_b,uminus_uminus(X_b),Ba) <-> ti(X_b,A_2) = ti(X_b,Ba))))) # label(fact_489_neg__equal__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 558 (all X_b all A_3 all B_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)),A_3),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3))))) # label(fact_490_Compl__anti__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 559 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3)),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),B_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_2),A_3)))) # label(fact_491_Compl__subset__Compl__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 560 (all X_a (ab_group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),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),B),A_1)))) # label(fact_492_minus__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 561 (all X_a (ordered_ab_group_add(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B)),hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))))) # label(fact_493_le__imp__neg__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 562 (all X_b (ordered_ab_group_add(X_b) -> (all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),Ba)),hAPP(X_b,X_b,uminus_uminus(X_b),A_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)))))) # label(fact_494_neg__le__iff__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 563 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),A_2)),Ba)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),Ba)),A_2)))))) # label(fact_495_minus__le__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 564 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),hAPP(X_b,X_b,uminus_uminus(X_b),Ba))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),hAPP(X_b,X_b,uminus_uminus(X_b),A_2))))))) # label(fact_496_le__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 565 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y)))))) # label(fact_497_compl__le__swap2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 566 (all X_a (boolean_algebra(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,uminus_uminus(X_a),X))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))))) # label(fact_498_compl__le__swap1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 567 (all X_a (boolean_algebra(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),hAPP(X_a,X_a,uminus_uminus(X_a),Y)),hAPP(X_a,X_a,uminus_uminus(X_a),X))))))) # label(fact_499_compl__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 568 (all X_b (boolean_algebra(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),X_1)),hAPP(X_b,X_b,uminus_uminus(X_b),Y_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)))))) # label(fact_500_compl__le__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 569 (all X_a (ab_group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_501_minus__add__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 570 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B)),hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))) # label(fact_502_minus__add) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 571 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)) = ti(X_a,B)))) # label(fact_503_add__minus__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 572 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)) = ti(X_a,B)))) # label(fact_504_minus__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 573 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_505_minus__mult__right) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 574 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)))) # label(fact_506_minus__mult__left) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 575 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_507_minus__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 576 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))) # label(fact_508_minus__mult__minus) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 577 (all X_b (idom(X_b) -> (all A_2 all Ba (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),A_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),Ba) <-> ti(X_b,A_2) = ti(X_b,Ba) | ti(X_b,A_2) = hAPP(X_b,X_b,uminus_uminus(X_b),Ba))))) # label(fact_509_square__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 578 (all X_c all X_b (ab_group_add(X_b) -> (all F all A_3 hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_b,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),combb(X_b,X_b,X_c),uminus_uminus(X_b)),F)),A_3) = hAPP(X_b,X_b,uminus_uminus(X_b),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),F),A_3))))) # label(fact_510_setsum__negf) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 579 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))) # label(fact_511_diff__minus__eq__add) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 580 (all X_a (comm_ring_1(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))) # label(fact_512_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 581 (all X_a (ab_group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_513_ab__diff__minus) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 582 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_514_diff__def) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 583 (all X_b all A_3 (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)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3))) <-> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)))) # label(fact_515_subset__Compl__self__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 584 (all X_b (ordered_ab_group_add(X_b) -> (all X_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),uminus_uminus(X_b)),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),X_1)) = hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),X_1))))) # label(fact_516_image__uminus__lessThan) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 585 (all X_b (ordered_ab_group_add(X_b) -> (all X_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),uminus_uminus(X_b)),hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),X_1)) = hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),X_1))))) # label(fact_517_image__uminus__greaterThan) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 586 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (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_3),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_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3) = ti(X_b,X_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_3),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_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),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_3),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_1),bot_bot(fun(X_b,bool)))))))))))) # label(fact_518_Max_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 587 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (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_3),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_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),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_1),A_3)) = ti(X_b,X_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_3),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_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),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_3),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_1),bot_bot(fun(X_b,bool))))))))))) # label(fact_519_Max_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 588 (all X_b all Ca all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3))))) # label(fact_520_ComplI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 589 (all X_b all Pa hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) # label(fact_521_Collect__neg__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 590 (all X_b all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3)))) # label(fact_522_Compl__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 591 (all X_b all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3)) = ti(fun(X_b,bool),A_3)) # label(fact_523_double__complement) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 592 (all X_b all Ca all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3))) <-> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)))) # label(fact_524_Compl__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 593 (all X_b all A_3 all B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),B_2) <-> ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2))) # label(fact_525_Compl__eq__Compl__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 594 (all X_b all Ca all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3))) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)))) # label(fact_526_ComplD) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 595 (all X_b all Ca all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3))) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)))) # label(fact_527_ComplE) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 596 (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_528_min__max_Oinf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 597 (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_529_min__max_Osup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 598 (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_530_min__max_Oinf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 599 (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_531_min__max_Osup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 600 (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_532_min__max_Oinf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 601 (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_533_min__max_Osup__inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 602 (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_534_max__add__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 603 (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_535_max__diff__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 604 (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_536_Max_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 605 (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_537_min__max_Osup__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 606 (all X_a (linorder(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),C))))) # label(fact_538_min__max_Osup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 607 (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_539_min__max_Osup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 608 (all X_a (linorder(X_a) -> (all B all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),C))))) # label(fact_540_min__max_Osup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 609 (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_541_min__max_Osup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 610 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)))) # label(fact_542_min__max_Osup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 611 (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_543_min__max_Osup__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 612 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),A_1)))) # label(fact_544_min__max_Osup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 613 (all X_a (linorder(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),A_1) = ti(X_a,A_1)))) # label(fact_545_min__max_Osup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 614 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),X_1) = hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),Y_2) <-> ti(X_b,X_1) = ti(X_b,Y_2))))) # label(fact_546_greaterThan__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 615 (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_547_le__maxI1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 616 (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_548_le__maxI2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 617 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),Y_2) = ti(X_b,Y_2))))) # label(fact_549_min__max_Ole__iff__sup) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 618 (all X_b (linorder(X_b) -> (all X_1 all Y_2 all Z_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),Y_2)),Z_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Z_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),Z_2)))))) # label(fact_550_min__max_Ole__sup__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 619 (all X_a (linorder(X_a) -> (all B all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_551_min__max_Ole__supI1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 620 (all X_a (linorder(X_a) -> (all A_1 all X all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_552_min__max_Ole__supI2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 621 (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_553_min__max_Osup__absorb2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 622 (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_554_min__max_Osup__absorb1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 623 (all X_a (linorder(X_a) -> (all B all A_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),X))))))) # label(fact_555_min__max_Ole__supI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 624 (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_556_min__max_Osup__least) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 625 (all X_a (linorder(X_a) -> (all B all D_1 all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),C),D_1)))))))) # label(fact_557_min__max_Osup__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 626 (all X_a (linorder(X_a) -> (all A_1 all B all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),X)) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X))))))) # label(fact_558_min__max_Ole__supE) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 627 (all X_b (linorder(X_b) -> (all Z_2 all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Z_2),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),Y_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Z_2),X_1)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Z_2),Y_2)))))) # label(fact_559_le__max__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 628 (all X_b (linorder(X_b) -> hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),ord_max(X_b))))) # label(fact_560_min__max_Ocomp__fun__idem__sup) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 629 (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_561_min__max_Odistrib__inf__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 630 (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_562_min__max_Odistrib__sup__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 631 (all X_a (linord219039673up_add(X_a) -> (all X all Y hAPP(X_a,X_a,uminus_uminus(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_max(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))) # label(fact_563_minus__min__eq__max) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 632 (all X_a (linord219039673up_add(X_a) -> (all X all Y hAPP(X_a,X_a,uminus_uminus(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_min(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))) # label(fact_564_minus__max__eq__min) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 633 (all N_1 all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M)),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N_1),M)) # label(fact_565_nat__minus__add__max) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 634 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)))))) # label(fact_566_Max_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 635 (all X_b (linorder(X_b) -> (all Ba all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),A_2),Ba)),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),Ba),A_3)))))))) # label(fact_567_min__max_Osup__le__fold__sup) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 636 (all X_b (ord(X_b) -> ord_max(X_b) = hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,X_b)),max(X_b),ord_less_eq(X_b)))) # label(fact_568_max__ord__max) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 637 (all X_b (linorder(X_b) -> (all Ba all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),Ba),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),A_2),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),Ba),A_3)))))) # label(fact_569_min__max_Ofold__sup__insert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 638 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),A_2),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)) = ti(X_b,A_2)))))) # label(fact_570_min__max_Osup__Inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 639 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),X_1)),hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),Y_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)))))) # label(fact_571_greaterThan__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 640 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_max(X_b)),A_3))))) # label(fact_572_Max_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 641 (all X_b (linorder(X_b) -> hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,X_b)),min(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),ord_less_eq(X_b))) = ord_max(X_b))) # label(fact_573_dual__min) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 642 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3))))))) # label(fact_574_Max__insert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 643 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)))))))) # label(fact_575_Max_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 644 (all X_b (linorder(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),B_2) != bot_bot(fun(X_b,bool)) -> (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_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),B_2)),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3))))))) # label(fact_576_Max_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 645 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),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_1),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),X_1),A_3)))))) # label(fact_577_Max_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 646 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),A_2),A_3))))) # label(fact_578_Max_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 647 (all X_b (linorder(X_b) -> (all N_3 all H ((all X_2 all Y_1 hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_2),Y_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (ti(fun(X_b,bool),N_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),N_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_3)))))))) # label(fact_579_Max_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 648 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_2),Y_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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)),A_3)))))))) # label(fact_580_Max_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 649 (all X_b (linorder(X_b) -> (all Ca all Ba all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Ba)))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),Ca),A_3)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),Ba),Ca)))))))) # label(fact_581_min__max_Ofold__sup__le__sup) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 650 (all X_a (linorder(X_a) -> (all X all Y all Z ((all X_2 all Y_1 all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y_1),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),Z_1))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z)) = 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_582_min__max_Odistrib__imp1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 651 (all X_a (linorder(X_a) -> (all X all Y all Z ((all X_2 all Y_1 all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y_1),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),Z_1))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)) = 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_583_min__max_Odistrib__imp2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 652 (all X_a (ord(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Least),X) = ti(X_a,X))))) # label(fact_584_max__leastL) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 653 (all X_a (order(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Least) = ti(X_a,X))))) # label(fact_585_max__leastR) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 654 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)))))))) # label(fact_586_min__max_OInf__le__Sup) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 655 (all X_b (linorder(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (ti(fun(X_b,bool),B_2) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),B_2)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b)),hAPP(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,bool)),hAPP(fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),fun(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,bool))),combb(fun(X_b,fun(X_b,bool)),fun(X_b,bool),X_b),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b))),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(X_b,bool)))),combc(X_b,fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),fun(X_b,fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)))),hAPP(fun(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),fun(X_b,fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool))))),combb(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool))),X_b),combs(X_b,fun(X_b,bool),fun(X_b,bool))),hAPP(fun(X_b,fun(X_b,fun(X_b,fun(bool,bool)))),fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),hAPP(fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),fun(fun(X_b,fun(X_b,fun(X_b,fun(bool,bool)))),fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))))),combb(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),X_b),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combs(X_b,bool,bool))),hAPP(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,fun(X_b,fun(bool,bool)))),hAPP(fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),fun(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,fun(X_b,fun(bool,bool))))),combb(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool))),X_b),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj))),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,fun(X_b,bool)))),combc(X_b,fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool)))),hAPP(fun(fun(fun(X_b,X_b),fun(X_b,bool)),fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool))))),combb(fun(fun(X_b,X_b),fun(X_b,bool)),fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool))),X_b),combb(fun(X_b,X_b),fun(X_b,bool),X_b)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool)),X_b),combb(X_b,bool,X_b)),fequal(X_b)))),ord_max(X_b)))))),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(bool,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(bool,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combb(bool,bool,X_b)),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2)))))))))))))) # label(fact_587_min__max_Osup__Inf2__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 656 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combs(X_b,bool,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool))),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj)),hAPP(fun(X_b,X_b),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,X_b),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,X_b),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool)),X_b),combb(X_b,bool,X_b)),fequal(X_b))),hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1))))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3)))))))))) # label(fact_588_min__max_Osup__Inf1__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 657 (all X_c all X_b all Q_3 all Pa (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),hAPP(fun(X_c,bool),fun(X_c,bool),collect(X_c),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_c,fun(X_b,bool)),fun(X_c,bool)),combb(fun(X_b,bool),bool,X_c),fEx(X_b)),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_c),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),Pa))),Q_3))))) <-> (all Y_1 (hBOOL(hAPP(X_b,bool,Pa,Y_1)) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),hAPP(fun(X_c,bool),fun(X_c,bool),collect(X_c),hAPP(X_b,fun(X_c,bool),hAPP(fun(X_c,fun(X_b,bool)),fun(X_b,fun(X_c,bool)),combc(X_c,X_b,bool),Q_3),Y_1))))))))) # label(fact_589_finite__Collect__bounded__ex) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 658 (all X_c all X_b all F all Pa (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),hAPP(fun(X_c,bool),fun(X_c,bool),collect(X_c),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_c,fun(X_b,bool)),fun(X_c,bool)),combb(fun(X_b,bool),bool,X_c),fEx(X_b)),hAPP(fun(X_b,bool),fun(X_c,fun(X_b,bool)),hAPP(fun(X_c,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_c,fun(X_b,bool))),combc(X_c,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_c,fun(X_b,fun(bool,bool))),fun(X_c,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_c,fun(X_b,fun(bool,bool))),fun(X_c,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_c),combs(X_b,bool,bool)),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,fun(bool,bool))),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_c),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj)),hAPP(fun(X_b,X_c),fun(X_c,fun(X_b,bool)),hAPP(fun(X_c,fun(fun(X_b,X_c),fun(X_b,bool))),fun(fun(X_b,X_c),fun(X_c,fun(X_b,bool))),combc(X_c,fun(X_b,X_c),fun(X_b,bool)),hAPP(fun(X_c,fun(X_c,bool)),fun(X_c,fun(fun(X_b,X_c),fun(X_b,bool))),hAPP(fun(fun(X_c,bool),fun(fun(X_b,X_c),fun(X_b,bool))),fun(fun(X_c,fun(X_c,bool)),fun(X_c,fun(fun(X_b,X_c),fun(X_b,bool)))),combb(fun(X_c,bool),fun(fun(X_b,X_c),fun(X_b,bool)),X_c),combb(X_c,bool,X_b)),fequal(X_c))),F)))),Pa))))))) # label(fact_590_finite__image__set) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.60 659 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combs(X_b,bool,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool))),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj)),hAPP(fun(X_b,X_b),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,X_b),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,X_b),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool)),X_b),combb(X_b,bool,X_b)),fequal(X_b))),hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1))))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3)))))))))) # label(fact_591_min__max_Oinf__Sup1__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 660 (all X_b (linorder(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (ti(fun(X_b,bool),B_2) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),B_2)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b)),hAPP(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,bool)),hAPP(fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),fun(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,bool))),combb(fun(X_b,fun(X_b,bool)),fun(X_b,bool),X_b),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b))),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(X_b,bool)))),combc(X_b,fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),fun(X_b,fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)))),hAPP(fun(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),fun(X_b,fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool))))),combb(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool))),X_b),combs(X_b,fun(X_b,bool),fun(X_b,bool))),hAPP(fun(X_b,fun(X_b,fun(X_b,fun(bool,bool)))),fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),hAPP(fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),fun(fun(X_b,fun(X_b,fun(X_b,fun(bool,bool)))),fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))))),combb(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),X_b),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combs(X_b,bool,bool))),hAPP(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,fun(X_b,fun(bool,bool)))),hAPP(fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),fun(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,fun(X_b,fun(bool,bool))))),combb(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool))),X_b),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj))),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,fun(X_b,bool)))),combc(X_b,fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool)))),hAPP(fun(fun(fun(X_b,X_b),fun(X_b,bool)),fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool))))),combb(fun(fun(X_b,X_b),fun(X_b,bool)),fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool))),X_b),combb(fun(X_b,X_b),fun(X_b,bool),X_b)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool)),X_b),combb(X_b,bool,X_b)),fequal(X_b)))),ord_min(X_b)))))),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(bool,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(bool,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combb(bool,bool,X_b)),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2)))))))))))))) # label(fact_592_min__max_Oinf__Sup2__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 661 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)))))) # label(fact_593_min__max_OSup__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 662 (all X_b (linorder(X_b) -> (all X_1 hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),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_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1)))) # label(fact_594_min__max_OSup__fin_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 663 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),A_2),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)) = ti(X_b,A_2)))))) # label(fact_595_min__max_Oinf__Sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 664 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_max(X_b)),A_3))))) # label(fact_596_min__max_OSup__fin_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 665 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)))))))) # label(fact_597_min__max_OSup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 666 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3))))))) # label(fact_598_min__max_OSup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 667 (all X_b (linorder(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),B_2) != bot_bot(fun(X_b,bool)) -> (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_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),B_2)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3))))))) # label(fact_599_min__max_OSup__fin_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 668 (all X_b (linord2061991079up_add(X_b) -> (all K_1 all N_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (ti(fun(X_b,bool),N_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),K_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),N_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combs(X_b,bool,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool))),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj)),hAPP(fun(X_b,X_b),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,X_b),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,X_b),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool)),X_b),combb(X_b,bool,X_b)),fequal(X_b))),hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),K_1))))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),N_3)))))))))) # label(fact_600_add__Max__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 669 (all X_b (linord2061991079up_add(X_b) -> (all K_1 all N_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (ti(fun(X_b,bool),N_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),K_1),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),N_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combs(X_b,bool,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool))),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj)),hAPP(fun(X_b,X_b),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,X_b),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,X_b),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool)),X_b),combb(X_b,bool,X_b)),fequal(X_b))),hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),K_1))))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),N_3)))))))))) # label(fact_601_add__Min__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 670 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),A_2),A_3))))) # label(fact_602_min__max_OSup__fin_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 671 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),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_1),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),X_1),A_3)))))) # label(fact_603_min__max_OSup__fin_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 672 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (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_3),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_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3) = ti(X_b,X_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_3),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_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),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_3),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_1),bot_bot(fun(X_b,bool)))))))))))) # label(fact_604_min__max_OSup__fin_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 673 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (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_3),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_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),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_1),A_3)) = ti(X_b,X_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_3),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_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),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_3),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_1),bot_bot(fun(X_b,bool))))))))))) # label(fact_605_min__max_OSup__fin_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 674 (all X_b (linorder(X_b) -> (all N_3 all H ((all X_2 all Y_1 hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_2),Y_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (ti(fun(X_b,bool),N_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),N_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_3)))))))) # label(fact_606_min__max_OSup__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 675 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_2),Y_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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)),A_3)))))))) # label(fact_607_min__max_OSup__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 676 (all X_b all Pa ((exists X1 hBOOL(hAPP(X_b,bool,Pa,X1))) <-> (all Q_2 ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> hBOOL(Q_2))) -> hBOOL(Q_2))))) # label(fact_608_Ex__def) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 677 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),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_3),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_1),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))) # label(fact_609_card__Diff1__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 678 (all X_c all X_b (order(X_b) & ord(X_c) -> (all Ca all F all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,Ba)),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Ca),Ba)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Y_1),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,Y_1)),hAPP(X_c,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,Ca)),A_2)))))))) # label(fact_610_xt2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 679 (all X_b (order(X_b) -> (all Ca all A_2 all F all Ba (ti(X_b,A_2) = hAPP(X_b,X_b,F,Ba) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),Ba)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,F,Y_1)),hAPP(X_b,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,F,Ca)),A_2)))))))) # label(fact_611_xt1_I15_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 680 (all U hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),ord_lessThan(nat),U)) = U) # label(fact_612_card__lessThan) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 681 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),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_1),A_3)))))) # label(fact_613_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 682 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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)),A_3),B_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))) -> ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2))))) # label(fact_614_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 683 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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)),A_3),B_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)))))) # label(fact_615_card__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 684 (all X_c all X_b all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_c,bool),nat,finite_card(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))) # label(fact_616_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 685 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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_2),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),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_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2))))) # label(fact_617_card__Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 686 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2))),hAPP(fun(X_b,bool),nat,finite_card(X_b),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_3),B_2)))))) # label(fact_618_diff__card__le__card__Diff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 687 (all X_c all X_b all R_1 all K_1 all T_4 all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),T_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),T_4)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S_1))),hAPP(X_c,fun(X_b,bool),hAPP(fun(X_b,fun(X_c,bool)),fun(X_c,fun(X_b,bool)),combc(X_b,X_c,bool),R_1),X_2)))) = K_1)) -> hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,nat),hAPP(fun(fun(X_c,bool),nat),fun(fun(X_b,fun(X_c,bool)),fun(X_b,nat)),combb(fun(X_c,bool),nat,X_b),finite_card(X_c)),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool)),hAPP(fun(fun(X_c,bool),fun(X_c,bool)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool))),combb(fun(X_c,bool),fun(X_c,bool),X_b),collect(X_c)),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool)),hAPP(fun(fun(X_c,bool),fun(X_c,bool)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool))),combb(fun(X_c,bool),fun(X_c,bool),X_b),hAPP(fun(X_c,fun(bool,bool)),fun(fun(X_c,bool),fun(X_c,bool)),combs(X_c,bool,bool),hAPP(fun(X_c,bool),fun(X_c,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_c,bool),fun(X_c,fun(bool,bool))),combb(bool,fun(bool,bool),X_c),fconj),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,fun(fun(X_c,bool),bool)),fun(fun(X_c,bool),fun(X_c,bool)),combc(X_c,fun(X_c,bool),bool),member(X_c)),T_4)))),R_1)))),S_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),hAPP(fun(X_c,bool),nat,finite_card(X_c),T_4)))))) # label(fact_619_setsum__multicount) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 688 (all X_c all X_b all R_1 all K_1 all T_5 all S_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),T_5)) -> ((all X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),T_5)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S_2))),hAPP(X_c,fun(X_b,bool),hAPP(fun(X_b,fun(X_c,bool)),fun(X_c,fun(X_b,bool)),combc(X_b,X_c,bool),R_1),X_2)))) = hAPP(X_c,nat,K_1,X_2))) -> hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,nat),hAPP(fun(fun(X_c,bool),nat),fun(fun(X_b,fun(X_c,bool)),fun(X_b,nat)),combb(fun(X_c,bool),nat,X_b),finite_card(X_c)),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool)),hAPP(fun(fun(X_c,bool),fun(X_c,bool)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool))),combb(fun(X_c,bool),fun(X_c,bool),X_b),collect(X_c)),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool)),hAPP(fun(fun(X_c,bool),fun(X_c,bool)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool))),combb(fun(X_c,bool),fun(X_c,bool),X_b),hAPP(fun(X_c,fun(bool,bool)),fun(fun(X_c,bool),fun(X_c,bool)),combs(X_c,bool,bool),hAPP(fun(X_c,bool),fun(X_c,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_c,bool),fun(X_c,fun(bool,bool))),combb(bool,fun(bool,bool),X_c),fconj),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,fun(fun(X_c,bool),bool)),fun(fun(X_c,bool),fun(X_c,bool)),combc(X_c,fun(X_c,bool),bool),member(X_c)),T_5)))),R_1)))),S_2) = hAPP(fun(X_c,bool),nat,hAPP(fun(X_c,nat),fun(fun(X_c,bool),nat),big_co1399186613setsum(X_c,nat),K_1),T_5))))) # label(fact_620_setsum__multicount__gen) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 689 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),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_3),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_1),bot_bot(fun(X_b,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),one_one(nat))))) # label(fact_621_card__Diff__singleton) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 690 (all X_c all X_b (comm_monoid_mult(X_b) -> (all A_3 hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),hAPP(X_b,fun(X_c,X_b),combk(X_b,X_c),one_one(X_b))),A_3) = one_one(X_b)))) # label(fact_622_setprod__1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 691 (all M_1 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N) = one_one(nat) <-> M_1 = one_one(nat) & N = one_one(nat))) # label(fact_623_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 692 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),one_one(nat)) = N_1) # label(fact_624_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 693 (all M_1 all N (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N) <-> M_1 = one_one(nat) & N = one_one(nat))) # label(fact_625_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 694 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N_1) = N_1) # label(fact_626_nat__mult__1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 695 (all X_a (comm_monoid_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)))) # label(fact_627_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 696 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)))) # label(fact_628_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 697 (all X_a (monoid_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)))) # label(fact_629_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 698 (all X_a (comm_monoid_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_630_mult__1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 699 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_631_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 700 (all X_a (monoid_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_632_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 701 (all X_b all F all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> (hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co302546470etprod(X_b,nat),F),F_2) = one_one(nat) <-> (all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_2)) -> hAPP(X_b,nat,F,X_2) = one_one(nat)))))) # label(fact_633_setprod__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 702 (all X_b (one(X_b) -> (all X_1 (one_one(X_b) = ti(X_b,X_1) <-> ti(X_b,X_1) = one_one(X_b))))) # label(fact_634_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 703 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M 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),M)),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_1),one_one(X_a))),M)))) # label(fact_635_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 704 (all X_a (comm_semiring_1(X_a) -> (all M all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),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_1),one_one(X_a))),M)))) # label(fact_636_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 705 (all X_a (comm_semiring_1(X_a) -> (all M hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),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),one_one(X_a)),one_one(X_a))),M)))) # label(fact_637_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 706 (all X_b (ring_11004092258visors(X_b) -> (all X_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1) = one_one(X_b) <-> ti(X_b,X_1) = one_one(X_b) | ti(X_b,X_1) = hAPP(X_b,X_b,uminus_uminus(X_b),one_one(X_b)))))) # label(fact_638_square__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 707 (all X_a (comm_ring_1(X_a) -> (all X hAPP(X_a,X_a,uminus_uminus(X_a),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),X)))) # label(fact_639_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 708 (all X_c all X_b (comm_monoid_mult(X_b) -> (all G hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),G),bot_bot(fun(X_c,bool))) = one_one(X_b)))) # label(fact_640_setprod_Oempty) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 709 (all X_c all X_b (comm_monoid_mult(X_b) -> (all F hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),F),bot_bot(fun(X_c,bool))) = one_one(X_b)))) # label(fact_641_setprod__empty) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 710 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),A_3) = one_one(X_c))))) # label(fact_642_setprod__infinite) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 711 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),A_3) = one_one(X_c))))) # label(fact_643_setprod_Oinfinite) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 712 (all X_b all X_c (comm_monoid_mult(X_c) -> (all Ba all A_2 all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),S_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(X_b,X_c)),combc(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_b,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combs(X_b,X_c,fun(X_c,X_c)),hAPP(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c))),hAPP(fun(bool,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c)))),combb(bool,fun(X_c,fun(X_c,X_c)),X_b),if(X_c)),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Ba)),one_one(X_c))),S_1) = hAPP(X_b,X_c,Ba,A_2)) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),S_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(X_b,X_c)),combc(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_b,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combs(X_b,X_c,fun(X_c,X_c)),hAPP(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c))),hAPP(fun(bool,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c)))),combb(bool,fun(X_c,fun(X_c,X_c)),X_b),if(X_c)),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Ba)),one_one(X_c))),S_1) = one_one(X_c)))))) # label(fact_644_setprod__delta_H) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 713 (all X_b all X_c (comm_monoid_mult(X_c) -> (all Ba all A_2 all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),S_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(X_b,X_c)),combc(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_b,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combs(X_b,X_c,fun(X_c,X_c)),hAPP(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c))),hAPP(fun(bool,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c)))),combb(bool,fun(X_c,fun(X_c,X_c)),X_b),if(X_c)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Ba)),one_one(X_c))),S_1) = hAPP(X_b,X_c,Ba,A_2)) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),S_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(X_b,X_c)),combc(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_b,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combs(X_b,X_c,fun(X_c,X_c)),hAPP(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c))),hAPP(fun(bool,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c)))),combb(bool,fun(X_c,fun(X_c,X_c)),X_b),if(X_c)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Ba)),one_one(X_c))),S_1) = one_one(X_c)))))) # label(fact_645_setprod__delta) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 714 (all X_b all A_3 hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),hAPP(nat,fun(X_b,nat),combk(nat,X_b),one_one(nat))),A_3)) # label(fact_646_card__eq__setsum) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 715 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),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_1),A_3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))) # label(fact_647_card_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 716 (all X_b all B_2 all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),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_3),B_2))),one_one(nat)))))) # label(fact_648_card__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 717 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),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_1),A_3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),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_3),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_1),bot_bot(fun(X_b,bool)))))))) # label(fact_649_card_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 718 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),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_3),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_1),bot_bot(fun(X_b,bool))))))))) # label(fact_650_card_Oremove) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 719 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),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_3),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_1),bot_bot(fun(X_b,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),one_one(nat))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),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_3),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_1),bot_bot(fun(X_b,bool))))) = hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))) # label(fact_651_card__Diff__singleton__if) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 720 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all S_1 all T_4 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),T_4)) -> (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)),S_1),T_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(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)),T_4),S_1))) -> hAPP(X_b,X_c,F,X_2) = one_one(X_c))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),T_4) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),S_1))))))) # label(fact_652_setprod__mono__one__right) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 721 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all S_1 all T_4 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),T_4)) -> (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)),S_1),T_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(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)),T_4),S_1))) -> hAPP(X_b,X_c,F,X_2) = one_one(X_c))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),S_1) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),T_4))))))) # label(fact_653_setprod__mono__one__left) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 722 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(X_b,X_c,G,X_2) = one_one(X_c))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),A_3) = one_one(X_c)))))) # label(fact_654_setprod_Oneutral) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 723 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all F_2 ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_2)) -> hAPP(X_b,X_c,F,X_2) = one_one(X_c))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),F_2) = one_one(X_c))))) # label(fact_655_setprod__1_H) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 724 (all X_b (comm_semiring_1(X_b) -> (all A_2 all D all N hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),one_one(X_b)),one_one(X_b))),hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(fun(X_b,X_b),fun(fun(nat,X_b),fun(nat,X_b)),combb(X_b,X_b,nat),hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2)),hAPP(X_b,fun(nat,X_b),hAPP(fun(nat,fun(X_b,X_b)),fun(X_b,fun(nat,X_b)),combc(nat,X_b,X_b),hAPP(fun(nat,X_b),fun(nat,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(nat,X_b),fun(nat,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),nat),times_times(X_b)),semiring_1_of_nat(X_b))),D))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),N)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))),D))))))) # label(fact_656_arith__series__general) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 725 (all X_c all X_b (comm_monoid_mult(X_b) -> (all H all G all S_1 all R_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,one_one(X_b)),one_one(X_b))) -> ((all X1 all Y1 all X2 all Y2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,X1),X2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,Y1),Y2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X1),Y1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X2),Y2))))) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),S_1)) -> ((all X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),S_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_c,X_b,H,X_2)),hAPP(X_c,X_b,G,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),H),S_1)),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),G),S_1)))))))))) # label(fact_657_setprod_Orelated) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 726 (all X_b (semiring_char_0(X_b) -> (all M_1 all N (hAPP(nat,X_b,semiring_1_of_nat(X_b),M_1) = hAPP(nat,X_b,semiring_1_of_nat(X_b),N) <-> M_1 = N)))) # label(fact_658_of__nat__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 727 (all X_b (linordered_semidom(X_b) -> (all M_1 all N (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),M_1)),hAPP(nat,X_b,semiring_1_of_nat(X_b),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))))) # label(fact_659_of__nat__le__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 728 (all X_a (semiring_1(X_a) -> (all M all N_1 hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))) # label(fact_660_of__nat__add) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 729 (all X_a (semiring_1(X_a) -> (all M all N_1 hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))) # label(fact_661_of__nat__mult) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 730 (all X_a (semiring_1(X_a) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),one_one(nat)) = one_one(X_a))) # label(fact_662_of__nat__1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 731 (all X_a (ring_1(X_a) -> (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)))))) # label(fact_663_of__nat__diff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 732 (all X_c all X_b (semiring_1(X_b) -> (all Y_2 all A_3 hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(X_b,fun(X_c,X_b),combk(X_b,X_c),Y_2)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),hAPP(fun(X_c,bool),nat,finite_card(X_c),A_3))),Y_2)))) # label(fact_664_setsum__constant) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 733 (all X_b all X_c (ordere779506340up_add(X_c) & semiring_1(X_c) -> (all F all K_2 all A_3 ((all I_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),I_2),A_3)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,I_2)),K_2)))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3)),hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(nat,X_c,semiring_1_of_nat(X_c),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))),K_2))))))) # label(fact_665_setsum__bounded) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 734 (all X_c all X_b (comm_monoid_mult(X_b) & semiring_1(X_b) -> (all F all A_3 hAPP(nat,X_b,semiring_1_of_nat(X_b),hAPP(fun(X_c,bool),nat,hAPP(fun(X_c,nat),fun(fun(X_c,bool),nat),big_co302546470etprod(X_c,nat),F),A_3)) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),hAPP(fun(X_c,nat),fun(X_c,X_b),hAPP(fun(nat,X_b),fun(fun(X_c,nat),fun(X_c,X_b)),combb(nat,X_b,X_c),semiring_1_of_nat(X_b)),F)),A_3)))) # label(fact_666_of__nat__setprod) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 735 (all X_c all X_b (semiring_1(X_b) -> (all F all A_3 hAPP(nat,X_b,semiring_1_of_nat(X_b),hAPP(fun(X_c,bool),nat,hAPP(fun(X_c,nat),fun(fun(X_c,bool),nat),big_co1399186613setsum(X_c,nat),F),A_3)) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_c,nat),fun(X_c,X_b),hAPP(fun(nat,X_b),fun(fun(X_c,nat),fun(X_c,X_b)),combb(nat,X_b,X_c),semiring_1_of_nat(X_b)),F)),A_3)))) # label(fact_667_of__nat__setsum) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 736 (all M all N_1 all Z hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)),Z)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))),Z)) # label(fact_668_zadd__int__left) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 737 (all M all N_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))) # label(fact_669_zadd__int) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 738 (all M_1 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))) # label(fact_670_zle__int) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 739 (all M all N_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))) # label(fact_671_zmult__int) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 740 (all M all N_1 hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1))) # label(fact_672_int__mult) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 741 (all X_b all F all A_3 hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),A_3)) = hAPP(fun(X_b,bool),int,hAPP(fun(X_b,int),fun(fun(X_b,bool),int),big_co1399186613setsum(X_b,int),hAPP(fun(X_b,nat),fun(X_b,int),hAPP(fun(nat,int),fun(fun(X_b,nat),fun(X_b,int)),combb(nat,int,X_b),semiring_1_of_nat(int)),F)),A_3)) # label(fact_674_int__setsum) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 742 (all X_b all F all A_3 hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co302546470etprod(X_b,nat),F),A_3)) = hAPP(fun(X_b,bool),int,hAPP(fun(X_b,int),fun(fun(X_b,bool),int),big_co302546470etprod(X_b,int),hAPP(fun(X_b,nat),fun(X_b,int),hAPP(fun(nat,int),fun(fun(X_b,nat),fun(X_b,int)),combb(nat,int,X_b),semiring_1_of_nat(int)),F)),A_3)) # label(fact_675_int__setprod) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 743 (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)))) # label(fact_676_zdiff__int) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 744 (all X_b (comm_semiring_1(X_b) -> (all N hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),one_one(X_b)),one_one(X_b))),hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),semiring_1_of_nat(X_b)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),N))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),N)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),N)),one_one(X_b)))))) # label(fact_677_gauss__sum) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 745 (all X_b all X_c (comm_monoid_mult(X_c) -> (all Ba all Ca all A_2 all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),S_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(X_b,X_c)),combc(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_b,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combs(X_b,X_c,fun(X_c,X_c)),hAPP(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c))),hAPP(fun(bool,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c)))),combb(bool,fun(X_c,fun(X_c,X_c)),X_b),if(X_c)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Ba)),Ca)),S_1) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,Ba,A_2)),hAPP(nat,X_c,hAPP(X_c,fun(nat,X_c),power_power(X_c),Ca),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),S_1)),one_one(nat))))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),S_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(X_b,X_c)),combc(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_b,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combs(X_b,X_c,fun(X_c,X_c)),hAPP(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c))),hAPP(fun(bool,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c)))),combb(bool,fun(X_c,fun(X_c,X_c)),X_b),if(X_c)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Ba)),Ca)),S_1) = hAPP(nat,X_c,hAPP(X_c,fun(nat,X_c),power_power(X_c),Ca),hAPP(fun(X_b,bool),nat,finite_card(X_b),S_1))))))) # label(fact_678_setprod__gen__delta) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 746 (all X_b all Y_2 all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),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)),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_3),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_1),bot_bot(fun(X_b,bool))))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))))) # label(fact_679_card__Diff2__less) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 747 (all N_1 all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N_1))),hAPP(nat,int,semiring_1_of_nat(int),M)))) # label(fact_680_negative__zle) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 748 (all L all U hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),L),U)))) # label(fact_681_finite__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 749 (all K_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),K_1))))) # label(fact_682_finite__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 750 (all W_1 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_2)) <-> (exists N_2 Z_2 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),N_2))))) # label(fact_683_zle__iff__zadd) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 751 (all M all N_1 hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N_1)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),M)),N_1)) # label(fact_684_int__power) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 752 (all M all N_1 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),M)),N_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N_1))) # label(fact_685_zpower__int) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 753 (all M_1 all N (hAPP(nat,int,semiring_1_of_nat(int),M_1) = hAPP(nat,int,semiring_1_of_nat(int),N) <-> M_1 = N)) # label(fact_686_int__int__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 754 (all Z all W_2 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),Z)),W_2) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),W_2))) # label(fact_687_zmult__zminus) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 755 (all Z all W_2 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),hAPP(int,int,uminus_uminus(int),W_2)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),W_2)) # label(fact_688_diff__int__def__symmetric) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.61 756 (all Z all W_2 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),W_2) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),hAPP(int,int,uminus_uminus(int),W_2))) # label(fact_689_diff__int__def) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 757 (all Z all W_2 hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),W_2)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),Z)),hAPP(int,int,uminus_uminus(int),W_2))) # label(fact_690_zminus__zadd__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 758 (all W_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_2),W_2))) # label(fact_691_zle__refl) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 759 (all Z all W_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),W_2)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_2),Z)))) # label(fact_692_zle__linear) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 760 (all K all I all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),J)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J),K)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),K))))) # label(fact_693_zle__trans) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 761 (all Z all W_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),W_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_2),Z)) -> Z = W_2))) # label(fact_694_zle__antisym) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 762 (all Z1 all Z2 all Z3 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),Z2)),Z3) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),Z3))) # label(fact_695_zmult__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 763 (all X all Y all Z hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),Z) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Y),Z))) # label(fact_696_zpower__zpower) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 764 (all Z all W_2 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),W_2) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_2),Z)) # label(fact_697_zmult__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 765 (all Z1 all Z2 all W_2 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z1),Z2)),W_2) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W_2))) # label(fact_698_zdiff__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 766 (all W_2 all Z1 all Z2 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z1),Z2)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_2),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_2),Z2))) # label(fact_699_zdiff__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 767 (all Z1 all Z2 all Z3 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)),Z3) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z2),Z3))) # label(fact_700_zadd__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 768 (all X all Y all Z hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y),Z)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Z))) # label(fact_701_zadd__left__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 769 (all Z all W_2 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),W_2) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_2),Z)) # label(fact_702_zadd__commute) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 770 (all X all Y all Z hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Z))) # label(fact_703_zpower__zadd__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 771 (all W_2 all Z1 all Z2 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_2),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_2),Z2))) # label(fact_704_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 772 (all Z1 all Z2 all W_2 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)),W_2) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W_2))) # label(fact_705_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 773 (all K all I all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),J)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),I)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),J))))) # label(fact_706_zadd__left__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 774 (all Z hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),one_one(int)) = Z) # label(fact_707_zmult__1__right) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 775 (all Z hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),Z) = Z) # label(fact_708_zmult__1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 776 (all X_a (comm_semiring_1(X_a) -> (all X hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),one_one(nat)) = ti(X_a,X)))) # label(fact_709_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 777 (all X_b (linorder(X_b) -> (all X_1 all Y_2 all Z_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),Y_2)),Z_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Z_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),Z_2)))))) # label(fact_710_max__less__iff__conj) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 778 (all X_b (linorder(X_b) -> (all Z_2 all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Z_2),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),Y_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Z_2),X_1)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Z_2),Y_2)))))) # label(fact_711_less__max__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 779 (all X_a (linorder(X_a) -> (all A_1 all X all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),B)) -> 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_1),B))))))) # label(fact_712_min__max_Oless__supI2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 780 (all X_a (linorder(X_a) -> (all B all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_713_min__max_Oless__supI1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 781 (all X_b all A_3 all F all N (ti(fun(X_b,bool),A_3) = hAPP(fun(nat,bool),fun(X_b,bool),hAPP(fun(nat,X_b),fun(fun(nat,bool),fun(X_b,bool)),image(nat,X_b),F),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)))) # label(fact_714_nat__seg__image__imp__finite) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 782 (all I all J all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K)))) # label(fact_715_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 783 (all M all N_1 all K all L_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),L_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))))) # label(fact_716_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 784 (all K all L_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1)))))) # label(fact_717_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 785 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))))) # label(fact_718_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 786 (all M all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J))))) # label(fact_719_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 787 (all M all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M))))) # label(fact_720_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 788 (all K_1 all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)))) # label(fact_721_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 789 (all J all I -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I)),I))) # label(fact_722_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 790 (all I all J -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),I))) # label(fact_723_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 791 (all X_a (comm_semiring_1(X_a) -> (all X all P_2 all Q_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),P_2)),Q_1) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_2),Q_1))))) # label(fact_724_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 792 (all X_a (ordere236663937imp_le(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_725_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 793 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_726_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 794 (all X_a (ordere223160158up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_727_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 795 (all X_a (ordere223160158up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))))))) # label(fact_728_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 796 (all X_a (ordere223160158up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))))) # label(fact_729_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 797 (all X_b (ordere236663937imp_le(X_b) -> (all Ca all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ca),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ca),Ba))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)))))) # label(fact_730_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 798 (all X_b (ordere236663937imp_le(X_b) -> (all A_2 all Ca all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ba),Ca))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)))))) # label(fact_731_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 799 (all X_a (comm_semiring_1(X_a) -> (all X all Y all Q_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),Q_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),Q_1))))) # label(fact_732_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 800 (all X_a (linorder(X_a) -> (all B all A_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_733_min__max_Oless__infI1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 801 (all X_a (linorder(X_a) -> (all A_1 all B all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_734_min__max_Oless__infI2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 802 (all X_b (linorder(X_b) -> (all Z_2 all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Z_2),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),Y_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Z_2),X_1)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Z_2),Y_2)))))) # label(fact_735_min__less__iff__conj) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 803 (all X_b (linorder(X_b) -> (all X_1 all Y_2 all Z_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),Y_2)),Z_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Z_2)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),Z_2)))))) # label(fact_736_min__less__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 804 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) & M_1 != N)) # label(fact_737_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 805 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) | M_1 = N)) # label(fact_738_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 806 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)))) # label(fact_739_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 807 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> (M != N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))))) # label(fact_740_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 808 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) | M = N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)))) # label(fact_741_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 809 (all N_1 all J all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),N_1)),K)))) # label(fact_742_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 810 (all L_1 all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M)))))) # label(fact_743_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 811 (all X_b (ord(X_b) -> (all I_1 all K_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),I_1),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),K_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),I_1),K_1)))))) # label(fact_744_lessThan__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 812 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)))))) # label(fact_745_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 813 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)))))) # label(fact_746_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 814 (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_747_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 815 (all X_b (order(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) & ti(X_b,X_1) != ti(X_b,Y_2))))) # label(fact_748_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 816 (all X_b (preorder(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) & -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)))))) # label(fact_749_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 817 (all X_b (order(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) | ti(X_b,X_1) = ti(X_b,Y_2))))) # label(fact_750_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 818 (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_751_leI) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 819 (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_752_not__leE) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 820 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) <-> ti(X_b,X_1) = ti(X_b,Y_2)))))) # label(fact_753_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 821 (all X_a (order(X_a) -> (all A_1 all B (ti(X_a,A_1) != ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_754_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 822 (all X_a (order(X_a) -> (all A_1 all B (ti(X_a,A_1) != ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_755_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 823 (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_756_leD) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 824 (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_757_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 825 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) -> (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) <-> ti(X_b,X_1) = ti(X_b,Y_2)))))) # label(fact_758_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 826 (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_759_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 827 (all X_a (order(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (ti(X_a,A_1) != ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_760_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 828 (all X_a (order(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (ti(X_a,A_1) != ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_761_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 829 (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_762_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 830 (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_763_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 831 (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_764_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 832 (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_765_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 833 (all X_a (bot(X_a) -> (all A_1 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),bot_bot(X_a)))))) # label(fact_766_not__less__bot) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 834 (all X_b (bot(X_b) -> (all A_2 (ti(X_b,A_2) != bot_bot(X_b) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),bot_bot(X_b)),A_2)))))) # label(fact_767_bot__less) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 835 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all Ba all Ca all D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),Ba) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ca),D) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),D))))))) # label(fact_768_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 836 (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_769_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 837 (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_770_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 838 (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_771_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 839 (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_772_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 840 (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_773_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 841 (all X_a (order(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1))))))) # label(fact_774_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 842 (all X_a (ord(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))))))) # label(fact_775_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 843 (all X_a (order(X_a) -> (all C all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1))))))) # label(fact_776_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 844 (all X_a (ord(X_a) -> (all C all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))))))) # label(fact_777_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 845 (all X_a (order(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_778_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 846 (all X_a (preorder(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)))))) # label(fact_779_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 847 (all X_b (preorder(X_b) -> (all Pa all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) -> hBOOL(Pa)))))) # label(fact_780_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 848 (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_781_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 849 (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_782_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 850 (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_783_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 851 (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_784_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 852 (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_785_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 853 (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_786_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 854 (all X_b (linorder(X_b) -> (all Y_2 all X_1 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) -> (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) <-> ti(X_b,X_1) = ti(X_b,Y_2)))))) # label(fact_787_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 855 (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_788_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 856 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) | ti(X_b,X_1) = ti(X_b,Y_2))))) # label(fact_789_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 857 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (ti(X_b,X_1) != ti(X_b,Y_2) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)))))) # label(fact_790_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 858 (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_791_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 859 (all X_b (order(X_b) -> (all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),A_2)) -> hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba) = bot_bot(fun(X_b,bool)))))) # label(fact_792_atLeastatMost__empty) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 860 (all X_b (linorder(X_b) -> (all M_1 all N (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),M_1)),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),N))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),M_1),N)))))) # label(fact_793_lessThan__strict__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 861 (all X_b (order(X_b) -> (all A_2 all Ba all Ca all D (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba)),hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),Ca),D))) <-> (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),A_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),D)) & (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),A_2)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),D)))) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),D)))))) # label(fact_794_atLeastatMost__psubset__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 862 (all Pa all M_1 all N ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N),M_1))) -> ((M_1 = N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N),M_1))) -> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N),M_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N),M_1)))))) # label(fact_795_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 863 (all S all T_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3)) -> S != T_3)) # label(fact_796_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 864 (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M)) -> M != N_1)) # label(fact_797_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 865 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))) # label(fact_798_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 866 (all X all Y (X != Y -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X))))) # label(fact_799_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 867 (all M_1 all N (M_1 != N <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_1)))) # label(fact_800_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 868 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))) # label(fact_801_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 869 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)))) # label(fact_802_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 870 (all Y all X all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))))) # label(fact_803_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 871 (all Z all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))))) # label(fact_804_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 872 (all K_1 all I_1 all J_1 hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),I_1),J_1)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),K_1))) # label(fact_805_image__add__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 873 (all N_3 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3)) <-> (exists M_2 all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),M_2)))))) # label(fact_806_finite__nat__set__iff__bounded) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 874 (all X_b (ord(X_b) -> (all I_1 all K_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),I_1),hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),K_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),K_1),I_1)))))) # label(fact_807_greaterThan__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 875 (all X_b (ordered_ab_group_add(X_b) -> (all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),Ba)),hAPP(X_b,X_b,uminus_uminus(X_b),A_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)))))) # label(fact_808_neg__less__iff__less) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 876 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),A_2)),Ba)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),Ba)),A_2)))))) # label(fact_809_minus__less__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 877 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_b,X_b,uminus_uminus(X_b),Ba))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),hAPP(X_b,X_b,uminus_uminus(X_b),A_2))))))) # label(fact_810_less__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 878 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y)))))) # label(fact_811_compl__less__swap2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 879 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),hAPP(X_a,X_a,uminus_uminus(X_a),X))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))))) # label(fact_812_compl__less__swap1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 880 (all X_b (boolean_algebra(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),X_1)),hAPP(X_b,X_b,uminus_uminus(X_b),Y_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)))))) # label(fact_813_compl__less__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 881 (all Pa all I_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),Pa)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1)))))) # label(fact_814_finite__M__bounded__by__nat) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 882 (all N hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N))) = N) # label(fact_815_card__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 883 (all X_a (comm_semiring_1(X_a) -> (all X all P_2 all Q_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),P_2)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_1)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),P_2),Q_1))))) # label(fact_816_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 884 (all X_b (linordered_semidom(X_b) -> (all M_1 all N (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),M_1)),hAPP(nat,X_b,semiring_1_of_nat(X_b),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)))))) # label(fact_817_of__nat__less__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 885 (all X_a (linordered_semidom(X_a) -> (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))))) # label(fact_818_less__imp__of__nat__less) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 886 (all X_a (linordered_semidom(X_a) -> (all M all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)))))) # label(fact_819_of__nat__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 887 (all X_a (ordere223160158up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_820_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 888 (all X_a (ordere223160158up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_821_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 889 (all X_a (linordered_semidom(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))))))) # label(fact_822_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 890 (all X_a (linordered_semidom(X_a) -> (all N_1 all M (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M),N_1)))))))) # label(fact_823_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 891 (all M all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)) = M)) # label(fact_824_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 892 (all I_1 all J_1 all K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_1)))) # label(fact_825_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 893 (all N all K_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)))))) # label(fact_826_less__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 894 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_1),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),C)))))) # label(fact_827_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 895 (all X_b (order(X_b) -> (all A_2 all Ba (hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba) = bot_bot(fun(X_b,bool)) <-> -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)))))) # label(fact_828_atLeastatMost__empty__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 896 (all X_b (order(X_b) -> (all A_2 all Ba (bot_bot(fun(X_b,bool)) = hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba) <-> -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)))))) # label(fact_829_atLeastatMost__empty__iff2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 897 (all X_b (order(X_b) -> (all A_2 all Ba all Ca all D (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba)),hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),Ca),D))) <-> -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),A_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),D)))))) # label(fact_830_atLeastatMost__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 898 (all X_b (order(X_b) -> (all A_2 all Ba (ti(X_b,A_2) = ti(X_b,Ba) -> hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))))) # label(fact_831_atLeastAtMost__singleton_H) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 899 (all X_b (order(X_b) -> (all A_2 all Ba all Ca (hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ca),bot_bot(fun(X_b,bool))) <-> ti(X_b,A_2) = ti(X_b,Ba) & ti(X_b,Ba) = ti(X_b,Ca))))) # label(fact_832_atLeastAtMost__singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 900 (all X_b (order(X_b) -> (all A_2 hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),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),A_2),bot_bot(fun(X_b,bool)))))) # label(fact_833_atLeastAtMost__singleton) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 901 (all X_b (ordered_ab_group_add(X_b) -> (all X_1 all Y_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),uminus_uminus(X_b)),hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),X_1),Y_2)) = hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),Y_2)),hAPP(X_b,X_b,uminus_uminus(X_b),X_1))))) # label(fact_834_image__uminus__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 902 (all X_b (comm_monoid_add(X_b) -> (all F all M_1 all K_1 all N hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_1))) = hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),hAPP(fun(nat,nat),fun(nat,X_b),hAPP(fun(nat,X_b),fun(fun(nat,nat),fun(nat,X_b)),combb(nat,X_b,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M_1),N))))) # label(fact_835_setsum__shift__bounds__cl__nat__ivl) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 903 (all X_b (ordered_ring(X_b) -> (all A_2 all E all Ca all Ba all D (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),E)),D))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),Ba)),E)),Ca)),D)))))) # label(fact_836_less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 904 (all X_b (ordered_ring(X_b) -> (all A_2 all E all Ca all Ba all D (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),E)),D))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ba),A_2)),E)),D))))))) # label(fact_837_less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 905 (all X_b all X_c (comm_monoid_mult(X_c) -> (all Y_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),Y_2)),A_3) = hAPP(nat,X_c,hAPP(X_c,fun(nat,X_c),power_power(X_c),Y_2),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))))) # label(fact_838_setprod__constant) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 906 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3)),X_1)) <-> (exists X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),X_1)))))))))) # label(fact_839_fold1__strict__below__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 907 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3))) <-> (all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),X_2)))))))))) # label(fact_840_strict__below__fold1__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 908 (all U all M_1 all N all J_1 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),I_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),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),minus_minus(nat),I_1),J_1)),U)),M_1)),N))))) # label(fact_841_nat__less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 909 (all U all M_1 all N all I_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),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),minus_minus(nat),J_1),I_1)),U)),N)))))) # label(fact_842_nat__less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 910 (all X_b (comm_monoid_add(X_b) -> (all F all P_1 all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat)))) -> hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),P_1))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M_1),N))),hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),P_1)))))))) # label(fact_843_setsum__ub__add__nat) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 911 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),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_3),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_1),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))))) # label(fact_844_card__Diff1__less) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 912 (all X_a (linordered_semidom(X_a) -> (all M all N_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1))))))) # label(fact_845_power__le__imp__le__exp) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 913 (all X_b (linordered_semidom(X_b) -> (all X_1 all Y_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),one_one(X_b)),Ba)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),Ba),X_1)),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),Ba),Y_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_2))))))) # label(fact_846_power__increasing__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.62 914 (all X_b all X_c (comm_monoid_add(X_c) & ordere223160158up_add(X_c) -> (all F all G all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),A_3))))))))) # label(fact_847_setsum__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 915 (all N_1 all M -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),M))))) # label(fact_848_not__int__zless__negative) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 916 (all Z_2 all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1)) & Z_2 != W_1)) # label(fact_849_zless__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 917 (all K all I all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),J)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I),K)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),J),K))))) # label(fact_850_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 918 (all X_b all X_c (ord(X_c) -> (all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less(fun(X_b,X_c)),F),G)) <-> hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) & -hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),G),F)))))) # label(fact_851_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 919 (all X_b all A_3 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool))))) # label(fact_852_not__psubset__empty) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 920 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_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)),A_3),B_2)) & ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_2))) # label(fact_853_psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 921 (all X_b all A_3 all B_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)),A_3),B_2)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) | ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2))) # label(fact_854_subset__iff__psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 922 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_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)),A_3),B_2)))) # label(fact_855_psubset__imp__subset) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 923 (all X_b all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_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_2),C_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_1))))) # label(fact_856_psubset__subset__trans) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 924 (all X_b all C_1 all A_3 all B_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)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),B_2),C_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_1))))) # label(fact_857_subset__psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 925 (all X_b all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),B_2),C_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_1))))) # label(fact_858_psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 926 (all X_b all Ca all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B_2))))) # label(fact_859_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 927 (all Z hAPP(int,int,uminus_uminus(int),hAPP(int,int,uminus_uminus(int),Z)) = Z) # label(fact_860_zminus__zminus) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 928 (all Z_3 all Z all W_3 all W_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_3),W_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_3),Z)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_3),Z_3)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_2),Z)))))) # label(fact_861_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 929 (all M_1 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)))) # label(fact_862_zless__int) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 930 (all W_1 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)) | W_1 = Z_2)) # label(fact_863_zless__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 931 (all M_1 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),N))) -> hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),M_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),N)) = hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),N)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),M_1),N)))) # label(fact_864_atLeastAtMostPlus1__int__conv) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 932 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)))))) # label(fact_865_psubset__card__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 933 (all W_2 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),Z)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_2),one_one(int))),Z)))) # label(fact_866_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 934 (all W_1 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),one_one(int))),Z_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)))) # label(fact_867_add1__zle__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 935 (all W_1 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_2)))) # label(fact_868_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 936 (all W_1 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_2),one_one(int)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)))) # label(fact_869_zle__diff1__eq) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 937 (all X_b all A_3 all X_1 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),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_1),B_2))) <-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),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_3),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_1),bot_bot(fun(X_b,bool))))),B_2))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> 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)),A_3),B_2)))))) # label(fact_870_psubset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 938 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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)),A_3),B_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)))))) # label(fact_871_card__psubset) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 939 (all X_a (comm_monoid_mult(X_a) -> (all A_1 all B all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),N_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N_1))))) # label(fact_872_power__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 940 (all X_a (monoid_mult(X_a) -> (all A_1 all N_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))))) # label(fact_873_power__commutes) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 941 (all X_a (monoid_mult(X_a) -> (all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),one_one(X_a)),N_1) = one_one(X_a)))) # label(fact_874_power__one) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 942 (all X_a (semiring_1(X_a) -> (all M all N_1 hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N_1)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),N_1)))) # label(fact_875_of__nat__power) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 943 (all X_a (monoid_mult(X_a) -> (all A_1 all M all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),N_1)))) # label(fact_876_power__mult) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 944 (all X_a (monoid_mult(X_a) -> (all A_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),one_one(nat)) = ti(X_a,A_1)))) # label(fact_877_power__one__right) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 945 (all X_a (linordered_semidom(X_a) -> (all N_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))))))) # label(fact_878_one__le__power) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 946 (all X_b (linordered_semidom(X_b) -> (all M_1 all N all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),one_one(X_b)),A_2)) -> (hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),A_2),M_1) = hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),A_2),N) <-> M_1 = N))))) # label(fact_879_power__inject__exp) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 947 (all X_a (monoid_mult(X_a) -> (all A_1 all M all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))))) # label(fact_880_power__add) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 948 (all X_a (linordered_semidom(X_a) -> (all N_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)))))))) # label(fact_881_power__less__power__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 949 (all X_a (linordered_semidom(X_a) -> (all N_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)))))))) # label(fact_882_power__gt1__lemma) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 950 (all X_a (linordered_semidom(X_a) -> (all A_1 all N_1 all N_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_4)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_4)))))))) # label(fact_883_power__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 951 (all X_a (linordered_semidom(X_a) -> (all M all N_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))))))) # label(fact_884_power__less__imp__less__exp) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 952 (all X_b (linordered_semidom(X_b) -> (all X_1 all Y_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),one_one(X_b)),Ba)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),Ba),X_1)),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),Ba),Y_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2))))))) # label(fact_885_power__strict__increasing__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 953 (all X_a (linordered_semidom(X_a) -> (all A_1 all N_1 all N_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_4)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_4)))))))) # label(fact_886_power__increasing) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 954 (all X_a (ring_1(X_a) -> (all A_1 all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),N_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))))) # label(fact_887_power__minus) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 955 (all X_b all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) <-> (exists N_2 exists F_1 ti(fun(X_b,bool),A_3) = hAPP(fun(nat,bool),fun(X_b,bool),hAPP(fun(nat,X_b),fun(fun(nat,bool),fun(X_b,bool)),image(nat,X_b),F_1),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_2)))))) # label(fact_888_finite__conv__nat__seg__image) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 956 (all Pa all I_1 all K_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_1),K_1)) -> (hBOOL(hAPP(int,bool,Pa,K_1)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),K_1)) -> (hBOOL(hAPP(int,bool,Pa,I_2)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,Pa,I_1)))))) # label(fact_889_int__le__induct) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 957 (all L all U hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),L),U)))) # label(fact_890_finite__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 958 (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),Y)) | X = Y | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X)))) # label(fact_891_zless__linear) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 959 (all J_1 all I_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J_1),I_1)) -> hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),I_1),J_1) = bot_bot(fun(int,bool))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J_1),I_1)) -> hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),I_1),J_1) = hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),I_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_1),one_one(int))),J_1))))) # label(fact_892_simp__from__to) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 960 (all Pa all I_1 all K_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),K_1)) -> (hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),one_one(int)))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),K_1)) -> (hBOOL(hAPP(int,bool,Pa,I_2)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,Pa,I_1)))))) # label(fact_893_int__less__induct) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 961 (all A_3 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A_3)) <-> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))))) # label(fact_894_transfer__nat__int__set__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 962 (all A_3 all B_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A_3),B_2)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_2))))) # label(fact_895_transfer__nat__int__set__relations_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 963 (all X_1 all A_3 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),A_3)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))))) # label(fact_896_transfer__nat__int__set__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 964 (all A_3 all B_2 (A_3 = B_2 <-> hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_2))) # label(fact_897_transfer__nat__int__set__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 965 (all X_1 all Y_2 all Pa ((hBOOL(Pa) -> hAPP(nat,int,semiring_1_of_nat(int),X_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),Pa),X_1),Y_2))) & (-hBOOL(Pa) -> hAPP(nat,int,semiring_1_of_nat(int),Y_2) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),Pa),X_1),Y_2))))) # label(fact_898_int__if__cong) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 966 (all X_1 all Y_2 (hAPP(nat,int,semiring_1_of_nat(int),X_1) = hAPP(nat,int,semiring_1_of_nat(int),Y_2) <-> X_1 = Y_2)) # label(fact_899_transfer__int__nat__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 967 (all A_3 all B_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),A_3),B_2)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_2))))) # label(fact_900_transfer__nat__int__set__relations_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 968 (all A_3 hAPP(fun(nat,bool),nat,finite_card(nat),A_3) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))) # label(fact_901_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 969 (all X_1 all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2)))) # label(fact_903_transfer__int__nat__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 970 (all X_1 all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_2)))) # label(fact_904_transfer__int__nat__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 971 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Y))) # label(fact_905_Nat__Transfer_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 972 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y))) # label(fact_906_Nat__Transfer_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 973 (all X all N_1 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),X)),N_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N_1))) # label(fact_908_Nat__Transfer_Otransfer__int__nat__functions_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 974 (all Pa all K_1 all I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),I_1)) -> (hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),one_one(int)))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),I_2)) -> (hBOOL(hAPP(int,bool,Pa,I_2)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,Pa,I_1)))))) # label(fact_909_int__gr__induct) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 975 (all Pa all K_1 all I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_1),I_1)) -> (hBOOL(hAPP(int,bool,Pa,K_1)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_1),I_2)) -> (hBOOL(hAPP(int,bool,Pa,I_2)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,Pa,I_1)))))) # label(fact_910_int__ge__induct) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 976 (all M_1 all K_1 all F ((all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M_2)),hAPP(nat,nat,F,N_2))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,F,M_1)),K_1)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)))))) # label(fact_911_mono__nat__linear__lb) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 977 (all N all N_3 ((all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),N)))) -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3)))) # label(fact_912_bounded__nat__set__is__finite) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 978 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) -> (exists B_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_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)),B_2),A_3)))))) # label(fact_913_psubset__imp__ex__mem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 979 (all Z -(all M_2 all N_2 Z != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M_2)),hAPP(nat,int,semiring_1_of_nat(int),N_2)))) # label(fact_914_int__diff__cases) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 980 (all I_1 all J_1 all F ((all I_2 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I_2)),hAPP(nat,nat,F,J_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,I_1)),hAPP(nat,nat,F,J_1)))))) # label(fact_915_less__mono__imp__le__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 981 (all X_b (power(X_b) -> power_power(X_b) = hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(nat,X_b)),hAPP(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(nat,X_b))),power_1(X_b),one_one(X_b)),times_times(X_b)))) # label(fact_916_power__power__power) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 982 (all X_a (dense_linorder(X_a) -> (all Z all Y ((all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z)))))) # label(fact_917_dense__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 983 (all X_a (linorder(X_a) -> (all T_3 exists Z_1 all X_2 (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_eq(X_a),T_3),X_2)))))) # label(fact_918_minf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 984 (all X_a (linorder(X_a) -> (all T_3 exists Z_1 all X_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_eq(X_a),T_3),X_2)))))) # label(fact_919_pinf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 985 (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_920_dense__le__bounded) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 986 (all X_c all X_b (order(X_b) & order(X_c) -> (all Ca all F all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Ca),hAPP(X_b,X_c,F,Ba))) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,Y_1)),hAPP(X_b,X_c,F,X_2))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Ca),hAPP(X_b,X_c,F,A_2))))))))) # label(fact_921_xt5) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 987 (all X_a (linorder(X_a) -> (all T_3 exists Z_1 all X_2 (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_eq(X_a),X_2),T_3)))))) # label(fact_922_minf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 988 (all X_a (linorder(X_a) -> (all T_3 exists Z_1 all X_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_eq(X_a),X_2),T_3)))))) # label(fact_923_pinf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 989 (all X_c all X_b (order(X_b) & order(X_c) -> (all Ca all F all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Ca),hAPP(X_b,X_c,F,Ba))) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_2)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,Y_1)),hAPP(X_b,X_c,F,X_2))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Ca),hAPP(X_b,X_c,F,A_2))))))))) # label(fact_924_xt7) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 990 (all X_b all X_c (order(X_c) & order(X_b) -> (all F all Ca all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,Ba)),Ca)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,F,Y_1))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,A_2)),Ca)))))))) # label(fact_925_order__less__le__subst2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 991 (all X_c all X_b (order(X_b) & ord(X_c) -> (all Ca all F all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,Ba)),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Ca),Ba)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Y_1),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,Y_1)),hAPP(X_c,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,Ca)),A_2)))))))) # label(fact_926_xt6) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 992 (all X_c all X_b (order(X_b) & order(X_c) -> (all Ca all F all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,Ba)),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Ca),Ba)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Y_1),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,Y_1)),hAPP(X_c,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,Ca)),A_2)))))))) # label(fact_927_xt4) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 993 (all X_b all X_c (order(X_c) & order(X_b) -> (all F all Ca all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,Ba)),Ca)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_1)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,F,Y_1))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,A_2)),Ca)))))))) # label(fact_928_order__le__less__subst2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 994 (all X_b all X_c (order(X_c) & order(X_b) -> (all Ca all A_2 all F all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,Ba))) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Ba),Ca)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),X_2),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,F,Y_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,Ca))))))))) # label(fact_929_order__less__le__subst1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 995 (all X_b all X_c (order(X_c) & order(X_b) -> (all Ca all A_2 all F all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),hAPP(X_c,X_b,F,Ba))) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Ba),Ca)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),X_2),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,F,Y_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,Ca))))))))) # label(fact_930_order__le__less__subst1) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 996 (all I_1 all Pa all K_1 (hBOOL(hAPP(int,bool,Pa,K_1)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_1),I_2)) -> (hBOOL(hAPP(int,bool,Pa,I_2)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),K_1)) -> (hBOOL(hAPP(int,bool,Pa,I_2)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,Pa,I_1)))))) # label(fact_931_int__induct) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 997 (all X_b (linorder(X_b) -> (all Pa all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))) -> ((all B_1 all A_4 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_4)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),B_1)))) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_4)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_1),A_4))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3)))))))) # label(fact_932_finite__linorder__max__induct) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 998 (all X_b (linorder(X_b) -> (all Pa all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))) -> ((all B_1 all A_4 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_4)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_1),X_2)))) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_4)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_1),A_4))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3)))))))) # label(fact_933_finite__linorder__min__induct) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 999 (all X_b (ab_group_add(X_b) -> (all F all M_1 all N ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(fun(nat,fun(X_b,X_b)),fun(fun(nat,X_b),fun(nat,X_b)),combs(nat,X_b,X_b),hAPP(fun(nat,X_b),fun(nat,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(nat,X_b),fun(nat,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),nat),minus_minus(X_b)),F)),hAPP(fun(nat,nat),fun(nat,X_b),hAPP(fun(nat,X_b),fun(fun(nat,nat),fun(nat,X_b)),combb(nat,X_b,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M_1),N)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(nat,X_b,F,M_1)),hAPP(nat,X_b,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))))) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(fun(nat,fun(X_b,X_b)),fun(fun(nat,X_b),fun(nat,X_b)),combs(nat,X_b,X_b),hAPP(fun(nat,X_b),fun(nat,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(nat,X_b),fun(nat,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),nat),minus_minus(X_b)),F)),hAPP(fun(nat,nat),fun(nat,X_b),hAPP(fun(nat,X_b),fun(fun(nat,nat),fun(nat,X_b)),combb(nat,X_b,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M_1),N)) = zero_zero(X_b)))))) # label(fact_934_setsum__natinterval__difff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1000 (all X_b (comm_monoid_add(X_b) -> (all Pa all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),Pa),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M_1),N)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(nat,X_b,Pa,M_1)),hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),Pa),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),M_1),N))))))) # label(fact_935_setsum__head) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1001 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))) # label(fact_936_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1002 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N_1))) # label(fact_937_le0) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1003 (all L all U hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),L),U)))) # label(fact_938_finite__greaterThanAtMost) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1004 (all X_a (linordered_semidom(X_a) -> (all A_1 all N_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_939_power__less__imp__less__base) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1005 (all X_a (linordered_idom(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),X)))))))) # label(fact_940_mult__right__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1006 (all X_a (linordered_idom(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),X)),X)))))))) # label(fact_941_mult__left__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1007 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)))))) # label(fact_942_zero__less__two) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1008 (all X_b all One all Times all A_2 hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(nat,X_b)),hAPP(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(nat,X_b))),power_1(X_b),One),Times),A_2),zero_zero(nat)) = ti(X_b,One)) # label(fact_943_power_Opower_Opower__0) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1009 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_944_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1010 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_945_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1011 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_946_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1012 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_947_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1013 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_948_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1014 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_949_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1015 (all N_1 all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N_1))))) # label(fact_950_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1016 (all Pa ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hBOOL(hAPP(int,bool,Pa,X_2)))) <-> (all X_2 hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),X_2)))))) # label(fact_951_transfer__int__nat__quantifiers_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1017 (all Pa ((exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) & hBOOL(hAPP(int,bool,Pa,X_2)))) <-> (exists X_2 hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),X_2)))))) # label(fact_952_transfer__int__nat__quantifiers_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1018 (all Z hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Z)))) # label(fact_953_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1019 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_955_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1020 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)))))) # label(fact_956_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1021 (all K -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K)),zero_zero(int)))) # label(fact_958_int__less__0__conv) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1022 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_959_zero__less__int__conv) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1023 (all K_1 all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),L)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),L)),zero_zero(int))))) # label(fact_960_less__bin__lemma) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1024 (all K all I all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),J)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),J)))))) # label(fact_961_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1025 (all X_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_1)) | N = zero_zero(nat))) # label(fact_963_nat__zero__less__power__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1026 (all X_a (linordered_semidom(X_a) -> (all N_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))))))) # label(fact_964_zero__less__power) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1027 (all M all N_1 all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),I)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))))) # label(fact_965_nat__power__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1028 (all X_a (linordered_semidom(X_a) -> (all A_1 all N_1 all B (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> ti(X_a,A_1) = ti(X_a,B)))))))) # label(fact_966_power__eq__imp__eq__base) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1029 (all X_a (linordered_semidom(X_a) -> (all N_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N_1))))))))) # label(fact_967_power__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1030 (all N_1 (N_1 != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)))) # label(fact_968_gr0I) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1031 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> N_1 != zero_zero(nat))) # label(fact_969_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1032 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))) # label(fact_970_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1033 (all N (N != zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_971_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1034 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))) # label(fact_972_not__less0) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1035 (all X_b (linordered_semidom(X_b) -> (all N (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(nat,X_b,semiring_1_of_nat(X_b),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))))) # label(fact_973_of__nat__0__less__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1036 (all X_b (linord219039673up_add(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),A_2)))))) # label(fact_974_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1037 (all X_b (linord219039673up_add(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))))))) # label(fact_975_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1038 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_976_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1039 (all X_a (linordered_semidom(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_977_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1040 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_978_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1041 (all X_b (linordered_idom(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))))))) # label(fact_979_even__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1042 (all X_a (linordered_ring(X_a) -> (all A_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),times_times(X_a),A_1),A_1)),zero_zero(X_a)))))) # label(fact_980_not__square__less__zero) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1043 (all X_b (linord581940658strict(X_b) -> (all A_2 all Ca all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),Ca))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),Ca)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),zero_zero(X_b))) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),A_2)))))) # label(fact_981_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1044 (all X_b (linord581940658strict(X_b) -> (all Ca all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ca),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ca),Ba))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),Ca)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),zero_zero(X_b))) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),A_2)))))) # label(fact_982_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1045 (all X_b (linord581940658strict(X_b) -> (all A_2 all Ba all Ca (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),Ca)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ca),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ca),Ba))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba))))))) # label(fact_983_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1046 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_984_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1047 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_985_mult__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1048 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),zero_zero(X_a)))))))) # label(fact_986_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1049 (all X_a (linord20386208strict(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))))))) # label(fact_987_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1050 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))))))) # label(fact_988_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.63 1051 (all X_b (linord581940658strict(X_b) -> (all A_2 all Ba all Ca (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),zero_zero(X_b))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ca),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ca),Ba))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),A_2))))))) # label(fact_989_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1052 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),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),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_990_mult__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1053 (all X_a (linord581940658strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_991_mult__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1054 (all X_a (linord20386208strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> 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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_992_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1055 (all X_a (linord20386208strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> 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),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_993_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1056 (all X_a (linord893533164strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> 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),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_994_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1057 (all X_a (linord581940658strict(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_995_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1058 (all X_a (linord581940658strict(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_996_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1059 (all T_2 all T_1 (boolean_algebra(T_1) -> boolean_algebra(fun(T_2,T_1)))) # label(arity_fun___Lattices_Oboolean__algebra) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1060 (all T_2 all T_1 (preorder(T_1) -> preorder(fun(T_2,T_1)))) # label(arity_fun___Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1061 (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].
% 2.13/2.64 1062 (all T_2 all T_1 (order(T_1) -> order(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oorder) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1063 (all T_2 all T_1 (ord(T_1) -> ord(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oord) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1064 (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].
% 2.13/2.64 1065 (all T_2 all T_1 (uminus(T_1) -> uminus(fun(T_2,T_1)))) # label(arity_fun___Groups_Ouminus) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1066 (all T_2 all T_1 (minus(T_1) -> minus(fun(T_2,T_1)))) # label(arity_fun___Groups_Ominus) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1067 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1068 (all X_a all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y) = ti(X_a,X)) # label(help_If_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1069 (all X_a all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X),Y) = ti(X_a,Y)) # label(help_If_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1070 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_If_3_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1071 (all X_a all P all X (-hBOOL(hAPP(X_a,bool,P,X)) | hBOOL(hAPP(fun(X_a,bool),bool,fEx(X_a),P)))) # label(help_fEx_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1072 (all P (-hBOOL(hAPP(bool,bool,fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1073 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.13/2.64 1074 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R) = hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R))) # label(help_COMBB_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.55/2.76 1075 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q)) # label(help_COMBC_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.55/2.76 1076 (all X_a all P hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P)) # label(help_COMBI_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.55/2.76 1077 (all X_b all X_a all P all Q hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P)) # label(help_COMBK_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.55/2.76 1078 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c)),combs(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R))) # label(help_COMBS_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.55/2.76 1079 (all Q all P (-hBOOL(P) | -hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.55/2.76 1080 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.55/2.76 1081 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.55/2.76 1082 (all Q all P (-hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.55/2.76 1083 (all P all Q (-hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.55/2.76 1084 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | hBOOL(P) | hBOOL(Q))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.55/2.76 1085 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.55/2.76 1086 (all X_a all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) | ti(X_a,X) = ti(X_a,Y))) # label(help_fequal_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.55/2.76 1087 (all X_a all X all Y (ti(X_a,X) != ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)))) # label(help_fequal_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.55/2.76 1088 (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].
% 2.55/2.76 1089 (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].
% 2.55/2.76 1090 (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].
% 2.55/2.76
% 2.55/2.76 ============================== end of process non-clausal formulas ===
% 2.55/2.76
% 2.55/2.76 ============================== PROCESS INITIAL CLAUSES ===============
% 2.55/2.76
% 2.55/2.76 ============================== PREDICATE ELIMINATION =================
% 2.55/2.76 1091 comm_monoid_add(int) # label(arity_Int_Oint___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 2.55/2.76 1092 -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)].
% 2.55/2.76 1093 -comm_monoid_add(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(C,bool),fun(B,A),hAPP(fun(B,fun(fun(C,bool),A)),fun(fun(C,bool),fun(B,A)),combc(B,fun(C,bool),A),hAPP(fun(B,fun(C,A)),fun(B,fun(fun(C,bool),A)),hAPP(fun(fun(C,A),fun(fun(C,bool),A)),fun(fun(B,fun(C,A)),fun(B,fun(fun(C,bool),A))),combb(fun(C,A),fun(fun(C,bool),A),B),big_co1399186613setsum(C,A)),hAPP(fun(C,fun(B,A)),fun(B,fun(C,A)),combc(C,B,A),D))),E)),F) = hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),hAPP(fun(B,bool),fun(C,A),hAPP(fun(C,fun(fun(B,bool),A)),fun(fun(B,bool),fun(C,A)),combc(C,fun(B,bool),A),hAPP(fun(C,fun(B,A)),fun(C,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(C,fun(B,A)),fun(C,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),C),big_co1399186613setsum(B,A)),D)),F)),E) # label(fact_180_setsum__commute) # label(axiom). [clausify(248)].
% 2.55/2.76 1094 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(D,bool),A,hAPP(fun(D,A),fun(fun(D,bool),A),big_co1399186613setsum(D,A),hAPP(fun(D,fun(B,bool)),fun(D,A),hAPP(fun(fun(B,bool),A),fun(fun(D,fun(B,bool)),fun(D,A)),combb(fun(B,bool),A,D),hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E)),hAPP(fun(D,fun(B,bool)),fun(D,fun(B,bool)),hAPP(fun(fun(B,bool),fun(B,bool)),fun(fun(D,fun(B,bool)),fun(D,fun(B,bool))),combb(fun(B,bool),fun(B,bool),D),collect(B)),hAPP(fun(D,fun(B,bool)),fun(D,fun(B,bool)),hAPP(fun(fun(B,bool),fun(B,bool)),fun(fun(D,fun(B,bool)),fun(D,fun(B,bool))),combb(fun(B,bool),fun(B,bool),D),hAPP(fun(B,fun(bool,bool)),fun(fun(B,bool),fun(B,bool)),combs(B,bool,bool),hAPP(fun(B,bool),fun(B,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(B,bool),fun(B,fun(bool,bool))),combb(bool,fun(bool,bool),B),fconj),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,fun(fun(B,bool),bool)),fun(fun(B,bool),fun(B,bool)),combc(B,fun(B,bool),bool),member(B)),C)))),hAPP(fun(B,fun(D,bool)),fun(D,fun(B,bool)),combc(B,D,bool),hAPP(fun(B,D),fun(B,fun(D,bool)),hAPP(fun(D,fun(D,bool)),fun(fun(B,D),fun(B,fun(D,bool))),combb(D,fun(D,bool),B),fequal(D)),F)))))),hAPP(fun(B,bool),fun(D,bool),hAPP(fun(B,D),fun(fun(B,bool),fun(D,bool)),image(B,D),F),C)) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) # label(fact_208_setsum__image__gen) # label(axiom). [clausify(276)].
% 2.55/2.76 1095 -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),f65(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_210_setsum_Ocong) # label(axiom). [clausify(278)].
% 2.55/2.76 1096 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(B,A,D,f65(B,A,E,D,C)) != hAPP(B,A,E,f65(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_210_setsum_Ocong) # label(axiom). [clausify(278)].
% 2.55/2.76 1097 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite_1(D),E)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,fun(D,bool)),fun(B,A),hAPP(fun(B,fun(fun(D,bool),A)),fun(fun(B,fun(D,bool)),fun(B,A)),combs(B,fun(D,bool),A),hAPP(fun(B,fun(D,A)),fun(B,fun(fun(D,bool),A)),hAPP(fun(fun(D,A),fun(fun(D,bool),A)),fun(fun(B,fun(D,A)),fun(B,fun(fun(D,bool),A))),combb(fun(D,A),fun(fun(D,bool),A),B),big_co1399186613setsum(D,A)),F)),hAPP(fun(B,fun(D,bool)),fun(B,fun(D,bool)),hAPP(fun(fun(D,bool),fun(D,bool)),fun(fun(B,fun(D,bool)),fun(B,fun(D,bool))),combb(fun(D,bool),fun(D,bool),B),collect(D)),hAPP(fun(B,fun(D,bool)),fun(B,fun(D,bool)),hAPP(fun(fun(D,bool),fun(D,bool)),fun(fun(B,fun(D,bool)),fun(B,fun(D,bool))),combb(fun(D,bool),fun(D,bool),B),hAPP(fun(D,fun(bool,bool)),fun(fun(D,bool),fun(D,bool)),combs(D,bool,bool),hAPP(fun(D,bool),fun(D,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(D,bool),fun(D,fun(bool,bool))),combb(bool,fun(bool,bool),D),fconj),hAPP(fun(D,bool),fun(D,bool),hAPP(fun(D,fun(fun(D,bool),bool)),fun(fun(D,bool),fun(D,bool)),combc(D,fun(D,bool),bool),member(D)),E)))),V6)))),C) = hAPP(fun(D,bool),A,hAPP(fun(D,A),fun(fun(D,bool),A),big_co1399186613setsum(D,A),hAPP(fun(D,fun(B,bool)),fun(D,A),hAPP(fun(D,fun(fun(B,bool),A)),fun(fun(D,fun(B,bool)),fun(D,A)),combs(D,fun(B,bool),A),hAPP(fun(D,fun(B,A)),fun(D,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(D,fun(B,A)),fun(D,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),D),big_co1399186613setsum(B,A)),hAPP(fun(B,fun(D,A)),fun(D,fun(B,A)),combc(B,D,A),F))),hAPP(fun(D,fun(B,bool)),fun(D,fun(B,bool)),hAPP(fun(fun(B,bool),fun(B,bool)),fun(fun(D,fun(B,bool)),fun(D,fun(B,bool))),combb(fun(B,bool),fun(B,bool),D),collect(B)),hAPP(fun(D,fun(B,bool)),fun(D,fun(B,bool)),hAPP(fun(fun(B,bool),fun(B,bool)),fun(fun(D,fun(B,bool)),fun(D,fun(B,bool))),combb(fun(B,bool),fun(B,bool),D),hAPP(fun(B,fun(bool,bool)),fun(fun(B,bool),fun(B,bool)),combs(B,bool,bool),hAPP(fun(B,bool),fun(B,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(B,bool),fun(B,fun(bool,bool))),combb(bool,fun(bool,bool),B),fconj),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,fun(fun(B,bool),bool)),fun(fun(B,bool),fun(B,bool)),combc(B,fun(B,bool),bool),member(B)),C)))),hAPP(fun(B,fun(D,bool)),fun(D,fun(B,bool)),combc(B,D,bool),V6))))),E) # label(fact_211_setsum__setsum__restrict) # label(axiom). [clausify(279)].
% 2.55/2.76 1098 -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_212_setsum_Oremove) # label(axiom). [clausify(280)].
% 2.55/2.76 1099 -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_213_setsum__diff1_H) # label(axiom). [clausify(281)].
% 2.55/2.76 1100 -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_214_setsum_Oinsert__remove) # label(axiom). [clausify(282)].
% 2.55/2.76 1101 -comm_monoid_add(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),plus_plus(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),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_215_setsum__addf) # label(axiom). [clausify(283)].
% 2.55/2.76 1102 -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),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),plus_plus(A)),D)),E)),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(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_216_setsum_Odistrib) # label(axiom). [clausify(284)].
% 2.55/2.76 1103 -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_217_setsum__insert) # label(axiom). [clausify(285)].
% 2.55/2.76 1104 -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_218_setsum_Oinsert) # label(axiom). [clausify(286)].
% 2.55/2.76 1105 -comm_monoid_add(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f68(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_254_setsum__cong2) # label(axiom). [clausify(322)].
% 2.55/2.76 1106 -comm_monoid_add(A) | hAPP(B,A,C,f68(B,A,D,C,E)) != hAPP(B,A,D,f68(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_254_setsum__cong2) # label(axiom). [clausify(322)].
% 2.55/2.76 1107 -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),f69(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_255_setsum__cong) # label(axiom). [clausify(323)].
% 2.55/2.76 1108 -comm_monoid_add(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hAPP(B,A,E,f69(B,A,F,E,D,C)) != hAPP(B,A,F,f69(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_255_setsum__cong) # label(axiom). [clausify(323)].
% 2.55/2.76 1109 -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),f70(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_256_setsum_OF__cong) # label(axiom). [clausify(324)].
% 2.55/2.76 1110 -comm_monoid_add(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hAPP(B,A,E,f70(B,A,E,F,D,C)) != hAPP(B,A,F,f70(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_256_setsum_OF__cong) # label(axiom). [clausify(324)].
% 2.55/2.76 1111 -comm_monoid_add(A) | -ordere779506340up_add(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f77(B,A,C,D,E)),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),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_333_setsum__mono) # label(axiom). [clausify(401)].
% 2.55/2.76 1112 -comm_monoid_add(A) | -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,f77(B,A,C,D,E))),hAPP(B,A,D,f77(B,A,C,D,E)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),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_333_setsum__mono) # label(axiom). [clausify(401)].
% 2.55/2.76 1113 -comm_monoid_add(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),B),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),D),E)) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),E),C))) # label(fact_835_setsum__shift__bounds__cl__nat__ivl) # label(axiom). [clausify(902)].
% 2.55/2.76 1114 -comm_monoid_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),one_one(nat)))) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),E))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),E)))) # label(fact_843_setsum__ub__add__nat) # label(axiom). [clausify(910)].
% 2.55/2.76 1115 -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),f145(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_847_setsum__strict__mono) # label(axiom). [clausify(914)].
% 2.55/2.76 1116 -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,f145(B,A,D,E,C))),hAPP(B,A,E,f145(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_847_setsum__strict__mono) # label(axiom). [clausify(914)].
% 2.55/2.76 1117 -comm_monoid_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,D,B)),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),B),C))) # label(fact_935_setsum__head) # label(axiom). [clausify(1000)].
% 2.55/2.76 Derived: ti(fun(fun(A,int),fun(fun(A,bool),int)),big_co1399186613setsum(A,int)) = big_co1399186613setsum(A,int). [resolve(1091,a,1092,a)].
% 2.55/2.76 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(B,bool),fun(A,int),hAPP(fun(A,fun(fun(B,bool),int)),fun(fun(B,bool),fun(A,int)),combc(A,fun(B,bool),int),hAPP(fun(A,fun(B,int)),fun(A,fun(fun(B,bool),int)),hAPP(fun(fun(B,int),fun(fun(B,bool),int)),fun(fun(A,fun(B,int)),fun(A,fun(fun(B,bool),int))),combb(fun(B,int),fun(fun(B,bool),int),A),big_co1399186613setsum(B,int)),hAPP(fun(B,fun(A,int)),fun(A,fun(B,int)),combc(B,A,int),C))),D)),E) = hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),hAPP(fun(A,bool),fun(B,int),hAPP(fun(B,fun(fun(A,bool),int)),fun(fun(A,bool),fun(B,int)),combc(B,fun(A,bool),int),hAPP(fun(B,fun(A,int)),fun(B,fun(fun(A,bool),int)),hAPP(fun(fun(A,int),fun(fun(A,bool),int)),fun(fun(B,fun(A,int)),fun(B,fun(fun(A,bool),int))),combb(fun(A,int),fun(fun(A,bool),int),B),big_co1399186613setsum(A,int)),C)),E)),D). [resolve(1091,a,1093,a)].
% 2.55/2.76 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(C,bool),int,hAPP(fun(C,int),fun(fun(C,bool),int),big_co1399186613setsum(C,int),hAPP(fun(C,fun(A,bool)),fun(C,int),hAPP(fun(fun(A,bool),int),fun(fun(C,fun(A,bool)),fun(C,int)),combb(fun(A,bool),int,C),hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),hAPP(fun(A,C),fun(A,fun(C,bool)),hAPP(fun(C,fun(C,bool)),fun(fun(A,C),fun(A,fun(C,bool))),combb(C,fun(C,bool),A),fequal(C)),E)))))),hAPP(fun(A,bool),fun(C,bool),hAPP(fun(A,C),fun(fun(A,bool),fun(C,bool)),image(A,C),E),B)) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B). [resolve(1091,a,1094,a)].
% 2.55/2.76 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),f65(A,int,C,D,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B). [resolve(1091,a,1095,a)].
% 2.55/2.76 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,int,C,f65(A,int,D,C,B)) != hAPP(A,int,D,f65(A,int,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B). [resolve(1091,a,1096,a)].
% 2.55/2.76 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),D)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,fun(C,bool)),fun(A,int),hAPP(fun(A,fun(fun(C,bool),int)),fun(fun(A,fun(C,bool)),fun(A,int)),combs(A,fun(C,bool),int),hAPP(fun(A,fun(C,int)),fun(A,fun(fun(C,bool),int)),hAPP(fun(fun(C,int),fun(fun(C,bool),int)),fun(fun(A,fun(C,int)),fun(A,fun(fun(C,bool),int))),combb(fun(C,int),fun(fun(C,bool),int),A),big_co1399186613setsum(C,int)),E)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),collect(C)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),hAPP(fun(C,fun(bool,bool)),fun(fun(C,bool),fun(C,bool)),combs(C,bool,bool),hAPP(fun(C,bool),fun(C,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(C,bool),fun(C,fun(bool,bool))),combb(bool,fun(bool,bool),C),fconj),hAPP(fun(C,bool),fun(C,bool),hAPP(fun(C,fun(fun(C,bool),bool)),fun(fun(C,bool),fun(C,bool)),combc(C,fun(C,bool),bool),member(C)),D)))),F)))),B) = hAPP(fun(C,bool),int,hAPP(fun(C,int),fun(fun(C,bool),int),big_co1399186613setsum(C,int),hAPP(fun(C,fun(A,bool)),fun(C,int),hAPP(fun(C,fun(fun(A,bool),int)),fun(fun(C,fun(A,bool)),fun(C,int)),combs(C,fun(A,bool),int),hAPP(fun(C,fun(A,int)),fun(C,fun(fun(A,bool),int)),hAPP(fun(fun(A,int),fun(fun(A,bool),int)),fun(fun(C,fun(A,int)),fun(C,fun(fun(A,bool),int))),combb(fun(A,int),fun(fun(A,bool),int),C),big_co1399186613setsum(A,int)),hAPP(fun(A,fun(C,int)),fun(C,fun(A,int)),combc(A,C,int),E))),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),F))))),D). [resolve(1091,a,1097,a)].
% 2.55/2.76 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),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,D,C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),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(1091,a,1098,a)].
% 2.55/2.76 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,C,D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),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(1091,a,1100,a)].
% 2.55/2.76 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(A,fun(int,int)),fun(fun(A,int),fun(A,int)),combs(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),plus_plus(int)),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D)). [resolve(1091,a,1101,a)].
% 2.55/2.76 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),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,D,C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B)). [resolve(1091,a,1103,a)].
% 2.55/2.76 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f68(A,int,B,C,D)),D)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D). [resolve(1091,a,1105,a)].
% 2.55/2.76 Derived: hAPP(A,int,B,f68(A,int,C,B,D)) != hAPP(A,int,C,f68(A,int,C,B,D)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D). [resolve(1091,a,1106,a)].
% 2.55/2.76 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),f69(A,int,D,E,C,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C). [resolve(1091,a,1107,a)].
% 2.55/2.76 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,int,D,f69(A,int,E,D,C,B)) != hAPP(A,int,E,f69(A,int,E,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),C). [resolve(1091,a,1108,a)].
% 2.55/2.76 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),f70(A,int,D,E,C,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),B). [resolve(1091,a,1109,a)].
% 2.55/2.76 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,int,D,f70(A,int,D,E,C,B)) != hAPP(A,int,E,f70(A,int,D,E,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),B). [resolve(1091,a,1110,a)].
% 2.55/2.76 Derived: -ordere779506340up_add(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f77(A,int,B,C,D)),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D))). [resolve(1091,a,1111,a)].
% 2.55/2.76 Derived: -ordere779506340up_add(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,B,f77(A,int,B,C,D))),hAPP(A,int,C,f77(A,int,B,C,D)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D))). [resolve(1091,a,1112,a)].
% 2.55/2.76 Derived: hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),C),D)) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),B))). [resolve(1091,a,1113,a)].
% 2.55/2.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D)))). [resolve(1091,a,1114,a)].
% 2.55/2.77 Derived: -ordere223160158up_add(int) | -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),f145(A,int,C,D,B)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B))). [resolve(1091,a,1115,a)].
% 2.55/2.77 Derived: -ordere223160158up_add(int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,C,f145(A,int,C,D,B))),hAPP(A,int,D,f145(A,int,C,D,B)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B))). [resolve(1091,a,1116,a)].
% 2.55/2.77 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,C,A)),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),A),B))). [resolve(1091,a,1117,a)].
% 2.55/2.77 1118 comm_monoid_add(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 2.55/2.77 Derived: ti(fun(fun(A,nat),fun(fun(A,bool),nat)),big_co1399186613setsum(A,nat)) = big_co1399186613setsum(A,nat). [resolve(1118,a,1092,a)].
% 2.55/2.77 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(fun(B,bool),fun(A,nat),hAPP(fun(A,fun(fun(B,bool),nat)),fun(fun(B,bool),fun(A,nat)),combc(A,fun(B,bool),nat),hAPP(fun(A,fun(B,nat)),fun(A,fun(fun(B,bool),nat)),hAPP(fun(fun(B,nat),fun(fun(B,bool),nat)),fun(fun(A,fun(B,nat)),fun(A,fun(fun(B,bool),nat))),combb(fun(B,nat),fun(fun(B,bool),nat),A),big_co1399186613setsum(B,nat)),hAPP(fun(B,fun(A,nat)),fun(A,fun(B,nat)),combc(B,A,nat),C))),D)),E) = hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),hAPP(fun(A,bool),fun(B,nat),hAPP(fun(B,fun(fun(A,bool),nat)),fun(fun(A,bool),fun(B,nat)),combc(B,fun(A,bool),nat),hAPP(fun(B,fun(A,nat)),fun(B,fun(fun(A,bool),nat)),hAPP(fun(fun(A,nat),fun(fun(A,bool),nat)),fun(fun(B,fun(A,nat)),fun(B,fun(fun(A,bool),nat))),combb(fun(A,nat),fun(fun(A,bool),nat),B),big_co1399186613setsum(A,nat)),C)),E)),D). [resolve(1118,a,1093,a)].
% 2.55/2.77 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(C,bool),nat,hAPP(fun(C,nat),fun(fun(C,bool),nat),big_co1399186613setsum(C,nat),hAPP(fun(C,fun(A,bool)),fun(C,nat),hAPP(fun(fun(A,bool),nat),fun(fun(C,fun(A,bool)),fun(C,nat)),combb(fun(A,bool),nat,C),hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),hAPP(fun(A,C),fun(A,fun(C,bool)),hAPP(fun(C,fun(C,bool)),fun(fun(A,C),fun(A,fun(C,bool))),combb(C,fun(C,bool),A),fequal(C)),E)))))),hAPP(fun(A,bool),fun(C,bool),hAPP(fun(A,C),fun(fun(A,bool),fun(C,bool)),image(A,C),E),B)) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B). [resolve(1118,a,1094,a)].
% 2.55/2.77 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),f65(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(1118,a,1095,a)].
% 2.55/2.77 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,nat,C,f65(A,nat,D,C,B)) != hAPP(A,nat,D,f65(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(1118,a,1096,a)].
% 2.55/2.77 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),D)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(fun(A,fun(C,bool)),fun(A,nat),hAPP(fun(A,fun(fun(C,bool),nat)),fun(fun(A,fun(C,bool)),fun(A,nat)),combs(A,fun(C,bool),nat),hAPP(fun(A,fun(C,nat)),fun(A,fun(fun(C,bool),nat)),hAPP(fun(fun(C,nat),fun(fun(C,bool),nat)),fun(fun(A,fun(C,nat)),fun(A,fun(fun(C,bool),nat))),combb(fun(C,nat),fun(fun(C,bool),nat),A),big_co1399186613setsum(C,nat)),E)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),collect(C)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),hAPP(fun(C,fun(bool,bool)),fun(fun(C,bool),fun(C,bool)),combs(C,bool,bool),hAPP(fun(C,bool),fun(C,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(C,bool),fun(C,fun(bool,bool))),combb(bool,fun(bool,bool),C),fconj),hAPP(fun(C,bool),fun(C,bool),hAPP(fun(C,fun(fun(C,bool),bool)),fun(fun(C,bool),fun(C,bool)),combc(C,fun(C,bool),bool),member(C)),D)))),F)))),B) = hAPP(fun(C,bool),nat,hAPP(fun(C,nat),fun(fun(C,bool),nat),big_co1399186613setsum(C,nat),hAPP(fun(C,fun(A,bool)),fun(C,nat),hAPP(fun(C,fun(fun(A,bool),nat)),fun(fun(C,fun(A,bool)),fun(C,nat)),combs(C,fun(A,bool),nat),hAPP(fun(C,fun(A,nat)),fun(C,fun(fun(A,bool),nat)),hAPP(fun(fun(A,nat),fun(fun(A,bool),nat)),fun(fun(C,fun(A,nat)),fun(C,fun(fun(A,bool),nat))),combb(fun(A,nat),fun(fun(A,bool),nat),C),big_co1399186613setsum(A,nat)),hAPP(fun(A,fun(C,nat)),fun(C,fun(A,nat)),combc(A,C,nat),E))),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),F))))),D). [resolve(1118,a,1097,a)].
% 2.55/2.77 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(1118,a,1098,a)].
% 2.55/2.77 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(1118,a,1100,a)].
% 2.55/2.77 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(fun(A,nat),fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(fun(A,nat),fun(A,nat)),combs(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),plus_plus(nat)),B)),C)),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),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(1118,a,1101,a)].
% 2.55/2.77 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(1118,a,1103,a)].
% 2.55/2.77 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f68(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(1118,a,1105,a)].
% 2.55/2.77 Derived: hAPP(A,nat,B,f68(A,nat,C,B,D)) != hAPP(A,nat,C,f68(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(1118,a,1106,a)].
% 2.55/2.77 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),f69(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(1118,a,1107,a)].
% 2.55/2.77 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,nat,D,f69(A,nat,E,D,C,B)) != hAPP(A,nat,E,f69(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(1118,a,1108,a)].
% 2.55/2.77 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),f70(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(1118,a,1109,a)].
% 2.55/2.77 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,nat,D,f70(A,nat,D,E,C,B)) != hAPP(A,nat,E,f70(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(1118,a,1110,a)].
% 2.55/2.77 Derived: -ordere779506340up_add(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f77(A,nat,B,C,D)),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),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(1118,a,1111,a)].
% 2.65/2.87 Derived: -ordere779506340up_add(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,f77(A,nat,B,C,D))),hAPP(A,nat,C,f77(A,nat,B,C,D)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),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(1118,a,1112,a)].
% 2.65/2.87 Derived: hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),C),D)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),B))). [resolve(1118,a,1113,a)].
% 2.65/2.87 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D)))). [resolve(1118,a,1114,a)].
% 2.65/2.87 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),f145(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(1118,a,1115,a)].
% 2.65/2.87 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,f145(A,nat,C,D,B))),hAPP(A,nat,D,f145(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(1118,a,1116,a)].
% 2.65/2.87 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,C,A)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),A),B))). [resolve(1118,a,1117,a)].
% 2.65/2.87 1119 comm_monoid_mult(int) # label(arity_Int_Oint___Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 2.65/2.87 1120 -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)].
% 2.65/2.87 1121 -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_175_setprod_Oinsert__remove) # label(axiom). [clausify(243)].
% 2.65/2.87 1122 -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_176_setprod_Oremove) # label(axiom). [clausify(244)].
% 2.65/2.87 1123 -comm_monoid_mult(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E)) # label(fact_186_setprod__timesf) # label(axiom). [clausify(254)].
% 2.65/2.87 1124 -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),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),D)),E)),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),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_194_setprod_Odistrib) # label(axiom). [clausify(262)].
% 2.65/2.87 1125 -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_197_setprod__insert) # label(axiom). [clausify(265)].
% 2.65/2.87 1126 -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_198_setprod_Oinsert) # label(axiom). [clausify(266)].
% 2.65/2.87 1127 -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),f64(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_209_setprod_Ocong) # label(axiom). [clausify(277)].
% 2.65/2.87 1128 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(B,A,D,f64(B,A,E,D,C)) != hAPP(B,A,E,f64(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_209_setprod_Ocong) # label(axiom). [clausify(277)].
% 2.65/2.87 1129 -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),f66(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_252_setprod__cong) # label(axiom). [clausify(320)].
% 2.65/2.87 1130 -comm_monoid_mult(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hAPP(B,A,E,f66(B,A,F,E,D,C)) != hAPP(B,A,F,f66(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_252_setprod__cong) # label(axiom). [clausify(320)].
% 2.65/2.87 1131 -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),f67(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_253_setprod_OF__cong) # label(axiom). [clausify(321)].
% 2.65/2.87 1132 -comm_monoid_mult(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hAPP(B,A,E,f67(B,A,E,F,D,C)) != hAPP(B,A,F,f67(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_253_setprod_OF__cong) # label(axiom). [clausify(321)].
% 2.65/2.87 1133 -comm_monoid_mult(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),combk(A,B),one_one(A))),C) = one_one(A) # label(fact_622_setprod__1) # label(axiom). [clausify(690)].
% 2.65/2.87 1134 -comm_monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) = ti(A,B) # label(fact_627_mult_Ocomm__neutral) # label(axiom). [clausify(695)].
% 2.65/2.87 1135 -comm_monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) = ti(A,B) # label(fact_630_mult__1) # label(axiom). [clausify(698)].
% 2.65/2.87 1136 -comm_monoid_mult(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),bot_bot(fun(B,bool))) = one_one(A) # label(fact_640_setprod_Oempty) # label(axiom). [clausify(708)].
% 2.65/2.87 1137 -comm_monoid_mult(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),bot_bot(fun(B,bool))) = one_one(A) # label(fact_641_setprod__empty) # label(axiom). [clausify(709)].
% 2.65/2.87 1138 -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),C) = one_one(A) # label(fact_642_setprod__infinite) # label(axiom). [clausify(710)].
% 2.65/2.87 1139 -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),C) = one_one(A) # label(fact_643_setprod_Oinfinite) # label(axiom). [clausify(711)].
% 2.65/2.87 1140 -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),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),fequal(B),D))),E)),one_one(A))),C) = hAPP(B,A,E,D) # label(fact_644_setprod__delta_H) # label(axiom). [clausify(712)].
% 2.65/2.87 1141 -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),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),fequal(B),D))),E)),one_one(A))),C) = one_one(A) # label(fact_644_setprod__delta_H) # label(axiom). [clausify(712)].
% 2.65/2.87 1142 -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),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),one_one(A))),C) = hAPP(B,A,E,D) # label(fact_645_setprod__delta) # label(axiom). [clausify(713)].
% 2.65/2.87 1143 -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),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),one_one(A))),C) = one_one(A) # label(fact_645_setprod__delta) # label(axiom). [clausify(713)].
% 2.65/2.87 1144 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f130(B,A,E,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | 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),E),D) # label(fact_652_setprod__mono__one__right) # label(axiom). [clausify(720)].
% 2.65/2.87 1145 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hAPP(B,A,E,f130(B,A,E,D,C)) != one_one(A) | 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),E),D) # label(fact_652_setprod__mono__one__right) # label(axiom). [clausify(720)].
% 2.65/2.87 1146 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f131(B,A,E,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | 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),E),D) # label(fact_653_setprod__mono__one__left) # label(axiom). [clausify(721)].
% 2.65/2.87 1147 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hAPP(B,A,E,f131(B,A,E,D,C)) != one_one(A) | 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),E),D) # label(fact_653_setprod__mono__one__left) # label(axiom). [clausify(721)].
% 2.65/2.87 1148 -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),f132(B,A,D,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) = one_one(A) # label(fact_654_setprod_Oneutral) # label(axiom). [clausify(722)].
% 2.65/2.87 1149 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(B,A,D,f132(B,A,D,C)) != one_one(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) = one_one(A) # label(fact_654_setprod_Oneutral) # label(axiom). [clausify(722)].
% 2.65/2.87 1150 -comm_monoid_mult(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f133(B,A,C,D)),D)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D) = one_one(A) # label(fact_655_setprod__1_H) # label(axiom). [clausify(723)].
% 2.65/2.87 1151 -comm_monoid_mult(A) | hAPP(B,A,C,f133(B,A,C,D)) != one_one(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D) = one_one(A) # label(fact_655_setprod__1_H) # label(axiom). [clausify(723)].
% 2.65/2.87 1152 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f134(C,A,D,E,F,B)),f136(C,A,D,E,F,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f138(C,A,D,E,F,B)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_657_setprod_Orelated) # label(axiom). [clausify(725)].
% 2.65/2.87 1153 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f134(C,A,D,E,F,B)),f136(C,A,D,E,F,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(C,A,D,f138(C,A,D,E,F,B))),hAPP(C,A,E,f138(C,A,D,E,F,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_657_setprod_Orelated) # label(axiom). [clausify(725)].
% 2.65/2.87 1154 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f135(C,A,D,E,F,B)),f137(C,A,D,E,F,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f138(C,A,D,E,F,B)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_657_setprod_Orelated) # label(axiom). [clausify(725)].
% 2.65/2.87 1155 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f135(C,A,D,E,F,B)),f137(C,A,D,E,F,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(C,A,D,f138(C,A,D,E,F,B))),hAPP(C,A,E,f138(C,A,D,E,F,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_657_setprod_Orelated) # label(axiom). [clausify(725)].
% 2.65/2.87 1156 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f134(C,A,D,E,F,B)),f135(C,A,D,E,F,B))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f136(C,A,D,E,F,B)),f137(C,A,D,E,F,B)))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f138(C,A,D,E,F,B)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_657_setprod_Orelated) # label(axiom). [clausify(725)].
% 2.65/2.87 1157 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f134(C,A,D,E,F,B)),f135(C,A,D,E,F,B))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f136(C,A,D,E,F,B)),f137(C,A,D,E,F,B)))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(C,A,D,f138(C,A,D,E,F,B))),hAPP(C,A,E,f138(C,A,D,E,F,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_657_setprod_Orelated) # label(axiom). [clausify(725)].
% 2.65/2.87 1158 -comm_monoid_mult(A) | -semiring_1(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(fun(B,nat),fun(B,A),hAPP(fun(nat,A),fun(fun(B,nat),fun(B,A)),combb(nat,A,B),semiring_1_of_nat(A)),C)),D) = hAPP(nat,A,semiring_1_of_nat(A),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),D)) # label(fact_666_of__nat__setprod) # label(axiom). [clausify(734)].
% 2.65/2.87 1159 -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),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),F)),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(B,A,E,D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),F),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(B,bool),nat,finite_card(B),C)),one_one(nat)))) # label(fact_678_setprod__gen__delta) # label(axiom). [clausify(745)].
% 2.65/2.87 1160 -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),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),F)),C) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),F),hAPP(fun(B,bool),nat,finite_card(B),C)) # label(fact_678_setprod__gen__delta) # label(axiom). [clausify(745)].
% 2.65/2.87 1161 -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),hAPP(A,fun(B,A),combk(A,B),D)),C) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),hAPP(fun(B,bool),nat,finite_card(B),C)) # label(fact_838_setprod__constant) # label(axiom). [clausify(905)].
% 2.65/2.87 1162 -comm_monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(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(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D)) # label(fact_872_power__mult__distrib) # label(axiom). [clausify(939)].
% 2.65/2.88 Derived: big_co302546470etprod(A,int) = ti(fun(fun(A,int),fun(fun(A,bool),int)),big_co302546470etprod(A,int)). [resolve(1119,a,1120,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(A,int,C,D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),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(1119,a,1121,a)].
% 2.65/2.88 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),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(A,int,D,C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),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(1119,a,1122,a)].
% 2.65/2.88 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(A,fun(int,int)),fun(fun(A,int),fun(A,int)),combs(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),times_times(int)),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),D)). [resolve(1119,a,1123,a)].
% 2.65/2.88 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),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(A,int,D,C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B)). [resolve(1119,a,1125,a)].
% 2.65/2.88 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),f64(A,int,C,D,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B). [resolve(1119,a,1127,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,int,C,f64(A,int,D,C,B)) != hAPP(A,int,D,f64(A,int,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B). [resolve(1119,a,1128,a)].
% 2.65/2.88 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),f66(A,int,D,E,C,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),E),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C). [resolve(1119,a,1129,a)].
% 2.65/2.88 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,int,D,f66(A,int,E,D,C,B)) != hAPP(A,int,E,f66(A,int,E,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),E),C). [resolve(1119,a,1130,a)].
% 2.65/2.88 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),f67(A,int,D,E,C,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),E),B). [resolve(1119,a,1131,a)].
% 2.65/2.88 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,int,D,f67(A,int,D,E,C,B)) != hAPP(A,int,E,f67(A,int,D,E,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),E),B). [resolve(1119,a,1132,a)].
% 2.65/2.88 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),combk(int,A),one_one(int))),B) = one_one(int). [resolve(1119,a,1133,a)].
% 2.65/2.88 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),one_one(int)) = ti(int,A). [resolve(1119,a,1134,a)].
% 2.65/2.88 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),A) = ti(int,A). [resolve(1119,a,1135,a)].
% 2.65/2.88 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),bot_bot(fun(A,bool))) = one_one(int). [resolve(1119,a,1136,a)].
% 2.65/2.88 Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B) = one_one(int). [resolve(1119,a,1138,a)].
% 2.65/2.88 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),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(int))),B) = hAPP(A,int,D,C). [resolve(1119,a,1140,a)].
% 2.65/2.88 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),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(int))),B) = one_one(int). [resolve(1119,a,1141,a)].
% 2.65/2.88 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),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(int))),B) = hAPP(A,int,D,C). [resolve(1119,a,1142,a)].
% 2.65/2.88 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),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(int))),B) = one_one(int). [resolve(1119,a,1143,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f130(A,int,D,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),C))) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C). [resolve(1119,a,1144,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(A,int,D,f130(A,int,D,C,B)) != one_one(int) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C). [resolve(1119,a,1145,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f131(A,int,D,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),C))) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C). [resolve(1119,a,1146,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(A,int,D,f131(A,int,D,C,B)) != one_one(int) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C). [resolve(1119,a,1147,a)].
% 2.65/2.88 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),f132(A,int,C,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B) = one_one(int). [resolve(1119,a,1148,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,int,C,f132(A,int,C,B)) != one_one(int) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B) = one_one(int). [resolve(1119,a,1149,a)].
% 2.65/2.88 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f133(A,int,B,C)),C)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C) = one_one(int). [resolve(1119,a,1150,a)].
% 2.65/2.88 Derived: hAPP(A,int,B,f133(A,int,B,C)) != one_one(int) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C) = one_one(int). [resolve(1119,a,1151,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f134(B,int,C,D,E,A)),f136(B,int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f138(B,int,C,D,E,A)),E)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))). [resolve(1119,a,1152,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f134(B,int,C,D,E,A)),f136(B,int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(B,int,C,f138(B,int,C,D,E,A))),hAPP(B,int,D,f138(B,int,C,D,E,A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))). [resolve(1119,a,1153,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f135(B,int,C,D,E,A)),f137(B,int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f138(B,int,C,D,E,A)),E)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))). [resolve(1119,a,1154,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f135(B,int,C,D,E,A)),f137(B,int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(B,int,C,f138(B,int,C,D,E,A))),hAPP(B,int,D,f138(B,int,C,D,E,A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))). [resolve(1119,a,1155,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f134(B,int,C,D,E,A)),f135(B,int,C,D,E,A))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f136(B,int,C,D,E,A)),f137(B,int,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f138(B,int,C,D,E,A)),E)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))). [resolve(1119,a,1156,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f134(B,int,C,D,E,A)),f135(B,int,C,D,E,A))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f136(B,int,C,D,E,A)),f137(B,int,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(B,int,C,f138(B,int,C,D,E,A))),hAPP(B,int,D,f138(B,int,C,D,E,A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))). [resolve(1119,a,1157,a)].
% 2.65/2.88 Derived: -semiring_1(int) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(fun(A,nat),fun(A,int),hAPP(fun(nat,int),fun(fun(A,nat),fun(A,int)),combb(nat,int,A),semiring_1_of_nat(int)),B)),C) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C)). [resolve(1119,a,1158,a)].
% 2.65/2.88 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),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(A,int,D,C)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),E),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(A,bool),nat,finite_card(A),B)),one_one(nat)))). [resolve(1119,a,1159,a)].
% 2.65/2.88 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),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),E),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(1119,a,1160,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),combk(int,A),C)),B) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(1119,a,1161,a)].
% 2.65/2.88 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),C)). [resolve(1119,a,1162,a)].
% 2.65/2.88 1163 comm_monoid_mult(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 2.65/2.88 Derived: big_co302546470etprod(A,nat) = ti(fun(fun(A,nat),fun(fun(A,bool),nat)),big_co302546470etprod(A,nat)). [resolve(1163,a,1120,a)].
% 2.65/2.88 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(1163,a,1121,a)].
% 2.65/2.88 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(1163,a,1122,a)].
% 2.65/2.88 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(fun(A,nat),fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(fun(A,nat),fun(A,nat)),combs(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),times_times(nat)),B)),C)),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),D)). [resolve(1163,a,1123,a)].
% 2.65/2.88 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(1163,a,1125,a)].
% 2.65/2.88 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),f64(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(1163,a,1127,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,nat,C,f64(A,nat,D,C,B)) != hAPP(A,nat,D,f64(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(1163,a,1128,a)].
% 2.65/2.88 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),f66(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(1163,a,1129,a)].
% 2.65/2.88 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,nat,D,f66(A,nat,E,D,C,B)) != hAPP(A,nat,E,f66(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(1163,a,1130,a)].
% 2.65/2.88 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),f67(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(1163,a,1131,a)].
% 2.65/2.88 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,nat,D,f67(A,nat,D,E,C,B)) != hAPP(A,nat,E,f67(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(1163,a,1132,a)].
% 2.65/2.88 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),combk(nat,A),one_one(nat))),B) = one_one(nat). [resolve(1163,a,1133,a)].
% 2.65/2.88 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),one_one(nat)) = ti(nat,A). [resolve(1163,a,1134,a)].
% 2.65/2.88 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),A) = ti(nat,A). [resolve(1163,a,1135,a)].
% 2.65/2.88 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),bot_bot(fun(A,bool))) = one_one(nat). [resolve(1163,a,1136,a)].
% 2.65/2.88 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),B) = one_one(nat). [resolve(1163,a,1138,a)].
% 2.65/2.88 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),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(nat))),B) = hAPP(A,nat,D,C). [resolve(1163,a,1140,a)].
% 2.65/2.88 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),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(nat))),B) = one_one(nat). [resolve(1163,a,1141,a)].
% 2.65/2.88 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),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(nat))),B) = hAPP(A,nat,D,C). [resolve(1163,a,1142,a)].
% 2.65/2.88 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),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(nat))),B) = one_one(nat). [resolve(1163,a,1143,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f130(A,nat,D,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),C))) | 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),D),C). [resolve(1163,a,1144,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(A,nat,D,f130(A,nat,D,C,B)) != one_one(nat) | 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),D),C). [resolve(1163,a,1145,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f131(A,nat,D,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),C))) | 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),D),C). [resolve(1163,a,1146,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(A,nat,D,f131(A,nat,D,C,B)) != one_one(nat) | 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),D),C). [resolve(1163,a,1147,a)].
% 2.65/2.88 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),f132(A,nat,C,B)),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B) = one_one(nat). [resolve(1163,a,1148,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,nat,C,f132(A,nat,C,B)) != one_one(nat) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B) = one_one(nat). [resolve(1163,a,1149,a)].
% 2.65/2.88 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f133(A,nat,B,C)),C)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C) = one_one(nat). [resolve(1163,a,1150,a)].
% 2.65/2.88 Derived: hAPP(A,nat,B,f133(A,nat,B,C)) != one_one(nat) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C) = one_one(nat). [resolve(1163,a,1151,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f134(B,nat,C,D,E,A)),f136(B,nat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f138(B,nat,C,D,E,A)),E)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))). [resolve(1163,a,1152,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f134(B,nat,C,D,E,A)),f136(B,nat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(B,nat,C,f138(B,nat,C,D,E,A))),hAPP(B,nat,D,f138(B,nat,C,D,E,A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))). [resolve(1163,a,1153,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f135(B,nat,C,D,E,A)),f137(B,nat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f138(B,nat,C,D,E,A)),E)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))). [resolve(1163,a,1154,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f135(B,nat,C,D,E,A)),f137(B,nat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(B,nat,C,f138(B,nat,C,D,E,A))),hAPP(B,nat,D,f138(B,nat,C,D,E,A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))). [resolve(1163,a,1155,a)].
% 2.65/2.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f134(B,nat,C,D,E,A)),f135(B,nat,C,D,E,A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f136(B,nat,C,D,E,A)),f137(B,nat,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f138(B,nat,C,D,E,A)),E)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))). [resolve(1163,a,1156,a)].
% 2.81/3.00 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f134(B,nat,C,D,E,A)),f135(B,nat,C,D,E,A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f136(B,nat,C,D,E,A)),f137(B,nat,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(B,nat,C,f138(B,nat,C,D,E,A))),hAPP(B,nat,D,f138(B,nat,C,D,E,A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))). [resolve(1163,a,1157,a)].
% 2.81/3.00 Derived: -semiring_1(nat) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(fun(A,nat),fun(A,nat),hAPP(fun(nat,nat),fun(fun(A,nat),fun(A,nat)),combb(nat,nat,A),semiring_1_of_nat(nat)),B)),C) = hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C)). [resolve(1163,a,1158,a)].
% 2.81/3.00 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),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(A,nat,D,C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),E),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(A,bool),nat,finite_card(A),B)),one_one(nat)))). [resolve(1163,a,1159,a)].
% 2.81/3.00 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),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),E),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(1163,a,1160,a)].
% 2.81/3.00 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),hAPP(nat,fun(A,nat),combk(nat,A),C)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(1163,a,1161,a)].
% 2.81/3.00 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(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),power_power(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),C)). [resolve(1163,a,1162,a)].
% 2.81/3.00 1164 linorder(int) # label(arity_Int_Oint___Orderings_Olinorder) # label(axiom). [assumption].
% 2.81/3.00 1165 -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)].
% 2.81/3.00 1166 -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)].
% 2.81/3.00 1167 -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)].
% 2.81/3.00 1168 -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)].
% 2.81/3.00 1169 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_265_linorder__le__cases) # label(axiom). [clausify(333)].
% 2.81/3.00 1170 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_279_linorder__linear) # label(axiom). [clausify(347)].
% 2.81/3.00 1171 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),ord_lessThan(A),B)),hAPP(A,fun(A,bool),ord_lessThan(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_292_lessThan__subset__iff) # label(axiom). [clausify(360)].
% 2.81/3.00 1172 -linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),ord_lessThan(A),B)),hAPP(A,fun(A,bool),ord_lessThan(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_292_lessThan__subset__iff) # label(axiom). [clausify(360)].
% 2.81/3.00 1173 -linorder(A) | hAPP(A,fun(A,bool),ord_lessThan(A),B) != hAPP(A,fun(A,bool),ord_lessThan(A),C) | ti(A,B) = ti(A,C) # label(fact_293_lessThan__eq__iff) # label(axiom). [clausify(361)].
% 2.81/3.00 1174 -linorder(A) | hAPP(A,fun(A,bool),ord_lessThan(A),B) = hAPP(A,fun(A,bool),ord_lessThan(A),C) | ti(A,B) != ti(A,C) # label(fact_293_lessThan__eq__iff) # label(axiom). [clausify(361)].
% 2.81/3.00 1175 -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_338_fold1__antimono) # label(axiom). [clausify(406)].
% 2.81/3.00 1176 -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_341_Min__antimono) # label(axiom). [clausify(409)].
% 2.81/3.00 1177 -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_342_Max__mono) # label(axiom). [clausify(410)].
% 2.81/3.00 1178 -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_346_Min_Oin__idem) # label(axiom). [clausify(414)].
% 2.81/3.00 1179 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),B) = ti(A,B) # label(fact_347_Min_Oidem) # label(axiom). [clausify(415)].
% 2.81/3.00 1180 -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_348_min__max_Oinf__assoc) # label(axiom). [clausify(416)].
% 2.81/3.00 1181 -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_349_min__max_Oinf_Oassoc) # label(axiom). [clausify(417)].
% 2.81/3.00 1182 -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_350_min__max_Oinf__left__commute) # label(axiom). [clausify(418)].
% 2.81/3.00 1183 -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_351_min__max_Oinf_Oleft__commute) # label(axiom). [clausify(419)].
% 2.81/3.00 1184 -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_352_min__max_Oinf__left__idem) # label(axiom). [clausify(420)].
% 2.81/3.00 1185 -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_353_min__max_Oinf_Oleft__idem) # label(axiom). [clausify(421)].
% 2.81/3.00 1186 -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_354_min__max_Oinf__commute) # label(axiom). [clausify(422)].
% 2.81/3.00 1187 -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_355_min__max_Oinf_Ocommute) # label(axiom). [clausify(423)].
% 2.81/3.00 1188 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),B) = ti(A,B) # label(fact_356_min__max_Oinf_Oidem) # label(axiom). [clausify(424)].
% 2.81/3.00 1189 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_357_min__le__iff__disj) # label(axiom). [clausify(425)].
% 2.81/3.00 1190 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_357_min__le__iff__disj) # label(axiom). [clausify(425)].
% 2.81/3.00 1191 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_357_min__le__iff__disj) # label(axiom). [clausify(425)].
% 2.81/3.00 1192 -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_358_min__max_Ole__infE) # label(axiom). [clausify(426)].
% 2.81/3.00 1193 -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_358_min__max_Ole__infE) # label(axiom). [clausify(426)].
% 2.81/3.00 1194 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),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_359_min__max_Oinf__mono) # label(axiom). [clausify(427)].
% 2.81/3.00 1195 -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_360_min__max_Oinf__greatest) # label(axiom). [clausify(428)].
% 2.81/3.00 1196 -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_361_min__max_Ole__infI) # label(axiom). [clausify(429)].
% 2.81/3.00 1197 -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_362_min__max_Oinf__absorb2) # label(axiom). [clausify(430)].
% 2.81/3.00 1198 -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_363_min__max_Oinf__absorb1) # label(axiom). [clausify(431)].
% 2.81/3.00 1199 -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_364_min__max_Ole__infI2) # label(axiom). [clausify(432)].
% 2.81/3.00 1200 -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_365_min__max_Ole__infI1) # label(axiom). [clausify(433)].
% 2.81/3.00 1201 -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_366_min__max_Ole__inf__iff) # label(axiom). [clausify(434)].
% 2.81/3.00 1202 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_366_min__max_Ole__inf__iff) # label(axiom). [clausify(434)].
% 2.81/3.00 1203 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_366_min__max_Ole__inf__iff) # label(axiom). [clausify(434)].
% 2.81/3.00 1204 -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_367_min__max_Ole__iff__inf) # label(axiom). [clausify(435)].
% 2.81/3.00 1205 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) != ti(A,B) # label(fact_367_min__max_Ole__iff__inf) # label(axiom). [clausify(435)].
% 2.81/3.00 1206 -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_368_min__max_Oinf__le2) # label(axiom). [clausify(436)].
% 2.81/3.00 1207 -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_369_min__max_Oinf__le1) # label(axiom). [clausify(437)].
% 2.81/3.00 1208 -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_372_Min_OF__eq) # label(axiom). [clausify(440)].
% 2.81/3.00 1209 -linorder(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite_comp_fun_idem(A,A),ord_min(A))) # label(fact_373_min__max_Ocomp__fun__idem__inf) # label(axiom). [clausify(441)].
% 2.81/3.00 1210 -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_374_Min__insert) # label(axiom). [clausify(442)].
% 2.81/3.00 1211 -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_375_Min_Oinsert) # label(axiom). [clausify(443)].
% 2.81/3.00 1212 -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_376_Min_Osubset__idem) # label(axiom). [clausify(444)].
% 2.81/3.00 1213 -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_377_Min_Oeq__fold_H) # label(axiom). [clausify(445)].
% 2.81/3.00 1214 -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_378_Min_Oeq__fold__idem_H) # label(axiom). [clausify(446)].
% 2.81/3.00 1215 -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_379_Min_Oinsert__remove) # label(axiom). [clausify(447)].
% 2.81/3.00 1216 -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_379_Min_Oinsert__remove) # label(axiom). [clausify(447)].
% 2.81/3.00 1217 -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_380_Min_Oremove) # label(axiom). [clausify(448)].
% 2.81/3.00 1218 -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_380_Min_Oremove) # label(axiom). [clausify(448)].
% 2.81/3.00 1219 -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_381_Max__ge) # label(axiom). [clausify(449)].
% 2.81/3.00 1220 -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_382_Min__le) # label(axiom). [clausify(450)].
% 2.81/3.00 1221 -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_383_Max__in) # label(axiom). [clausify(451)].
% 2.81/3.00 1222 -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_384_Min__in) # label(axiom). [clausify(452)].
% 2.81/3.00 1223 -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_385_Min_Osingleton) # label(axiom). [clausify(453)].
% 2.81/3.00 1224 -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_386_Max_Osingleton) # label(axiom). [clausify(454)].
% 2.81/3.00 1225 -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_387_min__max_Ofold__inf__le__inf) # label(axiom). [clausify(455)].
% 2.81/3.00 1226 -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_388_min__max_Ofold__inf__insert) # label(axiom). [clausify(456)].
% 2.81/3.00 1227 -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_389_min__max_Ofold1__belowI) # label(axiom). [clausify(457)].
% 2.81/3.00 1228 -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),f85(A,C,B)),B)) # label(fact_390_fold1__below__iff) # label(axiom). [clausify(458)].
% 2.81/3.00 1229 -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),f85(A,C,B)),C)) # label(fact_390_fold1__below__iff) # label(axiom). [clausify(458)].
% 2.81/3.00 1230 -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_390_fold1__below__iff) # label(axiom). [clausify(458)].
% 2.81/3.00 1231 -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_391_min__max_Obelow__fold1__iff) # label(axiom). [clausify(459)].
% 2.81/3.00 1232 -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),f86(A,C,B)),B)) # label(fact_391_min__max_Obelow__fold1__iff) # label(axiom). [clausify(459)].
% 2.81/3.00 1233 -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),f86(A,C,B))) # label(fact_391_min__max_Obelow__fold1__iff) # label(axiom). [clausify(459)].
% 2.81/3.00 1234 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,B,f87(A,C,B))),hAPP(A,A,B,f88(A,C,B))) != hAPP(A,A,B,hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f87(A,C,B)),f88(A,C,B))) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),C) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),B),C)) = hAPP(A,A,B,hAPP(fun(A,bool),A,big_linorder_Min(A),C)) # label(fact_392_Min_Ohom__commute) # label(axiom). [clausify(460)].
% 2.81/3.00 1235 -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),f89(A,B)),f90(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f89(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f90(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_393_Min_Oclosed) # label(axiom). [clausify(461)].
% 2.81/3.00 1236 -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),f91(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_394_min__max_Oinf__le__fold__inf) # label(axiom). [clausify(462)].
% 2.81/3.00 1237 -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),f91(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_394_min__max_Oinf__le__fold__inf) # label(axiom). [clausify(462)].
% 2.81/3.00 1238 -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),f92(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_395_Min__eqI) # label(axiom). [clausify(463)].
% 2.81/3.00 1239 -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),f92(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_395_Min__eqI) # label(axiom). [clausify(463)].
% 2.81/3.00 1240 -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),f93(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_396_Max__eqI) # label(axiom). [clausify(464)].
% 2.81/3.00 1241 -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),f93(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_396_Max__eqI) # label(axiom). [clausify(464)].
% 2.81/3.00 1242 -linorder(A) | hAPP(fun(A,fun(A,bool)),fun(A,fun(A,A)),max(A),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),ord_less_eq(A))) = ord_min(A) # label(fact_397_dual__max) # label(axiom). [clausify(465)].
% 2.81/3.00 1243 -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_468_min__max_OInf__fin_Oremove) # label(axiom). [clausify(536)].
% 2.81/3.00 1244 -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_468_min__max_OInf__fin_Oremove) # label(axiom). [clausify(536)].
% 2.81/3.00 1245 -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_469_min__max_OInf__fin_Oinsert__remove) # label(axiom). [clausify(537)].
% 2.81/3.00 1246 -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_469_min__max_OInf__fin_Oinsert__remove) # label(axiom). [clausify(537)].
% 2.81/3.00 1247 -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_470_min__max_OInf__fin_Oin__idem) # label(axiom). [clausify(538)].
% 2.81/3.00 1248 -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_471_min__max_OInf__fin_Osingleton) # label(axiom). [clausify(539)].
% 2.81/3.00 1249 -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_472_min__max_OInf__fin_OF__eq) # label(axiom). [clausify(540)].
% 2.81/3.00 1250 -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_473_min__max_OInf__fin_Oinsert__idem) # label(axiom). [clausify(541)].
% 2.81/3.00 1251 -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_474_min__max_OInf__fin_Oinsert) # label(axiom). [clausify(542)].
% 2.81/3.00 1252 -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_475_min__max_OInf__fin_Osubset__idem) # label(axiom). [clausify(543)].
% 2.81/3.00 1253 -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_476_min__max_OInf__fin_Oeq__fold_H) # label(axiom). [clausify(544)].
% 2.81/3.00 1254 -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_477_min__max_OInf__fin_Oeq__fold__idem_H) # label(axiom). [clausify(545)].
% 2.81/3.00 1255 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,B,f98(A,C,B))),hAPP(A,A,B,f99(A,C,B))) != hAPP(A,A,B,hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f98(A,C,B)),f99(A,C,B))) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),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,A),fun(fun(A,bool),fun(A,bool)),image(A,A),B),C)) = hAPP(A,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)),C)) # label(fact_478_min__max_OInf__fin_Ohom__commute) # label(axiom). [clausify(546)].
% 2.81/3.00 1256 -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),f100(A,B)),f101(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f100(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f101(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_479_min__max_OInf__fin_Oclosed) # label(axiom). [clausify(547)].
% 2.81/3.00 1257 -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_518_Max_Oremove) # label(axiom). [clausify(586)].
% 2.81/3.00 1258 -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_518_Max_Oremove) # label(axiom). [clausify(586)].
% 2.81/3.00 1259 -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_519_Max_Oinsert__remove) # label(axiom). [clausify(587)].
% 2.81/3.00 1260 -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_519_Max_Oinsert__remove) # label(axiom). [clausify(587)].
% 2.81/3.00 1261 -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_528_min__max_Oinf__sup__distrib2) # label(axiom). [clausify(596)].
% 2.81/3.00 1262 -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_529_min__max_Osup__inf__distrib2) # label(axiom). [clausify(597)].
% 2.81/3.00 1263 -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_530_min__max_Oinf__sup__distrib1) # label(axiom). [clausify(598)].
% 2.81/3.00 1264 -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_531_min__max_Osup__inf__distrib1) # label(axiom). [clausify(599)].
% 2.81/3.00 1265 -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_532_min__max_Oinf__sup__absorb) # label(axiom). [clausify(600)].
% 2.81/3.00 1266 -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_533_min__max_Osup__inf__absorb) # label(axiom). [clausify(601)].
% 2.81/3.00 1267 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),B) = ti(A,B) # label(fact_536_Max_Oidem) # label(axiom). [clausify(604)].
% 2.81/3.00 1268 -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_537_min__max_Osup__assoc) # label(axiom). [clausify(605)].
% 2.81/3.00 1269 -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_538_min__max_Osup_Oassoc) # label(axiom). [clausify(606)].
% 2.81/3.00 1270 -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_539_min__max_Osup__left__commute) # label(axiom). [clausify(607)].
% 2.81/3.00 1271 -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_540_min__max_Osup_Oleft__commute) # label(axiom). [clausify(608)].
% 2.81/3.00 1272 -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_541_min__max_Osup__left__idem) # label(axiom). [clausify(609)].
% 2.81/3.00 1273 -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_542_min__max_Osup_Oleft__idem) # label(axiom). [clausify(610)].
% 2.81/3.00 1274 -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_543_min__max_Osup__commute) # label(axiom). [clausify(611)].
% 2.81/3.00 1275 -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_544_min__max_Osup_Ocommute) # label(axiom). [clausify(612)].
% 2.81/3.00 1276 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),B) = ti(A,B) # label(fact_545_min__max_Osup_Oidem) # label(axiom). [clausify(613)].
% 2.81/3.00 1277 -linorder(A) | hAPP(A,fun(A,bool),ord_greaterThan(A),B) != hAPP(A,fun(A,bool),ord_greaterThan(A),C) | ti(A,B) = ti(A,C) # label(fact_546_greaterThan__eq__iff) # label(axiom). [clausify(614)].
% 2.81/3.00 1278 -linorder(A) | hAPP(A,fun(A,bool),ord_greaterThan(A),B) = hAPP(A,fun(A,bool),ord_greaterThan(A),C) | ti(A,B) != ti(A,C) # label(fact_546_greaterThan__eq__iff) # label(axiom). [clausify(614)].
% 2.81/3.00 1279 -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_547_le__maxI1) # label(axiom). [clausify(615)].
% 2.81/3.00 1280 -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_548_le__maxI2) # label(axiom). [clausify(616)].
% 2.81/3.00 1281 -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_549_min__max_Ole__iff__sup) # label(axiom). [clausify(617)].
% 2.81/3.00 1282 -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_549_min__max_Ole__iff__sup) # label(axiom). [clausify(617)].
% 2.81/3.00 1283 -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_550_min__max_Ole__sup__iff) # label(axiom). [clausify(618)].
% 2.81/3.00 1284 -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_550_min__max_Ole__sup__iff) # label(axiom). [clausify(618)].
% 2.81/3.00 1285 -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_550_min__max_Ole__sup__iff) # label(axiom). [clausify(618)].
% 2.81/3.00 1286 -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_551_min__max_Ole__supI1) # label(axiom). [clausify(619)].
% 2.81/3.00 1287 -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_552_min__max_Ole__supI2) # label(axiom). [clausify(620)].
% 2.81/3.00 1288 -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_553_min__max_Osup__absorb2) # label(axiom). [clausify(621)].
% 2.81/3.00 1289 -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_554_min__max_Osup__absorb1) # label(axiom). [clausify(622)].
% 2.81/3.00 1290 -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_555_min__max_Ole__supI) # label(axiom). [clausify(623)].
% 2.81/3.00 1291 -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_556_min__max_Osup__least) # label(axiom). [clausify(624)].
% 2.81/3.00 1292 -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_557_min__max_Osup__mono) # label(axiom). [clausify(625)].
% 2.81/3.00 1293 -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_558_min__max_Ole__supE) # label(axiom). [clausify(626)].
% 2.81/3.00 1294 -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_558_min__max_Ole__supE) # label(axiom). [clausify(626)].
% 2.81/3.00 1295 -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_559_le__max__iff__disj) # label(axiom). [clausify(627)].
% 2.81/3.00 1296 -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_559_le__max__iff__disj) # label(axiom). [clausify(627)].
% 2.81/3.00 1297 -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_559_le__max__iff__disj) # label(axiom). [clausify(627)].
% 2.81/3.00 1298 -linorder(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite_comp_fun_idem(A,A),ord_max(A))) # label(fact_560_min__max_Ocomp__fun__idem__sup) # label(axiom). [clausify(628)].
% 2.81/3.00 1299 -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_561_min__max_Odistrib__inf__le) # label(axiom). [clausify(629)].
% 2.81/3.00 1300 -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_562_min__max_Odistrib__sup__le) # label(axiom). [clausify(630)].
% 2.81/3.00 1301 -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_566_Max_Oin__idem) # label(axiom). [clausify(634)].
% 2.81/3.00 1302 -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_567_min__max_Osup__le__fold__sup) # label(axiom). [clausify(635)].
% 2.81/3.00 1303 -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_569_min__max_Ofold__sup__insert) # label(axiom). [clausify(637)].
% 2.81/3.00 1304 -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_570_min__max_Osup__Inf__absorb) # label(axiom). [clausify(638)].
% 2.81/3.00 1305 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),ord_greaterThan(A),B)),hAPP(A,fun(A,bool),ord_greaterThan(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_571_greaterThan__subset__iff) # label(axiom). [clausify(639)].
% 2.81/3.00 1306 -linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),ord_greaterThan(A),B)),hAPP(A,fun(A,bool),ord_greaterThan(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_571_greaterThan__subset__iff) # label(axiom). [clausify(639)].
% 2.81/3.00 1307 -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_572_Max_OF__eq) # label(axiom). [clausify(640)].
% 2.81/3.00 1308 -linorder(A) | hAPP(fun(A,fun(A,bool)),fun(A,fun(A,A)),min(A),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),ord_less_eq(A))) = ord_max(A) # label(fact_573_dual__min) # label(axiom). [clausify(641)].
% 2.81/3.00 1309 -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_574_Max__insert) # label(axiom). [clausify(642)].
% 2.81/3.00 1310 -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_575_Max_Oinsert) # label(axiom). [clausify(643)].
% 2.81/3.00 1311 -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_576_Max_Osubset__idem) # label(axiom). [clausify(644)].
% 2.81/3.00 1312 -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_577_Max_Oeq__fold_H) # label(axiom). [clausify(645)].
% 2.81/3.00 1313 -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_578_Max_Oeq__fold__idem_H) # label(axiom). [clausify(646)].
% 2.81/3.00 1314 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,B,f102(A,C,B))),hAPP(A,A,B,f103(A,C,B))) != hAPP(A,A,B,hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f102(A,C,B)),f103(A,C,B))) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),C) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),B),C)) = hAPP(A,A,B,hAPP(fun(A,bool),A,big_linorder_Max(A),C)) # label(fact_579_Max_Ohom__commute) # label(axiom). [clausify(647)].
% 2.81/3.00 1315 -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),f104(A,B)),f105(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f104(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f105(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_580_Max_Oclosed) # label(axiom). [clausify(648)].
% 2.81/3.00 1316 -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),f106(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_581_min__max_Ofold__sup__le__sup) # label(axiom). [clausify(649)].
% 2.81/3.00 1317 -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),f106(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_581_min__max_Ofold__sup__le__sup) # label(axiom). [clausify(649)].
% 2.81/3.00 1318 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f107(A,B,C,D)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f108(A,B,C,D)),f109(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),f107(A,B,C,D)),f108(A,B,C,D))),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f107(A,B,C,D)),f109(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_582_min__max_Odistrib__imp1) # label(axiom). [clausify(650)].
% 2.81/3.00 1319 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f110(A,B,C,D)),f111(A,B,C,D))),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f110(A,B,C,D)),f112(A,B,C,D))) != hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f110(A,B,C,D)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f111(A,B,C,D)),f112(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_583_min__max_Odistrib__imp2) # label(axiom). [clausify(651)].
% 2.81/3.01 1320 -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_586_min__max_OInf__le__Sup) # label(axiom). [clausify(654)].
% 2.81/3.01 1321 -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,finite_finite_1(A),C)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),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),collect(A),hAPP(fun(A,fun(A,bool)),fun(A,bool),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A)),hAPP(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,bool)),hAPP(fun(fun(A,fun(A,bool)),fun(A,bool)),fun(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,bool))),combb(fun(A,fun(A,bool)),fun(A,bool),A),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A))),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,fun(A,bool))),hAPP(fun(A,fun(fun(A,fun(A,bool)),fun(A,fun(A,bool)))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(A,bool)))),combc(A,fun(A,fun(A,bool)),fun(A,fun(A,bool))),hAPP(fun(A,fun(A,fun(fun(A,bool),fun(A,bool)))),fun(A,fun(fun(A,fun(A,bool)),fun(A,fun(A,bool)))),hAPP(fun(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,bool)))),fun(fun(A,fun(A,fun(fun(A,bool),fun(A,bool)))),fun(A,fun(fun(A,fun(A,bool)),fun(A,fun(A,bool))))),combb(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,bool))),A),combs(A,fun(A,bool),fun(A,bool))),hAPP(fun(A,fun(A,fun(A,fun(bool,bool)))),fun(A,fun(A,fun(fun(A,bool),fun(A,bool)))),hAPP(fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),fun(fun(A,fun(A,fun(A,fun(bool,bool)))),fun(A,fun(A,fun(fun(A,bool),fun(A,bool))))),combb(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool))),A),hAPP(fun(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),A),combs(A,bool,bool))),hAPP(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,fun(A,fun(bool,bool)))),hAPP(fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),fun(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,fun(A,fun(bool,bool))))),combb(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool))),A),hAPP(fun(fun(A,bool),fun(A,fun(bool,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),combb(fun(A,bool),fun(A,fun(bool,bool)),A),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj))),hAPP(fun(A,fun(A,A)),fun(A,fun(A,fun(A,bool))),hAPP(fun(A,fun(fun(A,fun(A,A)),fun(A,fun(A,bool)))),fun(fun(A,fun(A,A)),fun(A,fun(A,fun(A,bool)))),combc(A,fun(A,fun(A,A)),fun(A,fun(A,bool))),hAPP(fun(A,fun(fun(A,A),fun(A,bool))),fun(A,fun(fun(A,fun(A,A)),fun(A,fun(A,bool)))),hAPP(fun(fun(fun(A,A),fun(A,bool)),fun(fun(A,fun(A,A)),fun(A,fun(A,bool)))),fun(fun(A,fun(fun(A,A),fun(A,bool))),fun(A,fun(fun(A,fun(A,A)),fun(A,fun(A,bool))))),combb(fun(fun(A,A),fun(A,bool)),fun(fun(A,fun(A,A)),fun(A,fun(A,bool))),A),combb(fun(A,A),fun(A,bool),A)),hAPP(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool))),hAPP(fun(fun(A,bool),fun(fun(A,A),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool)))),combb(fun(A,bool),fun(fun(A,A),fun(A,bool)),A),combb(A,bool,A)),fequal(A)))),ord_max(A)))))),hAPP(fun(A,bool),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,bool),fun(A,fun(A,bool))),combc(A,fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(bool,bool)),fun(A,fun(fun(A,bool),fun(A,bool))),hAPP(fun(fun(bool,bool),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(bool,bool)),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(bool,bool),fun(fun(A,bool),fun(A,bool)),A),combb(bool,bool,A)),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),C))))))) = 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_Inf_fin(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)),C)) # label(fact_587_min__max_Osup__Inf2__distrib) # label(axiom). [clausify(655)].
% 2.81/3.01 1322 -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),collect(A),hAPP(fun(A,fun(A,bool)),fun(A,bool),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A)),hAPP(fun(A,bool),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,bool),fun(A,fun(A,bool))),combc(A,fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool))),hAPP(fun(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),A),combs(A,bool,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool))),hAPP(fun(fun(A,bool),fun(A,fun(bool,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),combb(fun(A,bool),fun(A,fun(bool,bool)),A),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj)),hAPP(fun(A,A),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,A),fun(A,bool))),fun(fun(A,A),fun(A,fun(A,bool))),combc(A,fun(A,A),fun(A,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool))),hAPP(fun(fun(A,bool),fun(fun(A,A),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool)))),combb(fun(A,bool),fun(fun(A,A),fun(A,bool)),A),combb(A,bool,A)),fequal(A))),hAPP(A,fun(A,A),ord_max(A),C))))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(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_Inf_fin(A),ord_min(A)),B)) # label(fact_588_min__max_Osup__Inf1__distrib) # label(axiom). [clausify(656)].
% 2.81/3.01 1323 -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),collect(A),hAPP(fun(A,fun(A,bool)),fun(A,bool),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A)),hAPP(fun(A,bool),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,bool),fun(A,fun(A,bool))),combc(A,fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool))),hAPP(fun(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),A),combs(A,bool,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool))),hAPP(fun(fun(A,bool),fun(A,fun(bool,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),combb(fun(A,bool),fun(A,fun(bool,bool)),A),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj)),hAPP(fun(A,A),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,A),fun(A,bool))),fun(fun(A,A),fun(A,fun(A,bool))),combc(A,fun(A,A),fun(A,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool))),hAPP(fun(fun(A,bool),fun(fun(A,A),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool)))),combb(fun(A,bool),fun(fun(A,A),fun(A,bool)),A),combb(A,bool,A)),fequal(A))),hAPP(A,fun(A,A),ord_min(A),C))))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(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_Sup_fin(A),ord_max(A)),B)) # label(fact_591_min__max_Oinf__Sup1__distrib) # label(axiom). [clausify(659)].
% 2.81/3.01 1324 -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,finite_finite_1(A),C)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),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),collect(A),hAPP(fun(A,fun(A,bool)),fun(A,bool),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A)),hAPP(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,bool)),hAPP(fun(fun(A,fun(A,bool)),fun(A,bool)),fun(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,bool))),combb(fun(A,fun(A,bool)),fun(A,bool),A),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A))),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,fun(A,bool))),hAPP(fun(A,fun(fun(A,fun(A,bool)),fun(A,fun(A,bool)))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(A,bool)))),combc(A,fun(A,fun(A,bool)),fun(A,fun(A,bool))),hAPP(fun(A,fun(A,fun(fun(A,bool),fun(A,bool)))),fun(A,fun(fun(A,fun(A,bool)),fun(A,fun(A,bool)))),hAPP(fun(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,bool)))),fun(fun(A,fun(A,fun(fun(A,bool),fun(A,bool)))),fun(A,fun(fun(A,fun(A,bool)),fun(A,fun(A,bool))))),combb(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,bool))),A),combs(A,fun(A,bool),fun(A,bool))),hAPP(fun(A,fun(A,fun(A,fun(bool,bool)))),fun(A,fun(A,fun(fun(A,bool),fun(A,bool)))),hAPP(fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),fun(fun(A,fun(A,fun(A,fun(bool,bool)))),fun(A,fun(A,fun(fun(A,bool),fun(A,bool))))),combb(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool))),A),hAPP(fun(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),A),combs(A,bool,bool))),hAPP(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,fun(A,fun(bool,bool)))),hAPP(fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),fun(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,fun(A,fun(bool,bool))))),combb(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool))),A),hAPP(fun(fun(A,bool),fun(A,fun(bool,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),combb(fun(A,bool),fun(A,fun(bool,bool)),A),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj))),hAPP(fun(A,fun(A,A)),fun(A,fun(A,fun(A,bool))),hAPP(fun(A,fun(fun(A,fun(A,A)),fun(A,fun(A,bool)))),fun(fun(A,fun(A,A)),fun(A,fun(A,fun(A,bool)))),combc(A,fun(A,fun(A,A)),fun(A,fun(A,bool))),hAPP(fun(A,fun(fun(A,A),fun(A,bool))),fun(A,fun(fun(A,fun(A,A)),fun(A,fun(A,bool)))),hAPP(fun(fun(fun(A,A),fun(A,bool)),fun(fun(A,fun(A,A)),fun(A,fun(A,bool)))),fun(fun(A,fun(fun(A,A),fun(A,bool))),fun(A,fun(fun(A,fun(A,A)),fun(A,fun(A,bool))))),combb(fun(fun(A,A),fun(A,bool)),fun(fun(A,fun(A,A)),fun(A,fun(A,bool))),A),combb(fun(A,A),fun(A,bool),A)),hAPP(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool))),hAPP(fun(fun(A,bool),fun(fun(A,A),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool)))),combb(fun(A,bool),fun(fun(A,A),fun(A,bool)),A),combb(A,bool,A)),fequal(A)))),ord_min(A)))))),hAPP(fun(A,bool),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,bool),fun(A,fun(A,bool))),combc(A,fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(bool,bool)),fun(A,fun(fun(A,bool),fun(A,bool))),hAPP(fun(fun(bool,bool),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(bool,bool)),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(bool,bool),fun(fun(A,bool),fun(A,bool)),A),combb(bool,bool,A)),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),C))))))) = 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_Sup_fin(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)),C)) # label(fact_592_min__max_Oinf__Sup2__distrib) # label(axiom). [clausify(660)].
% 2.81/3.01 1325 -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_593_min__max_OSup__fin_Oin__idem) # label(axiom). [clausify(661)].
% 2.81/3.01 1326 -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_594_min__max_OSup__fin_Osingleton) # label(axiom). [clausify(662)].
% 2.81/3.01 1327 -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_595_min__max_Oinf__Sup__absorb) # label(axiom). [clausify(663)].
% 2.81/3.01 1328 -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_596_min__max_OSup__fin_OF__eq) # label(axiom). [clausify(664)].
% 2.81/3.01 1329 -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_597_min__max_OSup__fin_Oinsert) # label(axiom). [clausify(665)].
% 2.81/3.01 1330 -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_598_min__max_OSup__fin_Oinsert__idem) # label(axiom). [clausify(666)].
% 2.81/3.01 1331 -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_599_min__max_OSup__fin_Osubset__idem) # label(axiom). [clausify(667)].
% 2.81/3.01 1332 -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_602_min__max_OSup__fin_Oeq__fold__idem_H) # label(axiom). [clausify(670)].
% 2.81/3.01 1333 -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_603_min__max_OSup__fin_Oeq__fold_H) # label(axiom). [clausify(671)].
% 2.81/3.01 1334 -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_604_min__max_OSup__fin_Oremove) # label(axiom). [clausify(672)].
% 2.81/3.01 1335 -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_604_min__max_OSup__fin_Oremove) # label(axiom). [clausify(672)].
% 2.81/3.01 1336 -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_605_min__max_OSup__fin_Oinsert__remove) # label(axiom). [clausify(673)].
% 2.81/3.01 1337 -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_605_min__max_OSup__fin_Oinsert__remove) # label(axiom). [clausify(673)].
% 2.81/3.01 1338 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,B,f116(A,C,B))),hAPP(A,A,B,f117(A,C,B))) != hAPP(A,A,B,hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f116(A,C,B)),f117(A,C,B))) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | bot_bot(fun(A,bool)) = ti(fun(A,bool),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,A),fun(fun(A,bool),fun(A,bool)),image(A,A),B),C)) = hAPP(A,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)),C)) # label(fact_606_min__max_OSup__fin_Ohom__commute) # label(axiom). [clausify(674)].
% 2.81/3.01 1339 -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),f118(A,B)),f119(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f118(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f119(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_607_min__max_OSup__fin_Oclosed) # label(axiom). [clausify(675)].
% 2.81/3.01 1340 -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_710_max__less__iff__conj) # label(axiom). [clausify(777)].
% 2.81/3.01 1341 -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_710_max__less__iff__conj) # label(axiom). [clausify(777)].
% 2.81/3.01 1342 -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_710_max__less__iff__conj) # label(axiom). [clausify(777)].
% 2.81/3.01 1343 -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_711_less__max__iff__disj) # label(axiom). [clausify(778)].
% 2.81/3.01 1344 -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_711_less__max__iff__disj) # label(axiom). [clausify(778)].
% 2.81/3.01 1345 -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_711_less__max__iff__disj) # label(axiom). [clausify(778)].
% 2.81/3.01 1346 -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_712_min__max_Oless__supI2) # label(axiom). [clausify(779)].
% 2.81/3.01 1347 -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_713_min__max_Oless__supI1) # label(axiom). [clausify(780)].
% 2.81/3.01 1348 -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_733_min__max_Oless__infI1) # label(axiom). [clausify(800)].
% 2.81/3.01 1349 -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_734_min__max_Oless__infI2) # label(axiom). [clausify(801)].
% 2.81/3.01 1350 -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_735_min__less__iff__conj) # label(axiom). [clausify(802)].
% 2.81/3.01 1351 -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_735_min__less__iff__conj) # label(axiom). [clausify(802)].
% 2.81/3.01 1352 -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_735_min__less__iff__conj) # label(axiom). [clausify(802)].
% 2.81/3.01 1353 -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_736_min__less__iff__disj) # label(axiom). [clausify(803)].
% 2.81/3.01 1354 -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_736_min__less__iff__disj) # label(axiom). [clausify(803)].
% 2.81/3.01 1355 -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_736_min__less__iff__disj) # label(axiom). [clausify(803)].
% 2.81/3.01 1356 -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_745_linorder__not__less) # label(axiom). [clausify(812)].
% 2.81/3.01 1357 -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_745_linorder__not__less) # label(axiom). [clausify(812)].
% 2.81/3.01 1358 -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_746_linorder__not__le) # label(axiom). [clausify(813)].
% 2.81/3.01 1359 -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_746_linorder__not__le) # label(axiom). [clausify(813)].
% 2.81/3.01 1360 -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_747_linorder__le__less__linear) # label(axiom). [clausify(814)].
% 2.81/3.01 1361 -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_751_leI) # label(axiom). [clausify(818)].
% 2.81/3.01 1362 -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_752_not__leE) # label(axiom). [clausify(819)].
% 2.81/3.01 1363 -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_753_linorder__antisym__conv1) # label(axiom). [clausify(820)].
% 2.81/3.01 1364 -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_753_linorder__antisym__conv1) # label(axiom). [clausify(820)].
% 2.81/3.01 1365 -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_756_leD) # label(axiom). [clausify(823)].
% 2.81/3.01 1366 -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_758_linorder__antisym__conv2) # label(axiom). [clausify(825)].
% 2.81/3.01 1367 -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_758_linorder__antisym__conv2) # label(axiom). [clausify(825)].
% 2.81/3.01 1368 -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_770_linorder__cases) # label(axiom). [clausify(837)].
% 2.81/3.01 1369 -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_786_linorder__neqE) # label(axiom). [clausify(853)].
% 2.81/3.01 1370 -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_787_linorder__antisym__conv3) # label(axiom). [clausify(854)].
% 2.81/3.01 1371 -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_787_linorder__antisym__conv3) # label(axiom). [clausify(854)].
% 2.81/3.01 1372 -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_788_linorder__less__linear) # label(axiom). [clausify(855)].
% 2.81/3.01 1373 -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_789_not__less__iff__gr__or__eq) # label(axiom). [clausify(856)].
% 2.81/3.01 1374 -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_789_not__less__iff__gr__or__eq) # label(axiom). [clausify(856)].
% 2.81/3.01 1375 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_789_not__less__iff__gr__or__eq) # label(axiom). [clausify(856)].
% 2.81/3.01 1376 -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_790_linorder__neq__iff) # label(axiom). [clausify(857)].
% 2.81/3.01 1377 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_790_linorder__neq__iff) # label(axiom). [clausify(857)].
% 2.81/3.01 1378 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_790_linorder__neq__iff) # label(axiom). [clausify(857)].
% 2.81/3.01 1379 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less(fun(A,bool)),hAPP(A,fun(A,bool),ord_lessThan(A),B)),hAPP(A,fun(A,bool),ord_lessThan(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_793_lessThan__strict__subset__iff) # label(axiom). [clausify(860)].
% 2.81/3.01 1380 -linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less(fun(A,bool)),hAPP(A,fun(A,bool),ord_lessThan(A),B)),hAPP(A,fun(A,bool),ord_lessThan(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_793_lessThan__strict__subset__iff) # label(axiom). [clausify(860)].
% 2.81/3.01 1381 -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),f143(A,C,B)),B)) # label(fact_839_fold1__strict__below__iff) # label(axiom). [clausify(906)].
% 2.81/3.01 1382 -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),f143(A,C,B)),C)) # label(fact_839_fold1__strict__below__iff) # label(axiom). [clausify(906)].
% 2.81/3.01 1383 -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_839_fold1__strict__below__iff) # label(axiom). [clausify(906)].
% 2.81/3.01 1384 -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_840_strict__below__fold1__iff) # label(axiom). [clausify(907)].
% 2.81/3.01 1385 -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),f144(A,C,B)),B)) # label(fact_840_strict__below__fold1__iff) # label(axiom). [clausify(907)].
% 2.81/3.01 1386 -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),f144(A,C,B))) # label(fact_840_strict__below__fold1__iff) # label(axiom). [clausify(907)].
% 2.81/3.01 1387 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f161(A,C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_918_minf_I8_J) # label(axiom). [clausify(983)].
% 2.81/3.01 1388 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f162(A,B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_919_pinf_I8_J) # label(axiom). [clausify(984)].
% 2.81/3.01 1389 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f166(A,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_922_minf_I6_J) # label(axiom). [clausify(987)].
% 2.81/3.01 1390 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f167(A,B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_923_pinf_I6_J) # label(axiom). [clausify(988)].
% 2.81/3.01 1391 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f185(A,C,B))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_932_finite__linorder__max__induct) # label(axiom). [clausify(997)].
% 2.81/3.01 1392 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),f185(A,C,B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),f184(A,C,B))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_932_finite__linorder__max__induct) # label(axiom). [clausify(997)].
% 2.81/3.01 1393 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | hBOOL(hAPP(fun(A,bool),bool,C,f185(A,C,B))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_932_finite__linorder__max__induct) # label(axiom). [clausify(997)].
% 2.81/3.01 1394 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | -hBOOL(hAPP(fun(A,bool),bool,C,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f184(A,C,B)),f185(A,C,B)))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_932_finite__linorder__max__induct) # label(axiom). [clausify(997)].
% 2.81/3.01 1395 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f187(A,C,B))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_933_finite__linorder__min__induct) # label(axiom). [clausify(998)].
% 2.81/3.01 1396 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),f187(A,C,B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f186(A,C,B)),D)) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_933_finite__linorder__min__induct) # label(axiom). [clausify(998)].
% 2.81/3.01 1397 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | hBOOL(hAPP(fun(A,bool),bool,C,f187(A,C,B))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_933_finite__linorder__min__induct) # label(axiom). [clausify(998)].
% 2.81/3.01 1398 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | -hBOOL(hAPP(fun(A,bool),bool,C,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f186(A,C,B)),f187(A,C,B)))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_933_finite__linorder__min__induct) # label(axiom). [clausify(998)].
% 2.81/3.01 Derived: big_Inf_fin(int) = ti(fun(fun(int,fun(int,int)),fun(fun(int,bool),int)),big_Inf_fin(int)). [resolve(1164,a,1165,a)].
% 2.81/3.01 Derived: big_Sup_fin(int) = ti(fun(fun(int,fun(int,int)),fun(fun(int,bool),int)),big_Sup_fin(int)). [resolve(1164,a,1166,a)].
% 2.81/3.01 Derived: big_linorder_Max(int) = ti(fun(fun(int,bool),int),big_linorder_Max(int)). [resolve(1164,a,1167,a)].
% 2.81/3.01 Derived: big_linorder_Min(int) = ti(fun(fun(int,bool),int),big_linorder_Min(int)). [resolve(1164,a,1168,a)].
% 2.81/3.01 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1164,a,1169,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(int,fun(int,bool),ord_lessThan(int),A)),hAPP(int,fun(int,bool),ord_lessThan(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1164,a,1171,a)].
% 2.81/3.01 Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(int,fun(int,bool),ord_lessThan(int),A)),hAPP(int,fun(int,bool),ord_lessThan(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1164,a,1172,a)].
% 2.81/3.01 Derived: hAPP(int,fun(int,bool),ord_lessThan(int),A) != hAPP(int,fun(int,bool),ord_lessThan(int),B) | ti(int,A) = ti(int,B). [resolve(1164,a,1173,a)].
% 2.81/3.01 Derived: hAPP(int,fun(int,bool),ord_lessThan(int),A) = hAPP(int,fun(int,bool),ord_lessThan(int),B) | ti(int,A) != ti(int,B). [resolve(1164,a,1174,a)].
% 2.81/3.01 Derived: bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),A),B)) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),B)),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))). [resolve(1164,a,1175,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),A),B)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,big_linorder_Min(int),B)),hAPP(fun(int,bool),int,big_linorder_Min(int),A))). [resolve(1164,a,1176,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),A),B)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,big_linorder_Max(int),A)),hAPP(fun(int,bool),int,big_linorder_Max(int),B))). [resolve(1164,a,1177,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,big_linorder_Min(int),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,big_linorder_Min(int),A)). [resolve(1164,a,1178,a)].
% 2.81/3.01 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),A) = ti(int,A). [resolve(1164,a,1179,a)].
% 2.81/3.01 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)). [resolve(1164,a,1180,a)].
% 2.81/3.01 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)). [resolve(1164,a,1182,a)].
% 2.81/3.01 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B). [resolve(1164,a,1184,a)].
% 2.81/3.01 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),A). [resolve(1164,a,1186,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)). [resolve(1164,a,1189,a)].
% 2.81/3.01 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(1164,a,1190,a)].
% 2.81/3.01 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)). [resolve(1164,a,1191,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1164,a,1192,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(1164,a,1193,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),D))). [resolve(1164,a,1194,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))). [resolve(1164,a,1195,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),A) = ti(int,A). [resolve(1164,a,1197,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B) = ti(int,A). [resolve(1164,a,1198,a)].
% 2.81/3.01 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B) != ti(int,A). [resolve(1164,a,1205,a)].
% 2.81/3.01 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),B)). [resolve(1164,a,1206,a)].
% 2.81/3.01 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),A)). [resolve(1164,a,1207,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A) = hAPP(fun(int,bool),int,big_linorder_Min(int),A). [resolve(1164,a,1208,a)].
% 2.81/3.01 Derived: hBOOL(hAPP(fun(int,fun(int,int)),bool,finite_comp_fun_idem(int,int),ord_min(int))). [resolve(1164,a,1209,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,big_linorder_Min(int),A)). [resolve(1164,a,1210,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),B) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),B),A)) | hAPP(fun(int,bool),int,big_linorder_Min(int),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(fun(int,bool),int,big_linorder_Min(int),B)),hAPP(fun(int,bool),int,big_linorder_Min(int),A)). [resolve(1164,a,1212,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),B),A) = hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)). [resolve(1164,a,1213,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),B),A) = hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)). [resolve(1164,a,1214,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) != bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = ti(int,B). [resolve(1164,a,1215,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))). [resolve(1164,a,1216,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) != bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Min(int),A) = ti(int,B). [resolve(1164,a,1217,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Min(int),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))). [resolve(1164,a,1218,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(fun(int,bool),int,big_linorder_Max(int),A))). [resolve(1164,a,1219,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,big_linorder_Min(int),A)),B)). [resolve(1164,a,1220,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,big_linorder_Max(int),A)),A)). [resolve(1164,a,1221,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,big_linorder_Min(int),A)),A)). [resolve(1164,a,1222,a)].
% 2.81/3.01 Derived: hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),A),bot_bot(fun(int,bool)))) = ti(int,A). [resolve(1164,a,1223,a)].
% 2.81/3.01 Derived: hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),A),bot_bot(fun(int,bool)))) = ti(int,A). [resolve(1164,a,1224,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),C),A)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))). [resolve(1164,a,1225,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),B),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),C),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),C),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),B),A)). [resolve(1164,a,1226,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),B)). [resolve(1164,a,1227,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),B)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f85(int,B,A)),A)). [resolve(1164,a,1228,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),f85(int,B,A)),B)). [resolve(1164,a,1229,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),B)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),C),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),B)). [resolve(1164,a,1230,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),C),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)). [resolve(1164,a,1231,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f86(int,B,A)),A)). [resolve(1164,a,1232,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),f86(int,B,A))). [resolve(1164,a,1233,a)].
% 2.81/3.01 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,A,f87(int,B,A))),hAPP(int,int,A,f88(int,B,A))) != hAPP(int,int,A,hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),f87(int,B,A)),f88(int,B,A))) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),B) | hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),A),B)) = hAPP(int,int,A,hAPP(fun(int,bool),int,big_linorder_Min(int),B)). [resolve(1164,a,1234,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f91(int,B,C,A)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),C),B)),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),B),A))). [resolve(1164,a,1236,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),f91(int,C,B,A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),C),A))). [resolve(1164,a,1237,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f92(int,B,A)),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,big_linorder_Min(int),A) = ti(int,B). [resolve(1164,a,1238,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),f92(int,B,A))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,big_linorder_Min(int),A) = ti(int,B). [resolve(1164,a,1239,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f93(int,B,A)),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,big_linorder_Max(int),A) = ti(int,B). [resolve(1164,a,1240,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),f93(int,B,A)),B)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,big_linorder_Max(int),A) = ti(int,B). [resolve(1164,a,1241,a)].
% 2.81/3.01 Derived: hAPP(fun(int,fun(int,bool)),fun(int,fun(int,int)),max(int),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int))) = ord_min(int). [resolve(1164,a,1242,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) != bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A) = ti(int,B). [resolve(1164,a,1243,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))). [resolve(1164,a,1244,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) != bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = ti(int,B). [resolve(1164,a,1245,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))). [resolve(1164,a,1246,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)). [resolve(1164,a,1247,a)].
% 2.81/3.01 Derived: hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),A),bot_bot(fun(int,bool)))) = ti(int,A). [resolve(1164,a,1248,a)].
% 2.81/3.01 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A). [resolve(1164,a,1249,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)). [resolve(1164,a,1250,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),B) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),B),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),B)),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)). [resolve(1164,a,1252,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),B),A). [resolve(1164,a,1253,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),B),A). [resolve(1164,a,1254,a)].
% 2.81/3.02 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,A,f98(int,B,A))),hAPP(int,int,A,f99(int,B,A))) != hAPP(int,int,A,hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),f98(int,B,A)),f99(int,B,A))) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),B) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),A),B)) = hAPP(int,int,A,hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),B)). [resolve(1164,a,1255,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),f100(int,A)),f101(int,A))),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f100(int,A)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f101(int,A)),bot_bot(fun(int,bool)))))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)),A)). [resolve(1164,a,1256,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) != bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Max(int),A) = ti(int,B). [resolve(1164,a,1257,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Max(int),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))). [resolve(1164,a,1258,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) != bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = ti(int,B). [resolve(1164,a,1259,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))). [resolve(1164,a,1260,a)].
% 2.81/3.02 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)). [resolve(1164,a,1261,a)].
% 2.81/3.02 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),B). [resolve(1164,a,1262,a)].
% 2.81/3.02 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)). [resolve(1164,a,1263,a)].
% 2.81/3.02 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)). [resolve(1164,a,1264,a)].
% 2.81/3.02 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)) = ti(int,A). [resolve(1164,a,1265,a)].
% 2.81/3.02 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)) = ti(int,A). [resolve(1164,a,1266,a)].
% 2.81/3.02 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),A) = ti(int,A). [resolve(1164,a,1267,a)].
% 2.81/3.02 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)). [resolve(1164,a,1268,a)].
% 2.81/3.02 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)). [resolve(1164,a,1270,a)].
% 2.81/3.02 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B). [resolve(1164,a,1272,a)].
% 2.81/3.02 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),A). [resolve(1164,a,1274,a)].
% 2.81/3.02 Derived: hAPP(int,fun(int,bool),ord_greaterThan(int),A) != hAPP(int,fun(int,bool),ord_greaterThan(int),B) | ti(int,A) = ti(int,B). [resolve(1164,a,1277,a)].
% 2.81/3.02 Derived: hAPP(int,fun(int,bool),ord_greaterThan(int),A) = hAPP(int,fun(int,bool),ord_greaterThan(int),B) | ti(int,A) != ti(int,B). [resolve(1164,a,1278,a)].
% 2.81/3.02 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B))). [resolve(1164,a,1279,a)].
% 2.81/3.02 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),A))). [resolve(1164,a,1280,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B) = ti(int,B). [resolve(1164,a,1281,a)].
% 2.81/3.02 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B) != ti(int,B). [resolve(1164,a,1282,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(1164,a,1283,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)). [resolve(1164,a,1284,a)].
% 2.81/3.02 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)). [resolve(1164,a,1285,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))). [resolve(1164,a,1286,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B))). [resolve(1164,a,1287,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),A) = ti(int,B). [resolve(1164,a,1289,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),D))). [resolve(1164,a,1292,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(1164,a,1295,a)].
% 2.81/3.02 Derived: hBOOL(hAPP(fun(int,fun(int,int)),bool,finite_comp_fun_idem(int,int),ord_max(int))). [resolve(1164,a,1298,a)].
% 2.81/3.02 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C))),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)))). [resolve(1164,a,1299,a)].
% 2.81/3.02 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)))). [resolve(1164,a,1300,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,big_linorder_Max(int),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,big_linorder_Max(int),A)). [resolve(1164,a,1301,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),C),A))). [resolve(1164,a,1302,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),B),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),C),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),B),A)). [resolve(1164,a,1303,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)) = ti(int,B). [resolve(1164,a,1304,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(int,fun(int,bool),ord_greaterThan(int),A)),hAPP(int,fun(int,bool),ord_greaterThan(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1164,a,1305,a)].
% 2.81/3.02 Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(int,fun(int,bool),ord_greaterThan(int),A)),hAPP(int,fun(int,bool),ord_greaterThan(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1164,a,1306,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_max(int)),A) = hAPP(fun(int,bool),int,big_linorder_Max(int),A). [resolve(1164,a,1307,a)].
% 2.81/3.02 Derived: hAPP(fun(int,fun(int,bool)),fun(int,fun(int,int)),min(int),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int))) = ord_max(int). [resolve(1164,a,1308,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,big_linorder_Max(int),A)). [resolve(1164,a,1309,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),B) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),B),A)) | hAPP(fun(int,bool),int,big_linorder_Max(int),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(fun(int,bool),int,big_linorder_Max(int),B)),hAPP(fun(int,bool),int,big_linorder_Max(int),A)). [resolve(1164,a,1311,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),B),A) = hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)). [resolve(1164,a,1312,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),B),A) = hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)). [resolve(1164,a,1313,a)].
% 2.81/3.02 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,A,f102(int,B,A))),hAPP(int,int,A,f103(int,B,A))) != hAPP(int,int,A,hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),f102(int,B,A)),f103(int,B,A))) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),B) | hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),A),B)) = hAPP(int,int,A,hAPP(fun(int,bool),int,big_linorder_Max(int),B)). [resolve(1164,a,1314,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f106(int,B,C,A)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),B),A)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B))). [resolve(1164,a,1316,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),f106(int,B,C,A)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),B),A)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B))). [resolve(1164,a,1317,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A))). [resolve(1164,a,1320,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),B) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,fun(int,bool)),fun(int,bool),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int)),hAPP(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,bool)),hAPP(fun(fun(int,fun(int,bool)),fun(int,bool)),fun(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,bool))),combb(fun(int,fun(int,bool)),fun(int,bool),int),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int))),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(int,bool))),hAPP(fun(int,fun(fun(int,fun(int,bool)),fun(int,fun(int,bool)))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(int,bool)))),combc(int,fun(int,fun(int,bool)),fun(int,fun(int,bool))),hAPP(fun(int,fun(int,fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(int,fun(int,bool)),fun(int,fun(int,bool)))),hAPP(fun(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool)))),fun(fun(int,fun(int,fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))))),combb(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))),int),combs(int,fun(int,bool),fun(int,bool))),hAPP(fun(int,fun(int,fun(int,fun(bool,bool)))),fun(int,fun(int,fun(fun(int,bool),fun(int,bool)))),hAPP(fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(int,fun(int,fun(bool,bool)))),fun(int,fun(int,fun(fun(int,bool),fun(int,bool))))),combb(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),int),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool))),hAPP(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,fun(int,fun(bool,bool)))),hAPP(fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),fun(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,fun(int,fun(bool,bool))))),combb(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),int),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),hAPP(fun(int,fun(int,int)),fun(int,fun(int,fun(int,bool))),hAPP(fun(int,fun(fun(int,fun(int,int)),fun(int,fun(int,bool)))),fun(fun(int,fun(int,int)),fun(int,fun(int,fun(int,bool)))),combc(int,fun(int,fun(int,int)),fun(int,fun(int,bool))),hAPP(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(int,fun(int,int)),fun(int,fun(int,bool)))),hAPP(fun(fun(fun(int,int),fun(int,bool)),fun(fun(int,fun(int,int)),fun(int,fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(int,fun(int,int)),fun(int,fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(int,fun(int,int)),fun(int,fun(int,bool))),int),combb(fun(int,int),fun(int,bool),int)),hAPP(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),hAPP(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),ord_max(int)))))),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(bool,bool)),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(bool,bool),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(bool,bool)),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(bool,bool),fun(fun(int,bool),fun(int,bool)),int),combb(bool,bool,int)),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),A)))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),B))))))) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),B)). [resolve(1164,a,1321,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,fun(int,bool)),fun(int,bool),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int)),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj)),hAPP(fun(int,int),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,int),fun(int,bool))),fun(fun(int,int),fun(int,fun(int,bool))),combc(int,fun(int,int),fun(int,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),hAPP(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int))),hAPP(int,fun(int,int),ord_max(int),B))))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),A))))) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)). [resolve(1164,a,1322,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,fun(int,bool)),fun(int,bool),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int)),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj)),hAPP(fun(int,int),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,int),fun(int,bool))),fun(fun(int,int),fun(int,fun(int,bool))),combc(int,fun(int,int),fun(int,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),hAPP(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int))),hAPP(int,fun(int,int),ord_min(int),B))))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),A))))) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)). [resolve(1164,a,1323,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),B) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,fun(int,bool)),fun(int,bool),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int)),hAPP(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,bool)),hAPP(fun(fun(int,fun(int,bool)),fun(int,bool)),fun(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,bool))),combb(fun(int,fun(int,bool)),fun(int,bool),int),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int))),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(int,bool))),hAPP(fun(int,fun(fun(int,fun(int,bool)),fun(int,fun(int,bool)))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(int,bool)))),combc(int,fun(int,fun(int,bool)),fun(int,fun(int,bool))),hAPP(fun(int,fun(int,fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(int,fun(int,bool)),fun(int,fun(int,bool)))),hAPP(fun(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool)))),fun(fun(int,fun(int,fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))))),combb(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))),int),combs(int,fun(int,bool),fun(int,bool))),hAPP(fun(int,fun(int,fun(int,fun(bool,bool)))),fun(int,fun(int,fun(fun(int,bool),fun(int,bool)))),hAPP(fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(int,fun(int,fun(bool,bool)))),fun(int,fun(int,fun(fun(int,bool),fun(int,bool))))),combb(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),int),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool))),hAPP(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,fun(int,fun(bool,bool)))),hAPP(fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),fun(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,fun(int,fun(bool,bool))))),combb(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),int),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),hAPP(fun(int,fun(int,int)),fun(int,fun(int,fun(int,bool))),hAPP(fun(int,fun(fun(int,fun(int,int)),fun(int,fun(int,bool)))),fun(fun(int,fun(int,int)),fun(int,fun(int,fun(int,bool)))),combc(int,fun(int,fun(int,int)),fun(int,fun(int,bool))),hAPP(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(int,fun(int,int)),fun(int,fun(int,bool)))),hAPP(fun(fun(fun(int,int),fun(int,bool)),fun(fun(int,fun(int,int)),fun(int,fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(int,fun(int,int)),fun(int,fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(int,fun(int,int)),fun(int,fun(int,bool))),int),combb(fun(int,int),fun(int,bool),int)),hAPP(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),hAPP(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),ord_min(int)))))),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(bool,bool)),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(bool,bool),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(bool,bool)),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(bool,bool),fun(fun(int,bool),fun(int,bool)),int),combb(bool,bool,int)),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),A)))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),B))))))) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),B)). [resolve(1164,a,1324,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)). [resolve(1164,a,1325,a)].
% 2.81/3.02 Derived: hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),A),bot_bot(fun(int,bool)))) = ti(int,A). [resolve(1164,a,1326,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)) = ti(int,B). [resolve(1164,a,1327,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_max(int)),A) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A). [resolve(1164,a,1328,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)). [resolve(1164,a,1329,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)). [resolve(1164,a,1330,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),B) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),B),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),B)),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)). [resolve(1164,a,1331,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),B),A). [resolve(1164,a,1332,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) != bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A) = ti(int,B). [resolve(1164,a,1334,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))). [resolve(1164,a,1335,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) != bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = ti(int,B). [resolve(1164,a,1336,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))). [resolve(1164,a,1337,a)].
% 2.81/3.02 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,A,f116(int,B,A))),hAPP(int,int,A,f117(int,B,A))) != hAPP(int,int,A,hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),f116(int,B,A)),f117(int,B,A))) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),B) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),A),B)) = hAPP(int,int,A,hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),B)). [resolve(1164,a,1338,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),f118(int,A)),f119(int,A))),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f118(int,A)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f119(int,A)),bot_bot(fun(int,bool)))))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)),A)). [resolve(1164,a,1339,a)].
% 2.81/3.02 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(1164,a,1340,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(1164,a,1341,a)].
% 2.81/3.03 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(1164,a,1342,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(1164,a,1343,a)].
% 2.81/3.03 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(1164,a,1344,a)].
% 2.81/3.03 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(1164,a,1345,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),B)). [resolve(1164,a,1348,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),C),A)),B)). [resolve(1164,a,1349,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(1164,a,1350,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(1164,a,1351,a)].
% 2.81/3.03 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(1164,a,1352,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(1164,a,1353,a)].
% 2.81/3.03 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1164,a,1356,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1164,a,1357,a)].
% 2.81/3.03 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,B) = ti(int,A). [resolve(1164,a,1363,a)].
% 2.81/3.03 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,B) != ti(int,A). [resolve(1164,a,1364,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,B) != ti(int,A). [resolve(1164,a,1367,a)].
% 2.81/3.03 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,B) = ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)). [resolve(1164,a,1368,a)].
% 2.81/3.03 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)) | ti(int,A) != ti(int,B). [resolve(1164,a,1371,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)). [resolve(1164,a,1374,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,B) != ti(int,A). [resolve(1164,a,1375,a)].
% 2.81/3.03 Derived: ti(int,A) != ti(int,B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(1164,a,1378,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(int,fun(int,bool),ord_lessThan(int),A)),hAPP(int,fun(int,bool),ord_lessThan(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(1164,a,1379,a)].
% 2.81/3.03 Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(int,fun(int,bool),ord_lessThan(int),A)),hAPP(int,fun(int,bool),ord_lessThan(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(1164,a,1380,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),B)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f143(int,B,A)),A)). [resolve(1164,a,1381,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f143(int,B,A)),B)). [resolve(1164,a,1382,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),B)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),C),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B)). [resolve(1164,a,1383,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),C),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(1164,a,1384,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f144(int,B,A)),A)). [resolve(1164,a,1385,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),f144(int,B,A))). [resolve(1164,a,1386,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),f161(int,B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1164,a,1387,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f162(int,A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1164,a,1388,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),f166(int,B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1164,a,1389,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f167(int,A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1164,a,1390,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),f185(int,B,A))) | hBOOL(hAPP(fun(int,bool),bool,B,A)). [resolve(1164,a,1391,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),C),f185(int,B,A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),f184(int,B,A))) | hBOOL(hAPP(fun(int,bool),bool,B,A)). [resolve(1164,a,1392,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | hBOOL(hAPP(fun(int,bool),bool,B,f185(int,B,A))) | hBOOL(hAPP(fun(int,bool),bool,B,A)). [resolve(1164,a,1393,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | -hBOOL(hAPP(fun(int,bool),bool,B,hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f184(int,B,A)),f185(int,B,A)))) | hBOOL(hAPP(fun(int,bool),bool,B,A)). [resolve(1164,a,1394,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),f187(int,B,A))) | hBOOL(hAPP(fun(int,bool),bool,B,A)). [resolve(1164,a,1395,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),C),f187(int,B,A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f186(int,B,A)),C)) | hBOOL(hAPP(fun(int,bool),bool,B,A)). [resolve(1164,a,1396,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | hBOOL(hAPP(fun(int,bool),bool,B,f187(int,B,A))) | hBOOL(hAPP(fun(int,bool),bool,B,A)). [resolve(1164,a,1397,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | -hBOOL(hAPP(fun(int,bool),bool,B,hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f186(int,B,A)),f187(int,B,A)))) | hBOOL(hAPP(fun(int,bool),bool,B,A)). [resolve(1164,a,1398,a)].
% 2.81/3.03 1399 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom). [assumption].
% 2.81/3.03 Derived: big_Inf_fin(nat) = ti(fun(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat)),big_Inf_fin(nat)). [resolve(1399,a,1165,a)].
% 2.81/3.03 Derived: big_Sup_fin(nat) = ti(fun(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat)),big_Sup_fin(nat)). [resolve(1399,a,1166,a)].
% 2.81/3.03 Derived: big_linorder_Max(nat) = ti(fun(fun(nat,bool),nat),big_linorder_Max(nat)). [resolve(1399,a,1167,a)].
% 2.81/3.03 Derived: big_linorder_Min(nat) = ti(fun(fun(nat,bool),nat),big_linorder_Min(nat)). [resolve(1399,a,1168,a)].
% 2.81/3.03 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(1399,a,1169,a)].
% 2.81/3.03 Derived: -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1399,a,1171,a)].
% 2.81/3.03 Derived: hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1399,a,1172,a)].
% 2.81/3.03 Derived: hAPP(nat,fun(nat,bool),ord_lessThan(nat),A) != hAPP(nat,fun(nat,bool),ord_lessThan(nat),B) | ti(nat,A) = ti(nat,B). [resolve(1399,a,1173,a)].
% 2.81/3.03 Derived: hAPP(nat,fun(nat,bool),ord_lessThan(nat),A) = hAPP(nat,fun(nat,bool),ord_lessThan(nat),B) | ti(nat,A) != ti(nat,B). [resolve(1399,a,1174,a)].
% 2.81/3.03 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(1399,a,1175,a)].
% 2.81/3.03 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(1399,a,1176,a)].
% 2.81/3.03 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(1399,a,1177,a)].
% 2.81/3.03 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(1399,a,1178,a)].
% 2.81/3.03 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),A) = ti(nat,A). [resolve(1399,a,1179,a)].
% 2.81/3.03 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(1399,a,1180,a)].
% 2.81/3.03 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(1399,a,1182,a)].
% 2.81/3.03 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(1399,a,1184,a)].
% 2.81/3.03 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(1399,a,1186,a)].
% 2.81/3.03 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(1399,a,1189,a)].
% 2.81/3.03 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1399,a,1190,a)].
% 2.81/3.03 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1399,a,1191,a)].
% 2.81/3.03 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(1399,a,1192,a)].
% 2.81/3.03 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(1399,a,1193,a)].
% 2.81/3.03 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(1399,a,1194,a)].
% 2.85/3.04 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))). [resolve(1399,a,1195,a)].
% 2.85/3.04 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(1399,a,1197,a)].
% 2.85/3.04 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(1399,a,1198,a)].
% 2.85/3.04 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(1399,a,1205,a)].
% 2.85/3.04 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(1399,a,1206,a)].
% 2.85/3.04 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(1399,a,1207,a)].
% 2.85/3.04 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(1399,a,1208,a)].
% 2.85/3.04 Derived: hBOOL(hAPP(fun(nat,fun(nat,nat)),bool,finite_comp_fun_idem(nat,nat),ord_min(nat))). [resolve(1399,a,1209,a)].
% 2.85/3.04 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(1399,a,1210,a)].
% 2.85/3.04 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(1399,a,1212,a)].
% 2.85/3.04 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(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(1399,a,1213,a)].
% 2.85/3.04 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(1399,a,1214,a)].
% 2.85/3.04 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(1399,a,1215,a)].
% 2.85/3.04 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(1399,a,1216,a)].
% 2.85/3.04 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(1399,a,1217,a)].
% 2.85/3.04 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(1399,a,1218,a)].
% 2.85/3.04 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(1399,a,1219,a)].
% 2.85/3.04 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(1399,a,1220,a)].
% 2.85/3.04 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(1399,a,1221,a)].
% 2.85/3.04 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(1399,a,1222,a)].
% 2.85/3.04 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(1399,a,1223,a)].
% 2.85/3.04 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(1399,a,1224,a)].
% 2.85/3.04 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(1399,a,1225,a)].
% 2.85/3.04 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(1399,a,1226,a)].
% 2.85/3.04 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(1399,a,1227,a)].
% 2.85/3.04 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),f85(nat,B,A)),A)). [resolve(1399,a,1228,a)].
% 2.85/3.04 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),f85(nat,B,A)),B)). [resolve(1399,a,1229,a)].
% 2.85/3.04 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(1399,a,1230,a)].
% 2.85/3.04 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(1399,a,1231,a)].
% 2.85/3.04 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),f86(nat,B,A)),A)). [resolve(1399,a,1232,a)].
% 2.85/3.04 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),f86(nat,B,A))). [resolve(1399,a,1233,a)].
% 2.85/3.04 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,A,f87(nat,B,A))),hAPP(nat,nat,A,f88(nat,B,A))) != hAPP(nat,nat,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),f87(nat,B,A)),f88(nat,B,A))) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),B) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),A),B)) = hAPP(nat,nat,A,hAPP(fun(nat,bool),nat,big_linorder_Min(nat),B)). [resolve(1399,a,1234,a)].
% 2.85/3.04 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),f91(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(1399,a,1236,a)].
% 2.85/3.04 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),f91(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(1399,a,1237,a)].
% 2.85/3.04 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),f92(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(1399,a,1238,a)].
% 2.85/3.04 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),f92(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(1399,a,1239,a)].
% 2.85/3.04 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),f93(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(1399,a,1240,a)].
% 2.85/3.04 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),f93(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(1399,a,1241,a)].
% 2.85/3.04 Derived: hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,nat)),max(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat))) = ord_min(nat). [resolve(1399,a,1242,a)].
% 2.85/3.04 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(1399,a,1243,a)].
% 2.85/3.04 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(1399,a,1244,a)].
% 2.85/3.04 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(1399,a,1245,a)].
% 2.85/3.04 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(1399,a,1246,a)].
% 2.85/3.04 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(1399,a,1247,a)].
% 2.85/3.04 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(1399,a,1248,a)].
% 2.85/3.04 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(1399,a,1249,a)].
% 2.85/3.04 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(1399,a,1250,a)].
% 2.85/3.04 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(1399,a,1252,a)].
% 2.85/3.04 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)),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(1399,a,1253,a)].
% 2.85/3.04 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(1399,a,1254,a)].
% 2.85/3.04 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,A,f98(nat,B,A))),hAPP(nat,nat,A,f99(nat,B,A))) != hAPP(nat,nat,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),f98(nat,B,A)),f99(nat,B,A))) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),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,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),A),B)) = hAPP(nat,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)),B)). [resolve(1399,a,1255,a)].
% 2.85/3.04 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),f100(nat,A)),f101(nat,A))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f100(nat,A)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f101(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(1399,a,1256,a)].
% 2.85/3.04 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(1399,a,1257,a)].
% 2.85/3.04 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(1399,a,1258,a)].
% 2.85/3.04 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(1399,a,1259,a)].
% 2.85/3.04 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(1399,a,1260,a)].
% 2.85/3.04 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(1399,a,1261,a)].
% 2.85/3.04 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(1399,a,1262,a)].
% 2.85/3.04 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(1399,a,1263,a)].
% 2.85/3.04 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(1399,a,1264,a)].
% 2.85/3.04 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(1399,a,1265,a)].
% 2.85/3.04 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(1399,a,1266,a)].
% 2.85/3.04 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),A) = ti(nat,A). [resolve(1399,a,1267,a)].
% 2.85/3.04 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(1399,a,1268,a)].
% 2.85/3.04 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(1399,a,1270,a)].
% 2.85/3.04 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(1399,a,1272,a)].
% 2.85/3.04 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(1399,a,1274,a)].
% 2.85/3.04 Derived: hAPP(nat,fun(nat,bool),ord_greaterThan(nat),A) != hAPP(nat,fun(nat,bool),ord_greaterThan(nat),B) | ti(nat,A) = ti(nat,B). [resolve(1399,a,1277,a)].
% 2.85/3.04 Derived: hAPP(nat,fun(nat,bool),ord_greaterThan(nat),A) = hAPP(nat,fun(nat,bool),ord_greaterThan(nat),B) | ti(nat,A) != ti(nat,B). [resolve(1399,a,1278,a)].
% 2.85/3.04 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(1399,a,1279,a)].
% 2.85/3.04 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(1399,a,1280,a)].
% 2.85/3.04 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(1399,a,1281,a)].
% 2.85/3.04 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(1399,a,1282,a)].
% 2.85/3.04 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(1399,a,1283,a)].
% 2.85/3.04 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(1399,a,1284,a)].
% 2.85/3.04 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(1399,a,1285,a)].
% 2.85/3.05 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(1399,a,1286,a)].
% 2.85/3.05 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(1399,a,1287,a)].
% 2.85/3.05 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(1399,a,1289,a)].
% 2.85/3.05 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(1399,a,1292,a)].
% 2.85/3.05 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(1399,a,1295,a)].
% 2.85/3.05 Derived: hBOOL(hAPP(fun(nat,fun(nat,nat)),bool,finite_comp_fun_idem(nat,nat),ord_max(nat))). [resolve(1399,a,1298,a)].
% 2.85/3.05 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(1399,a,1299,a)].
% 2.85/3.05 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(1399,a,1300,a)].
% 2.85/3.05 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(1399,a,1301,a)].
% 2.85/3.05 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(1399,a,1302,a)].
% 2.85/3.05 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(1399,a,1303,a)].
% 2.85/3.05 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(1399,a,1304,a)].
% 2.85/3.05 Derived: -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_greaterThan(nat),A)),hAPP(nat,fun(nat,bool),ord_greaterThan(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(1399,a,1305,a)].
% 2.85/3.05 Derived: hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_greaterThan(nat),A)),hAPP(nat,fun(nat,bool),ord_greaterThan(nat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(1399,a,1306,a)].
% 2.85/3.05 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(1399,a,1307,a)].
% 2.85/3.05 Derived: hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,nat)),min(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat))) = ord_max(nat). [resolve(1399,a,1308,a)].
% 2.85/3.05 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(1399,a,1309,a)].
% 2.85/3.05 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(1399,a,1311,a)].
% 2.85/3.05 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(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(1399,a,1312,a)].
% 2.85/3.05 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(1399,a,1313,a)].
% 2.85/3.05 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,A,f102(nat,B,A))),hAPP(nat,nat,A,f103(nat,B,A))) != hAPP(nat,nat,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),f102(nat,B,A)),f103(nat,B,A))) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),B) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),A),B)) = hAPP(nat,nat,A,hAPP(fun(nat,bool),nat,big_linorder_Max(nat),B)). [resolve(1399,a,1314,a)].
% 2.85/3.05 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),f106(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(1399,a,1316,a)].
% 2.85/3.05 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),f106(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(1399,a,1317,a)].
% 2.85/3.05 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(1399,a,1320,a)].
% 2.85/3.05 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,finite_finite_1(nat),B)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),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),collect(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,bool)),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,bool)),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,bool))),combb(fun(nat,fun(nat,bool)),fun(nat,bool),nat),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat))),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(nat,bool)))),combc(nat,fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool)))),fun(nat,fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)))),hAPP(fun(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool)))),fun(nat,fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))))),combb(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),nat),combs(nat,fun(nat,bool),fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,fun(bool,bool)))),fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool)))),hAPP(fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,fun(nat,fun(nat,fun(bool,bool)))),fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),nat),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,fun(bool,bool)))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,fun(bool,bool))))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),nat),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combc(nat,fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool)))),hAPP(fun(fun(fun(nat,nat),fun(nat,bool)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool))))),combb(fun(fun(nat,nat),fun(nat,bool)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool))),nat),combb(fun(nat,nat),fun(nat,bool),nat)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool))),hAPP(fun(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool)))),combb(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool)),nat),combb(nat,bool,nat)),fequal(nat)))),ord_max(nat)))))),hAPP(fun(nat,bool),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(nat,fun(nat,bool))),combc(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(bool,bool)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(bool,bool)),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),nat),combb(bool,bool,nat)),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),A)))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),B))))))) = 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_Inf_fin(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)),B)). [resolve(1399,a,1321,a)].
% 2.85/3.05 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),collect(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat)),hAPP(fun(nat,bool),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(nat,fun(nat,bool))),combc(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combc(nat,fun(nat,nat),fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool))),hAPP(fun(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool)))),combb(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool)),nat),combb(nat,bool,nat)),fequal(nat))),hAPP(nat,fun(nat,nat),ord_max(nat),B))))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),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)). [resolve(1399,a,1322,a)].
% 2.85/3.05 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),collect(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat)),hAPP(fun(nat,bool),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(nat,fun(nat,bool))),combc(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combc(nat,fun(nat,nat),fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool))),hAPP(fun(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool)))),combb(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool)),nat),combb(nat,bool,nat)),fequal(nat))),hAPP(nat,fun(nat,nat),ord_min(nat),B))))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),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)). [resolve(1399,a,1323,a)].
% 2.85/3.05 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,finite_finite_1(nat),B)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),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),collect(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,bool)),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,bool)),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,bool))),combb(fun(nat,fun(nat,bool)),fun(nat,bool),nat),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat))),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(nat,bool)))),combc(nat,fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool)))),fun(nat,fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)))),hAPP(fun(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool)))),fun(nat,fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))))),combb(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),nat),combs(nat,fun(nat,bool),fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,fun(bool,bool)))),fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool)))),hAPP(fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,fun(nat,fun(nat,fun(bool,bool)))),fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),nat),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,fun(bool,bool)))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,fun(bool,bool))))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),nat),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combc(nat,fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool)))),hAPP(fun(fun(fun(nat,nat),fun(nat,bool)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool))))),combb(fun(fun(nat,nat),fun(nat,bool)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool))),nat),combb(fun(nat,nat),fun(nat,bool),nat)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool))),hAPP(fun(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool)))),combb(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool)),nat),combb(nat,bool,nat)),fequal(nat)))),ord_min(nat)))))),hAPP(fun(nat,bool),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(nat,fun(nat,bool))),combc(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(bool,bool)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(bool,bool)),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),nat),combb(bool,bool,nat)),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),A)))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),B))))))) = 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_Sup_fin(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)),B)). [resolve(1399,a,1324,a)].
% 2.85/3.05 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(1399,a,1325,a)].
% 2.85/3.05 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(1399,a,1326,a)].
% 2.85/3.05 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(1399,a,1327,a)].
% 2.85/3.05 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(1399,a,1328,a)].
% 2.85/3.05 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_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(1399,a,1329,a)].
% 2.85/3.05 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(1399,a,1330,a)].
% 2.85/3.05 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(1399,a,1331,a)].
% 2.85/3.05 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(1399,a,1332,a)].
% 2.85/3.05 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(1399,a,1334,a)].
% 2.85/3.05 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(1399,a,1335,a)].
% 2.85/3.05 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(1399,a,1336,a)].
% 2.85/3.05 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(1399,a,1337,a)].
% 2.85/3.05 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,A,f116(nat,B,A))),hAPP(nat,nat,A,f117(nat,B,A))) != hAPP(nat,nat,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),f116(nat,B,A)),f117(nat,B,A))) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | bot_bot(fun(nat,bool)) = ti(fun(nat,bool),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,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),A),B)) = hAPP(nat,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)),B)). [resolve(1399,a,1338,a)].
% 2.85/3.05 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),f118(nat,A)),f119(nat,A))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f118(nat,A)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f119(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(1399,a,1339,a)].
% 2.85/3.05 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(1399,a,1340,a)].
% 2.85/3.05 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(1399,a,1341,a)].
% 2.85/3.05 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(1399,a,1342,a)].
% 2.85/3.05 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(1399,a,1343,a)].
% 2.85/3.05 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1399,a,1344,a)].
% 2.85/3.05 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1399,a,1345,a)].
% 2.85/3.05 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(1399,a,1348,a)].
% 2.85/3.05 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(1399,a,1349,a)].
% 2.85/3.05 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(1399,a,1350,a)].
% 2.85/3.05 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(1399,a,1351,a)].
% 2.85/3.06 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(1399,a,1352,a)].
% 2.85/3.06 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(1399,a,1353,a)].
% 2.85/3.06 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(1399,a,1356,a)].
% 2.85/3.06 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(1399,a,1357,a)].
% 2.85/3.06 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(1399,a,1363,a)].
% 2.85/3.06 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(1399,a,1364,a)].
% 2.85/3.06 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) != ti(nat,A). [resolve(1399,a,1367,a)].
% 2.85/3.06 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(1399,a,1368,a)].
% 2.85/3.06 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(1399,a,1371,a)].
% 2.85/3.06 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(1399,a,1374,a)].
% 2.85/3.06 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) != ti(nat,A). [resolve(1399,a,1375,a)].
% 2.85/3.06 Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1399,a,1378,a)].
% 2.85/3.06 Derived: -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1399,a,1379,a)].
% 2.85/3.06 Derived: hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1399,a,1380,a)].
% 2.85/3.06 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),f143(nat,B,A)),A)). [resolve(1399,a,1381,a)].
% 2.85/3.06 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),f143(nat,B,A)),B)). [resolve(1399,a,1382,a)].
% 2.85/3.06 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(1399,a,1383,a)].
% 2.85/3.06 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(1399,a,1384,a)].
% 2.85/3.06 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),f144(nat,B,A)),A)). [resolve(1399,a,1385,a)].
% 2.85/3.06 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),f144(nat,B,A))). [resolve(1399,a,1386,a)].
% 2.85/3.06 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),f161(nat,B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(1399,a,1387,a)].
% 2.85/3.06 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f162(nat,A)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1399,a,1388,a)].
% 2.85/3.06 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),f166(nat,B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1399,a,1389,a)].
% 2.85/3.06 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f167(nat,A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(1399,a,1390,a)].
% 2.85/3.06 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),f185(nat,B,A))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)). [resolve(1399,a,1391,a)].
% 2.85/3.06 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),C),f185(nat,B,A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),f184(nat,B,A))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)). [resolve(1399,a,1392,a)].
% 2.85/3.06 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | hBOOL(hAPP(fun(nat,bool),bool,B,f185(nat,B,A))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)). [resolve(1399,a,1393,a)].
% 2.85/3.06 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | -hBOOL(hAPP(fun(nat,bool),bool,B,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f184(nat,B,A)),f185(nat,B,A)))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)). [resolve(1399,a,1394,a)].
% 2.85/3.06 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),f187(nat,B,A))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)). [resolve(1399,a,1395,a)].
% 2.85/3.06 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),C),f187(nat,B,A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f186(nat,B,A)),C)) | hBOOL(hAPP(fun(nat,bool),bool,B,A)). [resolve(1399,a,1396,a)].
% 2.85/3.06 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | hBOOL(hAPP(fun(nat,bool),bool,B,f187(nat,B,A))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)). [resolve(1399,a,1397,a)].
% 3.24/3.44 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | -hBOOL(hAPP(fun(nat,bool),bool,B,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f186(nat,B,A)),f187(nat,B,A)))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)). [resolve(1399,a,1398,a)].
% 3.24/3.44 1400 one(int) # label(arity_Int_Oint___Groups_Oone) # label(axiom). [assumption].
% 3.24/3.44 1401 -one(A) | one_one(A) = ti(A,one_one(A)) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom). [clausify(26)].
% 3.24/3.44 Derived: one_one(int) = ti(int,one_one(int)). [resolve(1400,a,1401,a)].
% 3.24/3.44 1402 one(nat) # label(arity_Nat_Onat___Groups_Oone) # label(axiom). [assumption].
% 3.24/3.44 Derived: one_one(nat) = ti(nat,one_one(nat)). [resolve(1402,a,1401,a)].
% 3.24/3.44 1403 ab_semigroup_add(int) # label(arity_Int_Oint___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 3.24/3.44 1404 -ab_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(27)].
% 3.24/3.44 1405 -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_233_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom). [clausify(301)].
% 3.24/3.44 Derived: plus_plus(int) = ti(fun(int,fun(int,int)),plus_plus(int)). [resolve(1403,a,1404,a)].
% 3.24/3.44 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)). [resolve(1403,a,1405,a)].
% 3.24/3.44 1406 ab_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 3.24/3.44 Derived: plus_plus(nat) = ti(fun(nat,fun(nat,nat)),plus_plus(nat)). [resolve(1406,a,1404,a)].
% 3.24/3.44 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(1406,a,1405,a)].
% 3.24/3.44 1407 cancel_semigroup_add(int) # label(arity_Int_Oint___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.24/3.44 1408 -cancel_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(28)].
% 3.24/3.44 1409 -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_226_add__right__imp__eq) # label(axiom). [clausify(294)].
% 3.24/3.44 1410 -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_228_add__left__imp__eq) # label(axiom). [clausify(296)].
% 3.24/3.44 1411 -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_230_add__right__cancel) # label(axiom). [clausify(298)].
% 3.24/3.44 1412 -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_230_add__right__cancel) # label(axiom). [clausify(298)].
% 3.24/3.44 1413 -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_231_add__left__cancel) # label(axiom). [clausify(299)].
% 3.24/3.44 1414 -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_231_add__left__cancel) # label(axiom). [clausify(299)].
% 3.24/3.44 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B) | ti(int,A) = ti(int,C). [resolve(1407,a,1409,a)].
% 3.24/3.44 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C) | ti(int,B) = ti(int,C). [resolve(1407,a,1410,a)].
% 3.46/3.70 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B) | ti(int,A) != ti(int,C). [resolve(1407,a,1412,a)].
% 3.46/3.70 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C) | ti(int,B) != ti(int,C). [resolve(1407,a,1414,a)].
% 3.46/3.70 1415 cancel_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.46/3.70 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(1415,a,1409,a)].
% 3.46/3.70 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(1415,a,1410,a)].
% 3.46/3.70 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(1415,a,1412,a)].
% 3.46/3.70 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(1415,a,1414,a)].
% 3.46/3.70 1416 power(int) # label(arity_Int_Oint___Power_Opower) # label(axiom). [assumption].
% 3.46/3.70 1417 -power(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(29)].
% 3.46/3.70 1418 -power(A) | power_power(A) = ti(fun(A,fun(nat,A)),power_power(A)) # label(tsy_c_Power_Opower__class_Opower_res) # label(axiom). [clausify(53)].
% 3.46/3.70 1419 -power(A) | hAPP(fun(A,fun(A,A)),fun(A,fun(nat,A)),hAPP(A,fun(fun(A,fun(A,A)),fun(A,fun(nat,A))),power_1(A),one_one(A)),times_times(A)) = power_power(A) # label(fact_916_power__power__power) # label(axiom). [clausify(981)].
% 3.46/3.70 Derived: times_times(int) = ti(fun(int,fun(int,int)),times_times(int)). [resolve(1416,a,1417,a)].
% 3.46/3.70 Derived: power_power(int) = ti(fun(int,fun(nat,int)),power_power(int)). [resolve(1416,a,1418,a)].
% 3.46/3.70 Derived: hAPP(fun(int,fun(int,int)),fun(int,fun(nat,int)),hAPP(int,fun(fun(int,fun(int,int)),fun(int,fun(nat,int))),power_1(int),one_one(int)),times_times(int)) = power_power(int). [resolve(1416,a,1419,a)].
% 3.46/3.70 1420 power(nat) # label(arity_Nat_Onat___Power_Opower) # label(axiom). [assumption].
% 3.46/3.70 Derived: times_times(nat) = ti(fun(nat,fun(nat,nat)),times_times(nat)). [resolve(1420,a,1417,a)].
% 3.46/3.70 Derived: power_power(nat) = ti(fun(nat,fun(nat,nat)),power_power(nat)). [resolve(1420,a,1418,a)].
% 3.46/3.70 Derived: hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),hAPP(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat))),power_1(nat),one_one(nat)),times_times(nat)) = power_power(nat). [resolve(1420,a,1419,a)].
% 3.46/3.70 1421 semiring(int) # label(arity_Int_Oint___Rings_Osemiring) # label(axiom). [assumption].
% 3.46/3.70 1422 -semiring(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(30)].
% 3.46/3.70 1423 -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_224_combine__common__factor) # label(axiom). [clausify(292)].
% 3.46/3.70 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),D)). [resolve(1421,a,1423,a)].
% 3.46/3.70 1424 semiring(nat) # label(arity_Nat_Onat___Rings_Osemiring) # label(axiom). [assumption].
% 3.46/3.70 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(1424,a,1423,a)].
% 3.59/3.82 1425 ab_semigroup_mult(int) # label(arity_Int_Oint___Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.59/3.82 1426 -ab_semigroup_mult(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_2_res) # label(axiom). [clausify(31)].
% 3.59/3.82 1427 -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_125_fold1__insert) # label(axiom). [clausify(193)].
% 3.59/3.82 1428 -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_143_fold__graph__permute__diff) # label(axiom). [clausify(211)].
% 3.59/3.82 1429 -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_150_fold__graph__insert__swap) # label(axiom). [clausify(218)].
% 3.59/3.82 1430 -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),f55(A,B)),f56(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f55(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f56(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_154_fold1__in) # label(axiom). [clausify(222)].
% 3.59/3.82 1431 -ab_semigroup_mult(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite100568337ommute(A,A),times_times(A))) # label(fact_192_comp__fun__commute) # label(axiom). [clausify(260)].
% 3.59/3.82 1432 -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_205_fold1__eq__fold) # label(axiom). [clausify(273)].
% 3.59/3.82 1433 -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_243_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom). [clausify(311)].
% 3.59/3.82 Derived: bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),times_times(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),times_times(int)),A)). [resolve(1425,a,1427,a)].
% 3.59/3.82 Derived: -hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),fun(int,bool))),finite_fold_graph(int,int),times_times(int)),A),B),C)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),D),B)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),fun(int,bool))),finite_fold_graph(int,int),times_times(int)),D),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),A),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),B),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),D),bot_bot(fun(int,bool)))))),C)). [resolve(1425,a,1428,a)].
% 3.59/3.82 Derived: -hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),fun(int,bool))),finite_fold_graph(int,int),times_times(int)),A),B),C)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),fun(int,bool))),finite_fold_graph(int,int),times_times(int)),D),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),C))). [resolve(1425,a,1429,a)].
% 3.59/3.82 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f55(int,A)),f56(int,A))),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f55(int,A)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f56(int,A)),bot_bot(fun(int,bool)))))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),times_times(int)),A)),A)). [resolve(1425,a,1430,a)].
% 3.59/3.82 Derived: hBOOL(hAPP(fun(int,fun(int,int)),bool,finite100568337ommute(int,int),times_times(int))). [resolve(1425,a,1431,a)].
% 3.59/3.82 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),times_times(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),times_times(int)),B),A). [resolve(1425,a,1432,a)].
% 3.59/3.82 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)). [resolve(1425,a,1433,a)].
% 3.59/3.82 1434 ab_semigroup_mult(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.59/3.82 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(1434,a,1427,a)].
% 3.59/3.82 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(1434,a,1428,a)].
% 3.59/3.82 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(1434,a,1429,a)].
% 3.59/3.82 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),f55(nat,A)),f56(nat,A))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f55(nat,A)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f56(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(1434,a,1430,a)].
% 3.59/3.82 Derived: hBOOL(hAPP(fun(nat,fun(nat,nat)),bool,finite100568337ommute(nat,nat),times_times(nat))). [resolve(1434,a,1431,a)].
% 3.59/3.82 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(1434,a,1432,a)].
% 3.59/3.82 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(1434,a,1433,a)].
% 3.74/3.95 1435 ordere216010020id_add(int) # label(arity_Int_Oint___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 3.74/3.95 1436 -ordere216010020id_add(A) | zero_zero(A) = ti(A,zero_zero(A)) # label(tsy_c_Groups_Ozero__class_Ozero_0_res) # label(axiom). [clausify(33)].
% 3.74/3.95 1437 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_944_add__pos__nonneg) # label(axiom). [clausify(1009)].
% 3.74/3.95 1438 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_945_add__nonneg__pos) # label(axiom). [clausify(1010)].
% 3.74/3.95 1439 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_946_add__strict__increasing) # label(axiom). [clausify(1011)].
% 3.74/3.95 1440 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_947_add__strict__increasing2) # label(axiom). [clausify(1012)].
% 3.74/3.95 1441 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_948_add__neg__nonpos) # label(axiom). [clausify(1013)].
% 3.74/3.95 1442 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_949_add__nonpos__neg) # label(axiom). [clausify(1014)].
% 3.74/3.95 1443 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_976_add__pos__pos) # label(axiom). [clausify(1038)].
% 3.74/3.95 1444 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_978_add__neg__neg) # label(axiom). [clausify(1040)].
% 3.74/3.95 Derived: zero_zero(int) = ti(int,zero_zero(int)). [resolve(1435,a,1436,a)].
% 3.74/3.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))). [resolve(1435,a,1437,a)].
% 3.74/3.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))). [resolve(1435,a,1438,a)].
% 3.74/3.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))). [resolve(1435,a,1439,a)].
% 3.74/3.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))). [resolve(1435,a,1440,a)].
% 3.74/3.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),zero_zero(int))). [resolve(1435,a,1441,a)].
% 3.74/3.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),zero_zero(int))). [resolve(1435,a,1442,a)].
% 3.74/3.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))). [resolve(1435,a,1443,a)].
% 3.74/3.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),zero_zero(int))). [resolve(1435,a,1444,a)].
% 3.74/3.95 1445 ordere216010020id_add(nat) # label(arity_Nat_Onat___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 3.74/3.95 Derived: zero_zero(nat) = ti(nat,zero_zero(nat)). [resolve(1445,a,1436,a)].
% 3.74/3.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))). [resolve(1445,a,1437,a)].
% 3.74/3.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))). [resolve(1445,a,1438,a)].
% 3.74/3.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(1445,a,1439,a)].
% 3.74/3.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(1445,a,1440,a)].
% 3.74/3.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))). [resolve(1445,a,1441,a)].
% 3.74/3.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))). [resolve(1445,a,1442,a)].
% 3.74/3.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))). [resolve(1445,a,1443,a)].
% 3.87/4.07 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))). [resolve(1445,a,1444,a)].
% 3.87/4.07 1446 ab_group_add(int) # label(arity_Int_Oint___Groups_Oab__group__add) # label(axiom). [assumption].
% 3.87/4.07 1447 -ab_group_add(A) | zero_zero(A) = ti(A,zero_zero(A)) # label(tsy_c_Groups_Ozero__class_Ozero_1_res) # label(axiom). [clausify(34)].
% 3.87/4.07 1448 -ab_group_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(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))))) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C)),hAPP(B,A,E,D)) # label(fact_173_setsum__diff1) # label(axiom). [clausify(241)].
% 3.87/4.07 1449 -ab_group_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(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))))) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) # label(fact_173_setsum__diff1) # label(axiom). [clausify(241)].
% 3.87/4.07 1450 -ab_group_add(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),minus_minus(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),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_190_setsum__subtractf) # label(axiom). [clausify(258)].
% 3.87/4.07 1451 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | ti(A,C) != ti(A,B) | ti(A,E) = ti(A,D) # label(fact_247_diff__eq__diff__eq) # label(axiom). [clausify(315)].
% 3.87/4.07 1452 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | ti(A,C) = ti(A,B) | ti(A,E) != ti(A,D) # label(fact_247_diff__eq__diff__eq) # label(axiom). [clausify(315)].
% 3.87/4.07 1453 -ab_group_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),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(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),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),E),D)) # label(fact_329_setsum__diff) # label(axiom). [clausify(397)].
% 3.87/4.07 1454 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B)) # label(fact_492_minus__diff__eq) # label(axiom). [clausify(560)].
% 3.87/4.07 1455 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)) # label(fact_501_minus__add__distrib) # label(axiom). [clausify(569)].
% 3.87/4.07 1456 -ab_group_add(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),uminus_uminus(A)),C)),D) = hAPP(A,A,uminus_uminus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D)) # label(fact_510_setsum__negf) # label(axiom). [clausify(578)].
% 3.87/4.07 1457 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,uminus_uminus(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) # label(fact_513_ab__diff__minus) # label(axiom). [clausify(581)].
% 3.87/4.07 1458 -ab_group_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),D)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),D),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,D,B)),hAPP(nat,A,D,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),one_one(nat)))) # label(fact_934_setsum__natinterval__difff) # label(axiom). [clausify(999)].
% 3.87/4.07 1459 -ab_group_add(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),D)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),D),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = zero_zero(A) # label(fact_934_setsum__natinterval__difff) # label(axiom). [clausify(999)].
% 3.87/4.07 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),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),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))))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B)),hAPP(A,int,D,C)). [resolve(1446,a,1448,a)].
% 3.87/4.07 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),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),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))))) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B). [resolve(1446,a,1449,a)].
% 3.87/4.07 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(A,fun(int,int)),fun(fun(A,int),fun(A,int)),combs(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),minus_minus(int)),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D)). [resolve(1446,a,1450,a)].
% 4.13/4.32 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | ti(int,B) != ti(int,A) | ti(int,D) = ti(int,C). [resolve(1446,a,1451,a)].
% 4.13/4.32 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | ti(int,B) = ti(int,A) | ti(int,D) != ti(int,C). [resolve(1446,a,1452,a)].
% 4.13/4.32 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -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),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),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),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C)). [resolve(1446,a,1453,a)].
% 4.13/4.32 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),A)). [resolve(1446,a,1454,a)].
% 4.13/4.32 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)). [resolve(1446,a,1455,a)].
% 4.13/4.32 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(int,int),fun(fun(A,int),fun(A,int)),combb(int,int,A),uminus_uminus(int)),B)),C) = hAPP(int,int,uminus_uminus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C)). [resolve(1446,a,1456,a)].
% 4.13/4.32 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B). [resolve(1446,a,1457,a)].
% 4.13/4.32 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),minus_minus(int)),C)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,C,A)),hAPP(nat,int,C,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))). [resolve(1446,a,1458,a)].
% 4.13/4.32 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),minus_minus(int)),C)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = zero_zero(int). [resolve(1446,a,1459,a)].
% 4.13/4.32 1460 ring(int) # label(arity_Int_Oint___Rings_Oring) # label(axiom). [assumption].
% 4.13/4.32 1461 -ring(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(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))))) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C)),hAPP(B,A,E,D)) # label(fact_174_setsum__diff1__ring) # label(axiom). [clausify(242)].
% 4.13/4.32 1462 -ring(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)),D) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F) | 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),minus_minus(A),B),E)),C)),D) = ti(A,F) # label(fact_219_eq__add__iff2) # label(axiom). [clausify(287)].
% 4.13/4.32 1463 -ring(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)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F) | 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),minus_minus(A),B),E)),C)),D) != ti(A,F) # label(fact_219_eq__add__iff2) # label(axiom). [clausify(287)].
% 4.13/4.32 1464 -ring(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)),D) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F) | 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),minus_minus(A),E),B)),C)),F) = ti(A,D) # label(fact_220_eq__add__iff1) # label(axiom). [clausify(288)].
% 4.13/4.32 1465 -ring(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)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F) | 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),minus_minus(A),E),B)),C)),F) != ti(A,D) # label(fact_220_eq__add__iff1) # label(axiom). [clausify(288)].
% 4.13/4.32 1466 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,uminus_uminus(A),C)) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_505_minus__mult__right) # label(axiom). [clausify(573)].
% 4.13/4.32 1467 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),B)),C) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_506_minus__mult__left) # label(axiom). [clausify(574)].
% 4.13/4.32 1468 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),B)),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_507_minus__mult__commute) # label(axiom). [clausify(575)].
% 4.13/4.32 1469 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) # label(fact_508_minus__mult__minus) # label(axiom). [clausify(576)].
% 4.13/4.32 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B)),C) = ti(int,E). [resolve(1460,a,1462,a)].
% 4.13/4.32 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B)),C) != ti(int,E). [resolve(1460,a,1463,a)].
% 4.13/4.32 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),D),A)),B)),E) = ti(int,C). [resolve(1460,a,1464,a)].
% 4.19/4.45 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),D),A)),B)),E) != ti(int,C). [resolve(1460,a,1465,a)].
% 4.19/4.45 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)). [resolve(1460,a,1466,a)].
% 4.19/4.45 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),A)),B) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)). [resolve(1460,a,1467,a)].
% 4.19/4.45 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),A)),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,uminus_uminus(int),B)). [resolve(1460,a,1468,a)].
% 4.19/4.45 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B). [resolve(1460,a,1469,a)].
% 4.19/4.45 1470 semiring_0(int) # label(arity_Int_Oint___Rings_Osemiring__0) # label(axiom). [assumption].
% 4.19/4.45 1471 -semiring_0(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(C,bool),fun(B,A),hAPP(fun(B,fun(fun(C,bool),A)),fun(fun(C,bool),fun(B,A)),combc(B,fun(C,bool),A),hAPP(fun(B,fun(C,A)),fun(B,fun(fun(C,bool),A)),hAPP(fun(fun(C,A),fun(fun(C,bool),A)),fun(fun(B,fun(C,A)),fun(B,fun(fun(C,bool),A))),combb(fun(C,A),fun(fun(C,bool),A),B),big_co1399186613setsum(C,A)),hAPP(fun(C,A),fun(B,fun(C,A)),hAPP(fun(B,fun(fun(C,A),fun(C,A))),fun(fun(C,A),fun(B,fun(C,A))),combc(B,fun(C,A),fun(C,A)),hAPP(fun(B,fun(A,A)),fun(B,fun(fun(C,A),fun(C,A))),hAPP(fun(fun(A,A),fun(fun(C,A),fun(C,A))),fun(fun(B,fun(A,A)),fun(B,fun(fun(C,A),fun(C,A)))),combb(fun(A,A),fun(fun(C,A),fun(C,A)),B),combb(A,A,C)),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),D))),E))),F)),V6) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),V6)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),E),F)) # label(fact_187_setsum__product) # label(axiom). [clausify(255)].
% 4.19/4.45 1472 -semiring_0(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),D) # label(fact_188_setsum__left__distrib) # label(axiom). [clausify(256)].
% 4.19/4.45 1473 -semiring_0(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),hAPP(A,fun(A,A),times_times(A),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E)) # label(fact_189_setsum__right__distrib) # label(axiom). [clausify(257)].
% 4.19/4.45 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(B,bool),fun(A,int),hAPP(fun(A,fun(fun(B,bool),int)),fun(fun(B,bool),fun(A,int)),combc(A,fun(B,bool),int),hAPP(fun(A,fun(B,int)),fun(A,fun(fun(B,bool),int)),hAPP(fun(fun(B,int),fun(fun(B,bool),int)),fun(fun(A,fun(B,int)),fun(A,fun(fun(B,bool),int))),combb(fun(B,int),fun(fun(B,bool),int),A),big_co1399186613setsum(B,int)),hAPP(fun(B,int),fun(A,fun(B,int)),hAPP(fun(A,fun(fun(B,int),fun(B,int))),fun(fun(B,int),fun(A,fun(B,int))),combc(A,fun(B,int),fun(B,int)),hAPP(fun(A,fun(int,int)),fun(A,fun(fun(B,int),fun(B,int))),hAPP(fun(fun(int,int),fun(fun(B,int),fun(B,int))),fun(fun(A,fun(int,int)),fun(A,fun(fun(B,int),fun(B,int)))),combb(fun(int,int),fun(fun(B,int),fun(B,int)),A),combb(int,int,B)),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),times_times(int)),C))),D))),E)),F) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),F)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),D),E)). [resolve(1470,a,1471,a)].
% 4.19/4.45 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),times_times(int)),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),C). [resolve(1470,a,1472,a)].
% 4.19/4.45 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(int,int),fun(fun(A,int),fun(A,int)),combb(int,int,A),hAPP(int,fun(int,int),times_times(int),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D)). [resolve(1470,a,1473,a)].
% 4.19/4.45 1474 semiring_0(nat) # label(arity_Nat_Onat___Rings_Osemiring__0) # label(axiom). [assumption].
% 4.19/4.45 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(fun(B,bool),fun(A,nat),hAPP(fun(A,fun(fun(B,bool),nat)),fun(fun(B,bool),fun(A,nat)),combc(A,fun(B,bool),nat),hAPP(fun(A,fun(B,nat)),fun(A,fun(fun(B,bool),nat)),hAPP(fun(fun(B,nat),fun(fun(B,bool),nat)),fun(fun(A,fun(B,nat)),fun(A,fun(fun(B,bool),nat))),combb(fun(B,nat),fun(fun(B,bool),nat),A),big_co1399186613setsum(B,nat)),hAPP(fun(B,nat),fun(A,fun(B,nat)),hAPP(fun(A,fun(fun(B,nat),fun(B,nat))),fun(fun(B,nat),fun(A,fun(B,nat))),combc(A,fun(B,nat),fun(B,nat)),hAPP(fun(A,fun(nat,nat)),fun(A,fun(fun(B,nat),fun(B,nat))),hAPP(fun(fun(nat,nat),fun(fun(B,nat),fun(B,nat))),fun(fun(A,fun(nat,nat)),fun(A,fun(fun(B,nat),fun(B,nat)))),combb(fun(nat,nat),fun(fun(B,nat),fun(B,nat)),A),combb(nat,nat,B)),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),times_times(nat)),C))),D))),E)),F) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),F)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),D),E)). [resolve(1474,a,1471,a)].
% 4.19/4.45 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),times_times(nat)),B)),C)),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D)),C). [resolve(1474,a,1472,a)].
% 4.19/4.45 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(fun(A,nat),fun(A,nat),hAPP(fun(nat,nat),fun(fun(A,nat),fun(A,nat)),combb(nat,nat,A),hAPP(nat,fun(nat,nat),times_times(nat),B)),C)),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D)). [resolve(1474,a,1473,a)].
% 4.34/4.57 1475 group_add(int) # label(arity_Int_Oint___Groups_Ogroup__add) # label(axiom). [assumption].
% 4.34/4.57 1476 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),C) = ti(A,B) # label(fact_221_diff__add__cancel) # label(axiom). [clausify(289)].
% 4.34/4.57 1477 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),C) = ti(A,B) # label(fact_222_add__diff__cancel) # label(axiom). [clausify(290)].
% 4.34/4.57 1478 -group_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,uminus_uminus(A),B)) = ti(A,B) # label(fact_486_minus__minus) # label(axiom). [clausify(554)].
% 4.34/4.57 1479 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) != ti(A,C) | hAPP(A,A,uminus_uminus(A),C) = ti(A,B) # label(fact_487_equation__minus__iff) # label(axiom). [clausify(555)].
% 4.34/4.57 1480 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) = ti(A,C) | hAPP(A,A,uminus_uminus(A),C) != ti(A,B) # label(fact_487_equation__minus__iff) # label(axiom). [clausify(555)].
% 4.34/4.57 1481 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) != ti(A,C) | hAPP(A,A,uminus_uminus(A),C) = ti(A,B) # label(fact_488_minus__equation__iff) # label(axiom). [clausify(556)].
% 4.34/4.57 1482 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) = ti(A,C) | hAPP(A,A,uminus_uminus(A),C) != ti(A,B) # label(fact_488_minus__equation__iff) # label(axiom). [clausify(556)].
% 4.34/4.57 1483 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) != hAPP(A,A,uminus_uminus(A),C) | ti(A,B) = ti(A,C) # label(fact_489_neg__equal__iff__equal) # label(axiom). [clausify(557)].
% 4.34/4.57 1484 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,uminus_uminus(A),C) | ti(A,B) != ti(A,C) # label(fact_489_neg__equal__iff__equal) # label(axiom). [clausify(557)].
% 4.34/4.57 1485 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B)) # label(fact_502_minus__add) # label(axiom). [clausify(570)].
% 4.34/4.57 1486 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),B)),C)) = ti(A,C) # label(fact_503_add__minus__cancel) # label(axiom). [clausify(571)].
% 4.34/4.57 1487 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)) = ti(A,C) # label(fact_504_minus__add__cancel) # label(axiom). [clausify(572)].
% 4.34/4.57 1488 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_511_diff__minus__eq__add) # label(axiom). [clausify(579)].
% 4.34/4.57 1489 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,uminus_uminus(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) # label(fact_514_diff__def) # label(axiom). [clausify(582)].
% 4.34/4.57 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),B) = ti(int,A). [resolve(1475,a,1476,a)].
% 4.34/4.57 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),B) = ti(int,A). [resolve(1475,a,1477,a)].
% 4.34/4.57 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,uminus_uminus(int),A)) = ti(int,A). [resolve(1475,a,1478,a)].
% 4.34/4.57 Derived: hAPP(int,int,uminus_uminus(int),A) != ti(int,B) | hAPP(int,int,uminus_uminus(int),B) = ti(int,A). [resolve(1475,a,1479,a)].
% 4.34/4.57 Derived: hAPP(int,int,uminus_uminus(int),A) != hAPP(int,int,uminus_uminus(int),B) | ti(int,A) = ti(int,B). [resolve(1475,a,1483,a)].
% 4.34/4.57 Derived: hAPP(int,int,uminus_uminus(int),A) = hAPP(int,int,uminus_uminus(int),B) | ti(int,A) != ti(int,B). [resolve(1475,a,1484,a)].
% 4.34/4.57 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A)). [resolve(1475,a,1485,a)].
% 4.34/4.57 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),A)),B)) = ti(int,B). [resolve(1475,a,1486,a)].
% 4.34/4.57 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)) = ti(int,B). [resolve(1475,a,1487,a)].
% 4.48/4.70 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),hAPP(int,int,uminus_uminus(int),B)). [resolve(1475,a,1488,a)].
% 4.48/4.70 1490 semiri456707255roduct(int) # label(arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption].
% 4.48/4.70 1491 -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_223_crossproduct__eq) # label(axiom). [clausify(291)].
% 4.48/4.70 1492 -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_223_crossproduct__eq) # label(axiom). [clausify(291)].
% 4.48/4.70 1493 -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_223_crossproduct__eq) # label(axiom). [clausify(291)].
% 4.48/4.70 1494 -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_249_crossproduct__noteq) # label(axiom). [clausify(317)].
% 4.48/4.70 1495 -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_249_crossproduct__noteq) # label(axiom). [clausify(317)].
% 4.48/4.70 1496 -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_249_crossproduct__noteq) # label(axiom). [clausify(317)].
% 4.48/4.70 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) | ti(int,A) = ti(int,C) | ti(int,B) = ti(int,D). [resolve(1490,a,1491,a)].
% 4.48/4.70 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) | ti(int,A) != ti(int,C). [resolve(1490,a,1492,a)].
% 4.48/4.70 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) | ti(int,B) != ti(int,D). [resolve(1490,a,1493,a)].
% 4.61/4.82 Derived: ti(int,A) = ti(int,B) | ti(int,C) = ti(int,D) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)). [resolve(1490,a,1494,a)].
% 4.61/4.82 Derived: ti(int,A) != ti(int,B) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)). [resolve(1490,a,1495,a)].
% 4.61/4.82 1497 semiri456707255roduct(nat) # label(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption].
% 4.61/4.82 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(1497,a,1491,a)].
% 4.61/4.82 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(1497,a,1492,a)].
% 4.61/4.82 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(1497,a,1493,a)].
% 4.61/4.82 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(1497,a,1494,a)].
% 4.61/4.82 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(1497,a,1495,a)].
% 4.61/4.82 1498 comm_semiring_1(int) # label(arity_Int_Oint___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 4.61/4.82 1499 -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_225_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom). [clausify(293)].
% 4.61/4.82 1500 -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_229_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom). [clausify(297)].
% 4.61/4.82 1501 -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_232_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom). [clausify(300)].
% 4.61/4.82 1502 -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_234_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom). [clausify(302)].
% 4.61/4.82 1503 -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_235_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom). [clausify(303)].
% 4.61/4.82 1504 -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_236_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom). [clausify(304)].
% 4.61/4.82 1505 -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_237_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom). [clausify(305)].
% 4.61/4.82 1506 -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_238_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom). [clausify(306)].
% 4.61/4.82 1507 -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_239_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom). [clausify(307)].
% 4.61/4.82 1508 -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_240_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom). [clausify(308)].
% 4.61/4.82 1509 -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_241_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom). [clausify(309)].
% 4.61/4.82 1510 -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_242_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom). [clausify(310)].
% 4.61/4.82 1511 -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_244_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom). [clausify(312)].
% 4.61/4.82 1512 -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_245_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom). [clausify(313)].
% 4.61/4.82 1513 -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_246_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom). [clausify(314)].
% 4.61/4.82 1514 -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_248_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom). [clausify(316)].
% 4.61/4.82 1515 -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_251_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom). [clausify(319)].
% 4.61/4.82 1516 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) = ti(A,B) # label(fact_628_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom). [clausify(696)].
% 4.61/4.82 1517 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) = ti(A,B) # label(fact_631_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom). [clausify(699)].
% 4.61/4.82 1518 -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),one_one(A))),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),C) # label(fact_635_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom). [clausify(703)].
% 4.61/4.82 1519 -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),one_one(A))),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_636_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom). [clausify(704)].
% 4.61/4.82 1520 -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),one_one(A)),one_one(A))),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) # label(fact_637_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom). [clausify(705)].
% 4.61/4.82 1521 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),one_one(nat)))),D)))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),plus_plus(A),C)),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),semiring_1_of_nat(A))),D))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))) # label(fact_656_arith__series__general) # label(axiom). [clausify(724)].
% 4.61/4.82 1522 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,semiring_1_of_nat(A),B)),one_one(A))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),semiring_1_of_nat(A)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),B))) # label(fact_677_gauss__sum) # label(axiom). [clausify(744)].
% 4.61/4.82 1523 -comm_semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),one_one(nat)) = ti(A,B) # label(fact_709_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom). [clausify(776)].
% 4.61/4.82 1524 -comm_semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),D) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) # label(fact_724_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom). [clausify(791)].
% 4.61/4.82 1525 -comm_semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(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(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D)) # label(fact_732_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom). [clausify(799)].
% 4.61/4.82 1526 -comm_semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)) # label(fact_816_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom). [clausify(883)].
% 4.61/4.82 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)). [resolve(1498,a,1499,a)].
% 4.61/4.82 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D)). [resolve(1498,a,1500,a)].
% 4.61/4.82 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),B). [resolve(1498,a,1501,a)].
% 4.61/4.82 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)). [resolve(1498,a,1504,a)].
% 4.61/4.82 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A). [resolve(1498,a,1505,a)].
% 4.61/4.82 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)). [resolve(1498,a,1506,a)].
% 4.61/4.82 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),D)). [resolve(1498,a,1507,a)].
% 4.61/4.82 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),B). [resolve(1498,a,1509,a)].
% 4.61/4.82 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)). [resolve(1498,a,1512,a)].
% 4.61/4.82 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A). [resolve(1498,a,1513,a)].
% 4.61/4.82 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)). [resolve(1498,a,1514,a)].
% 4.61/4.82 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int))),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),B). [resolve(1498,a,1518,a)].
% 4.61/4.83 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int))),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)). [resolve(1498,a,1519,a)].
% 4.61/4.83 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int))),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A). [resolve(1498,a,1520,a)].
% 4.61/4.83 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),C)))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),hAPP(int,fun(int,int),plus_plus(int),B)),hAPP(int,fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(int,fun(nat,int)),combc(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),semiring_1_of_nat(int))),C))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A))). [resolve(1498,a,1521,a)].
% 4.61/4.83 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),A)),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),semiring_1_of_nat(int)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),A))). [resolve(1498,a,1522,a)].
% 4.61/4.83 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),one_one(nat)) = ti(int,A). [resolve(1498,a,1523,a)].
% 4.61/4.83 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),C) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(1498,a,1524,a)].
% 4.61/4.83 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C)). [resolve(1498,a,1526,a)].
% 4.61/4.83 1527 comm_semiring_1(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 4.61/4.83 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(1527,a,1499,a)].
% 4.61/4.83 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(1527,a,1500,a)].
% 4.61/4.83 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(1527,a,1501,a)].
% 4.61/4.83 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(1527,a,1504,a)].
% 4.61/4.83 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(1527,a,1505,a)].
% 4.61/4.83 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(1527,a,1506,a)].
% 4.61/4.83 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(1527,a,1507,a)].
% 4.61/4.83 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(1527,a,1509,a)].
% 4.61/4.83 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(1527,a,1512,a)].
% 4.61/4.83 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(1527,a,1513,a)].
% 4.61/4.83 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(1527,a,1514,a)].
% 4.61/4.83 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),B). [resolve(1527,a,1518,a)].
% 4.61/4.83 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)). [resolve(1527,a,1519,a)].
% 4.61/4.83 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat))),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),A). [resolve(1527,a,1520,a)].
% 4.61/4.83 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),C)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),plus_plus(nat),B)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),times_times(nat)),semiring_1_of_nat(nat))),C))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A))). [resolve(1527,a,1521,a)].
% 4.61/4.83 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),one_one(nat))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),semiring_1_of_nat(nat)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),A))). [resolve(1527,a,1522,a)].
% 5.02/5.21 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),one_one(nat)) = ti(nat,A). [resolve(1527,a,1523,a)].
% 5.02/5.21 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(1527,a,1524,a)].
% 5.02/5.21 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C)). [resolve(1527,a,1526,a)].
% 5.02/5.21 1528 cancel146912293up_add(int) # label(arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.02/5.21 1529 -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_227_add__imp__eq) # label(axiom). [clausify(295)].
% 5.02/5.21 1530 cancel146912293up_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.02/5.21 1531 comm_semiring(int) # label(arity_Int_Oint___Rings_Ocomm__semiring) # label(axiom). [assumption].
% 5.02/5.21 1532 -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_250_comm__semiring__class_Odistrib) # label(axiom). [clausify(318)].
% 5.02/5.21 1533 comm_semiring(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring) # label(axiom). [assumption].
% 5.02/5.21 1534 ordere236663937imp_le(int) # label(arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 5.02/5.21 1535 -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_294_add__le__imp__le__left) # label(axiom). [clausify(362)].
% 5.02/5.21 1536 -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_295_add__le__imp__le__right) # label(axiom). [clausify(363)].
% 5.02/5.21 1537 -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_299_add__le__cancel__left) # label(axiom). [clausify(367)].
% 5.02/5.21 1538 -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_299_add__le__cancel__left) # label(axiom). [clausify(367)].
% 5.02/5.21 1539 -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_300_add__le__cancel__right) # label(axiom). [clausify(368)].
% 5.02/5.21 1540 -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_300_add__le__cancel__right) # label(axiom). [clausify(368)].
% 5.02/5.21 1541 -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_370_min__add__distrib__left) # label(axiom). [clausify(438)].
% 5.02/5.21 1542 -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_534_max__add__distrib__left) # label(axiom). [clausify(602)].
% 5.02/5.21 1543 -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_725_add__less__imp__less__left) # label(axiom). [clausify(792)].
% 5.02/5.21 1544 -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_726_add__less__imp__less__right) # label(axiom). [clausify(793)].
% 5.02/5.21 1545 -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_730_add__less__cancel__left) # label(axiom). [clausify(797)].
% 5.02/5.21 1546 -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_730_add__less__cancel__left) # label(axiom). [clausify(797)].
% 5.02/5.21 1547 -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_731_add__less__cancel__right) # label(axiom). [clausify(798)].
% 5.02/5.21 1548 -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_731_add__less__cancel__right) # label(axiom). [clausify(798)].
% 5.02/5.21 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)). [resolve(1534,a,1535,a)].
% 5.02/5.21 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(1534,a,1536,a)].
% 5.02/5.21 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)). [resolve(1534,a,1538,a)].
% 5.02/5.21 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(1534,a,1540,a)].
% 5.02/5.21 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),B). [resolve(1534,a,1541,a)].
% 5.02/5.21 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)),B). [resolve(1534,a,1542,a)].
% 5.02/5.21 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(1534,a,1543,a)].
% 5.02/5.21 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(1534,a,1544,a)].
% 5.02/5.21 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(1534,a,1546,a)].
% 5.02/5.21 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(1534,a,1548,a)].
% 5.02/5.21 1549 ordere236663937imp_le(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 5.02/5.21 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(1549,a,1535,a)].
% 5.02/5.21 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(1549,a,1536,a)].
% 5.02/5.21 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(1549,a,1538,a)].
% 5.02/5.21 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(1549,a,1540,a)].
% 5.02/5.21 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(1549,a,1541,a)].
% 5.02/5.21 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(1549,a,1542,a)].
% 5.02/5.21 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(1549,a,1543,a)].
% 5.02/5.21 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(1549,a,1544,a)].
% 5.02/5.21 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(1549,a,1546,a)].
% 5.02/5.21 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(1549,a,1548,a)].
% 5.10/5.33 1550 ordered_ab_group_add(int) # label(arity_Int_Oint___Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 5.10/5.33 1551 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) # label(fact_304_diff__eq__diff__less__eq) # label(axiom). [clausify(372)].
% 5.10/5.33 1552 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) # label(fact_304_diff__eq__diff__less__eq) # label(axiom). [clausify(372)].
% 5.10/5.33 1553 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C) # label(fact_371_min__diff__distrib__left) # label(axiom). [clausify(439)].
% 5.10/5.33 1554 -ordered_ab_group_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,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B))) # label(fact_493_le__imp__neg__le) # label(axiom). [clausify(561)].
% 5.10/5.33 1555 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_494_neg__le__iff__le) # label(axiom). [clausify(562)].
% 5.10/5.33 1556 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_494_neg__le__iff__le) # label(axiom). [clausify(562)].
% 5.10/5.33 1557 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_495_minus__le__iff) # label(axiom). [clausify(563)].
% 5.10/5.33 1558 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_495_minus__le__iff) # label(axiom). [clausify(563)].
% 5.10/5.33 1559 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_496_le__minus__iff) # label(axiom). [clausify(564)].
% 5.10/5.33 1560 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_496_le__minus__iff) # label(axiom). [clausify(564)].
% 5.10/5.33 1561 -ordered_ab_group_add(A) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),hAPP(A,fun(A,bool),ord_lessThan(A),B)) = hAPP(A,fun(A,bool),ord_greaterThan(A),hAPP(A,A,uminus_uminus(A),B)) # label(fact_516_image__uminus__lessThan) # label(axiom). [clausify(584)].
% 5.10/5.33 1562 -ordered_ab_group_add(A) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),hAPP(A,fun(A,bool),ord_greaterThan(A),B)) = hAPP(A,fun(A,bool),ord_lessThan(A),hAPP(A,A,uminus_uminus(A),B)) # label(fact_517_image__uminus__greaterThan) # label(axiom). [clausify(585)].
% 5.10/5.33 1563 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C) # label(fact_535_max__diff__distrib__left) # label(axiom). [clausify(603)].
% 5.10/5.34 1564 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) # label(fact_768_diff__eq__diff__less) # label(axiom). [clausify(835)].
% 5.10/5.34 1565 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) # label(fact_768_diff__eq__diff__less) # label(axiom). [clausify(835)].
% 5.10/5.34 1566 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_808_neg__less__iff__less) # label(axiom). [clausify(875)].
% 5.10/5.34 1567 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_808_neg__less__iff__less) # label(axiom). [clausify(875)].
% 5.10/5.34 1568 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_809_minus__less__iff) # label(axiom). [clausify(876)].
% 5.10/5.34 1569 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_809_minus__less__iff) # label(axiom). [clausify(876)].
% 5.10/5.34 1570 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_810_less__minus__iff) # label(axiom). [clausify(877)].
% 5.10/5.34 1571 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_810_less__minus__iff) # label(axiom). [clausify(877)].
% 5.10/5.34 1572 -ordered_ab_group_add(A) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),B),C)) = hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B)) # label(fact_834_image__uminus__atLeastAtMost) # label(axiom). [clausify(901)].
% 5.10/5.34 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)). [resolve(1550,a,1551,a)].
% 5.10/5.34 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)). [resolve(1550,a,1552,a)].
% 5.10/5.34 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),B). [resolve(1550,a,1553,a)].
% 5.10/5.34 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,uminus_uminus(int),A))). [resolve(1550,a,1554,a)].
% 5.10/5.34 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1550,a,1555,a)].
% 5.25/5.46 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),B)),A)). [resolve(1550,a,1557,a)].
% 5.25/5.46 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,uminus_uminus(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,uminus_uminus(int),A))). [resolve(1550,a,1559,a)].
% 5.25/5.46 Derived: hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),uminus_uminus(int)),hAPP(int,fun(int,bool),ord_lessThan(int),A)) = hAPP(int,fun(int,bool),ord_greaterThan(int),hAPP(int,int,uminus_uminus(int),A)). [resolve(1550,a,1561,a)].
% 5.25/5.46 Derived: hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),uminus_uminus(int)),hAPP(int,fun(int,bool),ord_greaterThan(int),A)) = hAPP(int,fun(int,bool),ord_lessThan(int),hAPP(int,int,uminus_uminus(int),A)). [resolve(1550,a,1562,a)].
% 5.25/5.46 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)),B). [resolve(1550,a,1563,a)].
% 5.25/5.46 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)). [resolve(1550,a,1564,a)].
% 5.25/5.46 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)). [resolve(1550,a,1565,a)].
% 5.25/5.46 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)). [resolve(1550,a,1566,a)].
% 5.25/5.46 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)). [resolve(1550,a,1567,a)].
% 5.25/5.46 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),B)),A)). [resolve(1550,a,1568,a)].
% 5.25/5.46 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,uminus_uminus(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,uminus_uminus(int),A))). [resolve(1550,a,1570,a)].
% 5.25/5.46 Derived: hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),uminus_uminus(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),A),B)) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,uminus_uminus(int),A)). [resolve(1550,a,1572,a)].
% 5.25/5.46 1573 ordered_ring(int) # label(arity_Int_Oint___Rings_Oordered__ring) # label(axiom). [assumption].
% 5.25/5.46 1574 -ordered_ring(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),hAPP(A,A,hAPP(A,fun(A,A),times_times(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),E),C)),F))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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),minus_minus(A),B),E)),C)),D)),F)) # label(fact_324_le__add__iff1) # label(axiom). [clausify(392)].
% 5.25/5.46 1575 -ordered_ring(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),hAPP(A,A,hAPP(A,fun(A,A),times_times(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),E),C)),F))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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),minus_minus(A),B),E)),C)),D)),F)) # label(fact_324_le__add__iff1) # label(axiom). [clausify(392)].
% 5.25/5.47 1576 -ordered_ring(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),hAPP(A,A,hAPP(A,fun(A,A),times_times(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),E),C)),F))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),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),minus_minus(A),E),B)),C)),F))) # label(fact_325_le__add__iff2) # label(axiom). [clausify(393)].
% 5.25/5.47 1577 -ordered_ring(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),hAPP(A,A,hAPP(A,fun(A,A),times_times(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),E),C)),F))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),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),minus_minus(A),E),B)),C)),F))) # label(fact_325_le__add__iff2) # label(axiom). [clausify(393)].
% 5.25/5.47 1578 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(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),E),C)),F))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C)),D)),F)) # label(fact_836_less__add__iff1) # label(axiom). [clausify(903)].
% 5.25/5.47 1579 -ordered_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(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),E),C)),F))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C)),D)),F)) # label(fact_836_less__add__iff1) # label(axiom). [clausify(903)].
% 5.25/5.47 1580 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(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),E),C)),F))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),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),minus_minus(A),E),B)),C)),F))) # label(fact_837_less__add__iff2) # label(axiom). [clausify(904)].
% 5.25/5.47 1581 -ordered_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(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),E),C)),F))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),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),minus_minus(A),E),B)),C)),F))) # label(fact_837_less__add__iff2) # label(axiom). [clausify(904)].
% 5.25/5.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B)),C)),E)). [resolve(1573,a,1574,a)].
% 5.25/5.47 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B)),C)),E)). [resolve(1573,a,1575,a)].
% 5.34/5.59 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),D),A)),B)),E))). [resolve(1573,a,1576,a)].
% 5.34/5.59 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),D),A)),B)),E))). [resolve(1573,a,1577,a)].
% 5.34/5.59 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B)),C)),E)). [resolve(1573,a,1578,a)].
% 5.34/5.59 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B)),C)),E)). [resolve(1573,a,1579,a)].
% 5.34/5.59 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),D),A)),B)),E))). [resolve(1573,a,1580,a)].
% 5.34/5.59 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),D),A)),B)),E))). [resolve(1573,a,1581,a)].
% 5.34/5.59 1582 linord219039673up_add(int) # label(arity_Int_Oint___Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 5.34/5.59 1583 -linord219039673up_add(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(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),B)) = hAPP(A,A,uminus_uminus(A),hAPP(fun(A,bool),A,big_linorder_Max(A),B)) # label(fact_480_minus__Max__eq__Min) # label(axiom). [clausify(548)].
% 5.34/5.59 1584 -linord219039673up_add(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(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),B)) = hAPP(A,A,uminus_uminus(A),hAPP(fun(A,bool),A,big_linorder_Min(A),B)) # label(fact_481_minus__Min__eq__Max) # label(axiom). [clausify(549)].
% 5.34/5.59 1585 -linord219039673up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) # label(fact_563_minus__min__eq__max) # label(axiom). [clausify(631)].
% 5.34/5.59 1586 -linord219039673up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) # label(fact_564_minus__max__eq__min) # label(axiom). [clausify(632)].
% 5.34/5.59 1587 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_974_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(1036)].
% 5.34/5.59 1588 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_974_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(1036)].
% 5.34/5.59 1589 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_975_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(1037)].
% 5.34/5.59 1590 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_975_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(1037)].
% 5.34/5.59 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),uminus_uminus(int)),A)) = hAPP(int,int,uminus_uminus(int),hAPP(fun(int,bool),int,big_linorder_Max(int),A)). [resolve(1582,a,1583,a)].
% 5.34/5.59 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),uminus_uminus(int)),A)) = hAPP(int,int,uminus_uminus(int),hAPP(fun(int,bool),int,big_linorder_Min(int),A)). [resolve(1582,a,1584,a)].
% 5.34/5.59 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)). [resolve(1582,a,1585,a)].
% 5.34/5.59 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)). [resolve(1582,a,1586,a)].
% 5.34/5.59 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(1582,a,1587,a)].
% 5.34/5.59 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(1582,a,1589,a)].
% 5.71/5.96 1591 idom(int) # label(arity_Int_Oint___Rings_Oidom) # label(axiom). [assumption].
% 5.71/5.96 1592 -idom(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C) | ti(A,B) = ti(A,C) | hAPP(A,A,uminus_uminus(A),B) = ti(A,C) # label(fact_509_square__eq__iff) # label(axiom). [clausify(577)].
% 5.71/5.96 1593 -idom(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C) | ti(A,B) != ti(A,C) # label(fact_509_square__eq__iff) # label(axiom). [clausify(577)].
% 5.71/5.96 1594 -idom(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C) | hAPP(A,A,uminus_uminus(A),B) != ti(A,C) # label(fact_509_square__eq__iff) # label(axiom). [clausify(577)].
% 5.71/5.96 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B) | ti(int,A) = ti(int,B) | hAPP(int,int,uminus_uminus(int),A) = ti(int,B). [resolve(1591,a,1592,a)].
% 5.71/5.96 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B) | ti(int,A) != ti(int,B). [resolve(1591,a,1593,a)].
% 5.71/5.96 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B) | hAPP(int,int,uminus_uminus(int),A) != ti(int,B). [resolve(1591,a,1594,a)].
% 5.71/5.96 1595 comm_ring_1(int) # label(arity_Int_Oint___Rings_Ocomm__ring__1) # label(axiom). [assumption].
% 5.71/5.96 1596 -comm_ring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,uminus_uminus(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) # label(fact_512_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom). [clausify(580)].
% 5.71/5.96 1597 -comm_ring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),one_one(A))),B) = hAPP(A,A,uminus_uminus(A),B) # label(fact_639_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom). [clausify(707)].
% 5.71/5.96 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),one_one(int))),A) = hAPP(int,int,uminus_uminus(int),A). [resolve(1595,a,1597,a)].
% 5.71/5.96 1598 linord2061991079up_add(int) # label(arity_Int_Oint___Groups_Olinordered__ab__semigroup__add) # label(axiom). [assumption].
% 5.71/5.96 1599 -linord2061991079up_add(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),collect(A),hAPP(fun(A,fun(A,bool)),fun(A,bool),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A)),hAPP(fun(A,bool),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,bool),fun(A,fun(A,bool))),combc(A,fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool))),hAPP(fun(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),A),combs(A,bool,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool))),hAPP(fun(fun(A,bool),fun(A,fun(bool,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),combb(fun(A,bool),fun(A,fun(bool,bool)),A),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj)),hAPP(fun(A,A),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,A),fun(A,bool))),fun(fun(A,A),fun(A,fun(A,bool))),combc(A,fun(A,A),fun(A,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool))),hAPP(fun(fun(A,bool),fun(fun(A,A),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool)))),combb(fun(A,bool),fun(fun(A,A),fun(A,bool)),A),combb(A,bool,A)),fequal(A))),hAPP(A,fun(A,A),plus_plus(A),C))))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),B)) # label(fact_600_add__Max__commute) # label(axiom). [clausify(668)].
% 5.71/5.97 1600 -linord2061991079up_add(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),collect(A),hAPP(fun(A,fun(A,bool)),fun(A,bool),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A)),hAPP(fun(A,bool),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,bool),fun(A,fun(A,bool))),combc(A,fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool))),hAPP(fun(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),A),combs(A,bool,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool))),hAPP(fun(fun(A,bool),fun(A,fun(bool,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),combb(fun(A,bool),fun(A,fun(bool,bool)),A),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj)),hAPP(fun(A,A),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,A),fun(A,bool))),fun(fun(A,A),fun(A,fun(A,bool))),combc(A,fun(A,A),fun(A,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool))),hAPP(fun(fun(A,bool),fun(fun(A,A),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool)))),combb(fun(A,bool),fun(fun(A,A),fun(A,bool)),A),combb(A,bool,A)),fequal(A))),hAPP(A,fun(A,A),plus_plus(A),C))))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(fun(A,bool),A,big_linorder_Min(A),B)) # label(fact_601_add__Min__commute) # label(axiom). [clausify(669)].
% 5.71/5.97 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,fun(int,bool)),fun(int,bool),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int)),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj)),hAPP(fun(int,int),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,int),fun(int,bool))),fun(fun(int,int),fun(int,fun(int,bool))),combc(int,fun(int,int),fun(int,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),hAPP(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int))),hAPP(int,fun(int,int),plus_plus(int),B))))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),A))))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(fun(int,bool),int,big_linorder_Max(int),A)). [resolve(1598,a,1599,a)].
% 5.71/5.97 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = ti(fun(int,bool),A) | hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,fun(int,bool)),fun(int,bool),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int)),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj)),hAPP(fun(int,int),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,int),fun(int,bool))),fun(fun(int,int),fun(int,fun(int,bool))),combc(int,fun(int,int),fun(int,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),hAPP(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int))),hAPP(int,fun(int,int),plus_plus(int),B))))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),A))))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(fun(int,bool),int,big_linorder_Min(int),A)). [resolve(1598,a,1600,a)].
% 5.71/5.97 1601 linord2061991079up_add(nat) # label(arity_Nat_Onat___Groups_Olinordered__ab__semigroup__add) # label(axiom). [assumption].
% 5.71/5.97 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),collect(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat)),hAPP(fun(nat,bool),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(nat,fun(nat,bool))),combc(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combc(nat,fun(nat,nat),fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool))),hAPP(fun(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool)))),combb(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool)),nat),combb(nat,bool,nat)),fequal(nat))),hAPP(nat,fun(nat,nat),plus_plus(nat),B))))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),A))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)). [resolve(1601,a,1599,a)].
% 5.71/5.97 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),collect(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat)),hAPP(fun(nat,bool),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(nat,fun(nat,bool))),combc(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combc(nat,fun(nat,nat),fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool))),hAPP(fun(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool)))),combb(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool)),nat),combb(nat,bool,nat)),fequal(nat))),hAPP(nat,fun(nat,nat),plus_plus(nat),B))))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),A))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)). [resolve(1601,a,1600,a)].
% 6.01/6.22 1602 monoid_mult(int) # label(arity_Int_Oint___Groups_Omonoid__mult) # label(axiom). [assumption].
% 6.01/6.22 1603 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) = ti(A,B) # label(fact_629_mult__1__right) # label(axiom). [clausify(697)].
% 6.01/6.22 1604 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) = ti(A,B) # label(fact_632_mult__1__left) # label(axiom). [clausify(700)].
% 6.01/6.22 1605 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) # label(fact_873_power__commutes) # label(axiom). [clausify(940)].
% 6.01/6.22 1606 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),one_one(A)),B) = one_one(A) # label(fact_874_power__one) # label(axiom). [clausify(941)].
% 6.01/6.22 1607 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),D) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) # label(fact_876_power__mult) # label(axiom). [clausify(943)].
% 6.01/6.22 1608 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),one_one(nat)) = ti(A,B) # label(fact_877_power__one__right) # label(axiom). [clausify(944)].
% 6.01/6.22 1609 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)) # label(fact_880_power__add) # label(axiom). [clausify(947)].
% 6.01/6.22 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),one_one(int)),A) = one_one(int). [resolve(1602,a,1606,a)].
% 6.01/6.22 1610 monoid_mult(nat) # label(arity_Nat_Onat___Groups_Omonoid__mult) # label(axiom). [assumption].
% 6.01/6.22 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),one_one(nat)),A) = one_one(nat). [resolve(1610,a,1606,a)].
% 6.01/6.22 1611 ring_11004092258visors(int) # label(arity_Int_Oint___Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 6.01/6.22 1612 -ring_11004092258visors(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) != one_one(A) | one_one(A) = ti(A,B) | hAPP(A,A,uminus_uminus(A),one_one(A)) = ti(A,B) # label(fact_638_square__eq__1__iff) # label(axiom). [clausify(706)].
% 6.01/6.22 1613 -ring_11004092258visors(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) = one_one(A) | one_one(A) != ti(A,B) # label(fact_638_square__eq__1__iff) # label(axiom). [clausify(706)].
% 6.25/6.47 1614 -ring_11004092258visors(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) = one_one(A) | hAPP(A,A,uminus_uminus(A),one_one(A)) != ti(A,B) # label(fact_638_square__eq__1__iff) # label(axiom). [clausify(706)].
% 6.25/6.47 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) != one_one(int) | one_one(int) = ti(int,A) | hAPP(int,int,uminus_uminus(int),one_one(int)) = ti(int,A). [resolve(1611,a,1612,a)].
% 6.25/6.47 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) = one_one(int) | one_one(int) != ti(int,A). [resolve(1611,a,1613,a)].
% 6.25/6.47 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) = one_one(int) | hAPP(int,int,uminus_uminus(int),one_one(int)) != ti(int,A). [resolve(1611,a,1614,a)].
% 6.25/6.47 1615 semiring_char_0(int) # label(arity_Int_Oint___Nat_Osemiring__char__0) # label(axiom). [assumption].
% 6.25/6.47 1616 -semiring_char_0(A) | hAPP(nat,A,semiring_1_of_nat(A),B) != hAPP(nat,A,semiring_1_of_nat(A),C) | B = C # label(fact_658_of__nat__eq__iff) # label(axiom). [clausify(726)].
% 6.25/6.47 1617 -semiring_char_0(A) | hAPP(nat,A,semiring_1_of_nat(A),B) = hAPP(nat,A,semiring_1_of_nat(A),C) | B != C # label(fact_658_of__nat__eq__iff) # label(axiom). [clausify(726)].
% 6.25/6.47 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) != hAPP(nat,int,semiring_1_of_nat(int),B) | A = B. [resolve(1615,a,1616,a)].
% 6.25/6.47 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(nat,int,semiring_1_of_nat(int),B) | A != B. [resolve(1615,a,1617,a)].
% 6.25/6.47 1618 semiring_char_0(nat) # label(arity_Nat_Onat___Nat_Osemiring__char__0) # label(axiom). [assumption].
% 6.25/6.47 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) != hAPP(nat,nat,semiring_1_of_nat(nat),B) | A = B. [resolve(1618,a,1616,a)].
% 6.25/6.47 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) = hAPP(nat,nat,semiring_1_of_nat(nat),B) | A != B. [resolve(1618,a,1617,a)].
% 6.25/6.47 1619 linordered_semidom(int) # label(arity_Int_Oint___Rings_Olinordered__semidom) # label(axiom). [assumption].
% 6.25/6.47 1620 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) # label(fact_659_of__nat__le__iff) # label(axiom). [clausify(727)].
% 6.25/6.47 1621 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) # label(fact_659_of__nat__le__iff) # label(axiom). [clausify(727)].
% 6.25/6.47 1622 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) # label(fact_817_of__nat__less__iff) # label(axiom). [clausify(884)].
% 6.25/6.47 1623 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) # label(fact_817_of__nat__less__iff) # label(axiom). [clausify(884)].
% 6.25/6.47 1624 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) # label(fact_818_less__imp__of__nat__less) # label(axiom). [clausify(885)].
% 6.25/6.47 1625 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) # label(fact_819_of__nat__less__imp__less) # label(axiom). [clausify(886)].
% 6.25/6.47 1626 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A)))) # label(fact_822_less__add__one) # label(axiom). [clausify(889)].
% 6.25/6.47 1627 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_823_less__1__mult) # label(axiom). [clausify(890)].
% 6.25/6.47 1628 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) # label(fact_845_power__le__imp__le__exp) # label(axiom). [clausify(912)].
% 6.25/6.47 1629 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) # label(fact_846_power__increasing__iff) # label(axiom). [clausify(913)].
% 6.25/6.47 1630 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) # label(fact_846_power__increasing__iff) # label(axiom). [clausify(913)].
% 6.25/6.47 1631 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_878_one__le__power) # label(axiom). [clausify(945)].
% 6.25/6.47 1632 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) != hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D) | C = D # label(fact_879_power__inject__exp) # label(axiom). [clausify(946)].
% 6.25/6.47 1633 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D) | C != D # label(fact_879_power__inject__exp) # label(axiom). [clausify(946)].
% 6.25/6.47 1634 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)))) # label(fact_881_power__less__power__Suc) # label(axiom). [clausify(948)].
% 6.25/6.47 1635 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)))) # label(fact_882_power__gt1__lemma) # label(axiom). [clausify(949)].
% 6.25/6.47 1636 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C))) # label(fact_883_power__strict__increasing) # label(axiom). [clausify(950)].
% 6.25/6.47 1637 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) # label(fact_884_power__less__imp__less__exp) # label(axiom). [clausify(951)].
% 6.25/6.47 1638 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) # label(fact_885_power__strict__increasing__iff) # label(axiom). [clausify(952)].
% 6.25/6.47 1639 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) # label(fact_885_power__strict__increasing__iff) # label(axiom). [clausify(952)].
% 6.25/6.47 1640 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C))) # label(fact_886_power__increasing) # label(axiom). [clausify(953)].
% 6.25/6.47 1641 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_939_power__less__imp__less__base) # label(axiom). [clausify(1004)].
% 6.25/6.47 1642 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A)))) # label(fact_942_zero__less__two) # label(axiom). [clausify(1007)].
% 6.25/6.47 1643 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_964_zero__less__power) # label(axiom). [clausify(1026)].
% 6.25/6.47 1644 -linordered_semidom(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) != hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | ti(A,B) = ti(A,D) # label(fact_966_power__eq__imp__eq__base) # label(axiom). [clausify(1028)].
% 6.25/6.47 1645 -linordered_semidom(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),zero_zero(A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D))) # label(fact_967_power__strict__mono) # label(axiom). [clausify(1029)].
% 6.25/6.47 1646 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) # label(fact_973_of__nat__0__less__iff) # label(axiom). [clausify(1035)].
% 6.25/6.47 1647 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) # label(fact_973_of__nat__0__less__iff) # label(axiom). [clausify(1035)].
% 6.25/6.47 1648 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_977_pos__add__strict) # label(axiom). [clausify(1039)].
% 6.25/6.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1619,a,1620,a)].
% 6.25/6.47 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1619,a,1621,a)].
% 6.25/6.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1619,a,1622,a)].
% 6.25/6.47 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1619,a,1623,a)].
% 6.25/6.47 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int)))). [resolve(1619,a,1626,a)].
% 6.25/6.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(1619,a,1627,a)].
% 6.25/6.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1619,a,1628,a)].
% 6.25/6.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1619,a,1630,a)].
% 6.25/6.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B))). [resolve(1619,a,1631,a)].
% 6.25/6.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C) | B = C. [resolve(1619,a,1632,a)].
% 6.25/6.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C) | B != C. [resolve(1619,a,1633,a)].
% 6.25/6.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)))). [resolve(1619,a,1634,a)].
% 6.25/6.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)))). [resolve(1619,a,1635,a)].
% 6.25/6.47 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B))). [resolve(1619,a,1636,a)].
% 6.25/6.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(1619,a,1637,a)].
% 6.25/6.47 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B))). [resolve(1619,a,1640,a)].
% 6.25/6.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(1619,a,1641,a)].
% 6.25/6.47 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int)))). [resolve(1619,a,1642,a)].
% 6.25/6.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B))). [resolve(1619,a,1643,a)].
% 6.25/6.47 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(int,A) = ti(int,C). [resolve(1619,a,1644,a)].
% 6.25/6.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),C))). [resolve(1619,a,1645,a)].
% 6.25/6.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(1619,a,1646,a)].
% 6.25/6.47 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(1619,a,1647,a)].
% 6.25/6.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))). [resolve(1619,a,1648,a)].
% 6.25/6.47 1649 linordered_semidom(nat) # label(arity_Nat_Onat___Rings_Olinordered__semidom) # label(axiom). [assumption].
% 6.25/6.47 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1649,a,1620,a)].
% 6.25/6.47 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1649,a,1621,a)].
% 6.25/6.47 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1649,a,1622,a)].
% 6.25/6.47 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1649,a,1623,a)].
% 6.25/6.47 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat)))). [resolve(1649,a,1626,a)].
% 6.25/6.47 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))). [resolve(1649,a,1627,a)].
% 6.25/6.47 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1649,a,1628,a)].
% 6.25/6.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1649,a,1630,a)].
% 6.25/6.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B))). [resolve(1649,a,1631,a)].
% 6.25/6.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C) | B = C. [resolve(1649,a,1632,a)].
% 6.25/6.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C) | B != C. [resolve(1649,a,1633,a)].
% 6.25/6.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)))). [resolve(1649,a,1634,a)].
% 6.25/6.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)))). [resolve(1649,a,1635,a)].
% 6.25/6.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B))). [resolve(1649,a,1636,a)].
% 6.25/6.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(1649,a,1637,a)].
% 6.25/6.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B))). [resolve(1649,a,1640,a)].
% 6.25/6.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1649,a,1641,a)].
% 6.25/6.48 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat)))). [resolve(1649,a,1642,a)].
% 6.25/6.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B))). [resolve(1649,a,1643,a)].
% 6.25/6.48 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(nat,A) = ti(nat,C). [resolve(1649,a,1644,a)].
% 6.47/6.73 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),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),C))). [resolve(1649,a,1645,a)].
% 6.47/6.73 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,semiring_1_of_nat(nat),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(1649,a,1646,a)].
% 6.47/6.73 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,semiring_1_of_nat(nat),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(1649,a,1647,a)].
% 6.47/6.73 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(1649,a,1648,a)].
% 6.47/6.73 1650 ring_1(int) # label(arity_Int_Oint___Rings_Oring__1) # label(axiom). [assumption].
% 6.47/6.73 1651 -ring_1(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,semiring_1_of_nat(A),C)),hAPP(nat,A,semiring_1_of_nat(A),B)) # label(fact_663_of__nat__diff) # label(axiom). [clausify(731)].
% 6.47/6.73 1652 -ring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),B)),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),one_one(A))),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) # label(fact_887_power__minus) # label(axiom). [clausify(954)].
% 6.47/6.73 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),B)),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(1650,a,1651,a)].
% 6.47/6.73 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),A)),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),one_one(int))),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)). [resolve(1650,a,1652,a)].
% 6.47/6.73 1653 linordered_idom(int) # label(arity_Int_Oint___Rings_Olinordered__idom) # label(axiom). [assumption].
% 6.47/6.73 1654 -linordered_idom(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_769_linorder__neqE__linordered__idom) # label(axiom). [clausify(836)].
% 6.47/6.73 1655 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),B)) # label(fact_940_mult__right__le__one__le) # label(axiom). [clausify(1005)].
% 6.47/6.73 1656 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),B)) # label(fact_941_mult__left__le__one__le) # label(axiom). [clausify(1006)].
% 6.87/7.10 1657 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_979_even__less__0__iff) # label(axiom). [clausify(1041)].
% 6.87/7.10 1658 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_979_even__less__0__iff) # label(axiom). [clausify(1041)].
% 6.87/7.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),A)). [resolve(1653,a,1655,a)].
% 6.87/7.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)),A)). [resolve(1653,a,1656,a)].
% 6.87/7.10 1659 linordered_ring(int) # label(arity_Int_Oint___Rings_Olinordered__ring) # label(axiom). [assumption].
% 6.87/7.10 1660 -linordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),zero_zero(A))) # label(fact_980_not__square__less__zero) # label(axiom). [clausify(1042)].
% 6.87/7.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),zero_zero(int))). [resolve(1659,a,1660,a)].
% 6.87/7.10 1661 linord581940658strict(int) # label(arity_Int_Oint___Rings_Olinordered__ring__strict) # label(axiom). [assumption].
% 6.87/7.10 1662 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_981_mult__less__cancel__right__disj) # label(axiom). [clausify(1043)].
% 6.87/7.10 1663 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B)) # label(fact_981_mult__less__cancel__right__disj) # label(axiom). [clausify(1043)].
% 6.87/7.10 1664 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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),C))) | 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),zero_zero(A))) # label(fact_981_mult__less__cancel__right__disj) # label(axiom). [clausify(1043)].
% 6.87/7.10 1665 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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),C))) | 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),D),B)) # label(fact_981_mult__less__cancel__right__disj) # label(axiom). [clausify(1043)].
% 6.87/7.10 1666 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_981_mult__less__cancel__right__disj) # label(axiom). [clausify(1043)].
% 6.87/7.10 1667 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B)) # label(fact_981_mult__less__cancel__right__disj) # label(axiom). [clausify(1043)].
% 6.87/7.10 1668 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_982_mult__less__cancel__left__disj) # label(axiom). [clausify(1044)].
% 6.87/7.10 1669 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) # label(fact_982_mult__less__cancel__left__disj) # label(axiom). [clausify(1044)].
% 6.87/7.10 1670 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_982_mult__less__cancel__left__disj) # label(axiom). [clausify(1044)].
% 6.87/7.10 1671 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) # label(fact_982_mult__less__cancel__left__disj) # label(axiom). [clausify(1044)].
% 6.87/7.10 1672 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_982_mult__less__cancel__left__disj) # label(axiom). [clausify(1044)].
% 6.87/7.10 1673 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) # label(fact_982_mult__less__cancel__left__disj) # label(axiom). [clausify(1044)].
% 6.87/7.10 1674 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_983_mult__less__cancel__left__pos) # label(axiom). [clausify(1045)].
% 6.87/7.10 1675 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_983_mult__less__cancel__left__pos) # label(axiom). [clausify(1045)].
% 6.87/7.10 1676 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) # label(fact_989_mult__less__cancel__left__neg) # label(axiom). [clausify(1051)].
% 6.87/7.10 1677 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) # label(fact_989_mult__less__cancel__left__neg) # label(axiom). [clausify(1051)].
% 6.87/7.10 1678 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_991_mult__neg__neg) # label(axiom). [clausify(1053)].
% 6.87/7.10 1679 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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),D))) # label(fact_995_mult__strict__right__mono__neg) # label(axiom). [clausify(1057)].
% 6.87/7.10 1680 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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),D),B))) # label(fact_996_mult__strict__left__mono__neg) # label(axiom). [clausify(1058)].
% 6.87/7.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))). [resolve(1661,a,1662,a)].
% 6.87/7.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),A)). [resolve(1661,a,1663,a)].
% 6.87/7.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))). [resolve(1661,a,1664,a)].
% 6.87/7.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),A)). [resolve(1661,a,1665,a)].
% 6.87/7.10 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(1661,a,1666,a)].
% 6.87/7.10 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),A)). [resolve(1661,a,1667,a)].
% 6.87/7.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(1661,a,1668,a)].
% 6.87/7.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B)). [resolve(1661,a,1669,a)].
% 6.97/7.23 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(1661,a,1670,a)].
% 6.97/7.23 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B)). [resolve(1661,a,1671,a)].
% 6.97/7.23 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(1661,a,1672,a)].
% 6.97/7.23 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B)). [resolve(1661,a,1673,a)].
% 6.97/7.23 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(1661,a,1674,a)].
% 6.97/7.23 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B)). [resolve(1661,a,1676,a)].
% 6.97/7.23 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(1661,a,1678,a)].
% 6.97/7.23 1681 linord20386208strict(int) # label(arity_Int_Oint___Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 6.97/7.23 1682 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_984_mult__pos__pos) # label(axiom). [clausify(1046)].
% 6.97/7.23 1683 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_985_mult__pos__neg) # label(axiom). [clausify(1047)].
% 6.97/7.23 1684 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),zero_zero(A))) # label(fact_986_mult__pos__neg2) # label(axiom). [clausify(1048)].
% 6.97/7.23 1685 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_987_zero__less__mult__pos) # label(axiom). [clausify(1049)].
% 6.97/7.23 1686 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_988_zero__less__mult__pos2) # label(axiom). [clausify(1050)].
% 6.97/7.23 1687 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_990_mult__neg__pos) # label(axiom). [clausify(1052)].
% 6.97/7.23 1688 -linord20386208strict(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),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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_992_mult__strict__right__mono) # label(axiom). [clausify(1054)].
% 6.97/7.23 1689 -linord20386208strict(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),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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),D),C))) # label(fact_993_mult__strict__left__mono) # label(axiom). [clausify(1055)].
% 6.97/7.23 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(1681,a,1682,a)].
% 6.97/7.23 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),zero_zero(int))). [resolve(1681,a,1683,a)].
% 6.97/7.23 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)),zero_zero(int))). [resolve(1681,a,1684,a)].
% 6.97/7.23 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)). [resolve(1681,a,1685,a)].
% 6.97/7.23 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(1681,a,1686,a)].
% 6.97/7.23 1690 linord20386208strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 6.97/7.23 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))). [resolve(1690,a,1682,a)].
% 6.97/7.23 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),zero_zero(nat))). [resolve(1690,a,1683,a)].
% 6.97/7.23 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A)),zero_zero(nat))). [resolve(1690,a,1684,a)].
% 8.08/8.29 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)). [resolve(1690,a,1685,a)].
% 8.08/8.29 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(1690,a,1686,a)].
% 8.08/8.29 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),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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(1690,a,1688,a)].
% 8.08/8.29 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),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))). [resolve(1690,a,1689,a)].
% 8.08/8.29 1691 linord893533164strict(int) # label(arity_Int_Oint___Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 8.08/8.29 1692 -linord893533164strict(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),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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),D),C))) # label(fact_994_comm__mult__strict__left__mono) # label(axiom). [clausify(1056)].
% 8.08/8.29 1693 linord893533164strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 8.08/8.29
% 8.08/8.29 ============================== end predicate elimination =============
% 8.08/8.29
% 8.08/8.29 Auto_denials: (non-Horn, no changes).
% 8.08/8.29
% 8.08/8.29 Term ordering decisions:
% 8.08/8.29 Function symbol KB weights: bool=1. nat=1. int=1. state=1. com=1. fconj=1. vname=1. fdisj=1. fimplies=1. ass=1. fNot=1. semi=1. fFalse=1. fTrue=1. skip=1. update=1. b=1. c=1. g=1. p=1. x_a=1. fun=1. ti=1. big_co1399186613setsum=1. big_co302546470etprod=1. image=1. finite_fold=1. finite_fold_graph=1. finite100568337ommute=1. combk=1. finite_comp_fun_idem=1. finite1357897459simple=1. finite908156982e_idem=1. fold_graph=1. hoare_1759541758le_rec=1. hoare_225284258e_case=1. f10=1. f11=1. f12=1. f13=1. f14=1. f15=1. f16=1. f19=1. f23=1. f24=1. f35=1. f36=1. f55=1. f56=1. f84=1. f94=1. f97=1. f100=1. f101=1. f118=1. f119=1. f121=1. f122=1. f140=1. f142=1. f146=1. f147=1. f154=1. f161=1. f162=1. f166=1. f167=1. ord_less_eq=1. ord_less=1. plus_plus=1. hoare_2118899576triple=1. finite_finite_1=1. bot_bot=1. times_times=1. insert=1. member=1. minus_minus=1. ord_min=1. ord_max=1. one_one=1. zero_zero=1. semiring_1_of_nat=1. uminus_uminus=1. power_power=1. collect=1. finite_card=1. big_Sup_fin=1. big_linorder_Max=1. big_linorder_Min=1. ord_atLeastAtMost=1. big_Inf_fin=1. finite_fold1=1. fequal=1. hoare_759811442triple=1. hoare_1301688828derivs=1. ord_lessThan=1. fEx=1. ord_greaterThan=1. if=1. the=1. finite_fold1Set=1. finite_folding_one=1. finite2073411215e_idem=1. max=1. min=1. ord_gr1471790799AtMost=1. power_1=1. combi=1. partial_flat_lub=1. the_elem=1. big_semilattice_big=1. undefined=1. f83=1. f141=1. f156=1. f157=1. f188=1. f189=1. f190=1. f191=1. combb=1. combc=1. combs=1. f17=1. f18=1. f29=1. f34=1. f37=1. f38=1. f44=1. f46=1. f50=1. f51=1. f52=1. f59=1. f60=1. f75=1. f80=1. f81=1. f82=1. f85=1. f86=1. f87=1. f88=1. f92=1. f93=1. f95=1. f96=1. f98=1. f99=1. f102=1. f103=1. f113=1. f114=1. f116=1. f117=1. f120=1. f129=1. f143=1. f144=1. f148=1. f149=1. f150=1. f151=1. f152=1. f153=1. f155=1. f158=1. f159=1. f182=1. f183=1. f184=1. f185=1. f186=1. f187=1. hAPP=1. f26=1. f30=1. f31=1. f39=1. f41=1. f42=1. f43=1. f45=1. f71=1. f73=1. f74=1. f79=1. f91=1. f106=1. f115=1. f132=1. f133=1. f1=1. f2=1. f20=1. f21=1. f25=1. f27=1. f32=1. f33=1. f40=1. f57=1. f58=1. f64=1. f65=1. f68=1. f72=1. f76=1. f77=1. f78=1. f125=1. f126=1. f130=1. f131=1. f139=1. f145=1. f3=1. f4=1. f5=1. f6=1. f28=1. f47=1. f48=1. f49=1. f66=1. f67=1. f69=1. f70=1. f123=1. f124=1. f127=1. f128=1. f134=1. f135=1. f136=1. f137=1. f138=1. f164=1. f165=1. f168=1. f169=1. f170=1. f171=1. f172=1. f173=1. f174=1. f175=1. f176=1. f177=1. f178=1. f179=1. f180=1. f181=1. f7=1. f8=1. f9=1. f22=1. f61=1. f62=1. f63=1.
% 10.64/10.82
% 10.64/10.82 ============================== end of process initial clauses ========
% 10.64/10.82
% 10.64/10.82 ============================== CLAUSES FOR SEARCH ====================
% 10.64/10.82
% 10.64/10.82 ============================== end of clauses for search =============
% 10.64/10.82
% 10.64/10.82 ============================== SEARCH ================================
% 10.64/10.82
% 10.64/10.82 % Starting search at 5.95 seconds.
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=183.000, iters=3472
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=176.000, iters=3620
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=174.000, iters=3635
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=171.000, iters=3558
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=160.000, iters=3357
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=156.000, iters=3411
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=151.000, iters=3341
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=148.000, iters=3400
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=147.000, iters=3383
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=145.000, iters=3406
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=140.000, iters=3338
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=135.000, iters=3429
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=133.000, iters=3404
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=129.000, iters=3389
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=128.000, iters=3411
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=125.000, iters=3373
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=123.000, iters=3388
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=120.000, iters=3346
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=119.000, iters=3445
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=118.000, iters=3473
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=117.000, iters=3440
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=113.000, iters=3339
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=111.000, iters=3334
% 10.64/10.82
% 10.64/10.82 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 93 (0.00 of 7.94 sec).
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=110.000, iters=3371
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=104.000, iters=3381
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=103.000, iters=3477
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=102.000, iters=3452
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=101.000, iters=3413
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=97.000, iters=3336
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=95.000, iters=3417
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=91.000, iters=3387
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=89.000, iters=3378
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=87.000, iters=3597
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=84.000, iters=3543
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=81.000, iters=3364
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=80.000, iters=3352
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=77.000, iters=3427
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=75.000, iters=3447
% 10.64/10.82
% 10.64/10.82 Low Water (keep): wt=72.000, iters=3423
% 10.64/10.82
% 10.64/10.82 ============================== PROOF =================================
% 10.64/10.82 % SZS status Theorem
% 10.64/10.82 % SZS output start Refutation
% 10.64/10.82
% 10.64/10.82 % Proof 1 at 8.46 (+ 0.04) seconds.
% 10.64/10.82 % Length of proof is 27.
% 10.64/10.82 % Level of proof is 6.
% 10.64/10.82 % Maximum clause weight is 298.000.
% 10.64/10.82 % Given clauses 625.
% 10.64/10.82
% 10.64/10.82 65 (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].
% 10.64/10.82 80 (all X_b all A_2 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),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),A_2),bot_bot(fun(X_b,bool)))) # label(fact_12_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 10.64/10.82 109 (all X_b all X_1 hAPP(fun(X_b,bool),X_b,the_elem(X_b),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_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1)) # label(fact_41_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 10.64/10.82 119 (all X_b all Q_3 all Ga all Ca all Pa ((all Z_4 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_4),S_3)) -> (exists P_3 exists Q_4 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),P_3),Ca),Q_4)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) & (all S_4 ((all Z_5 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_3,Z_5),S_3)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_4,Z_5),S_4)))) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_3,Z_4),S_4)))))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))) # label(fact_51_conseq) # label(axiom) # label(non_clause). [assumption].
% 10.64/10.82 156 (all X_b all X_1 hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),X_1)) = ti(X_b,X_1)) # label(fact_88_the__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 10.64/10.82 1076 (all X_a all P hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P)) # label(help_COMBI_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 10.64/10.82 1077 (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].
% 10.64/10.82 1791 ti(bool,fFalse) = fFalse # label(tsy_c_fFalse_res) # label(hypothesis). [assumption].
% 10.64/10.82 1801 hAPP(A,B,C,D) = ti(B,hAPP(A,B,C,D)) # label(tsy_c_hAPP_res) # label(axiom). [clausify(65)].
% 10.64/10.82 1802 ti(A,hAPP(B,A,C,D)) = hAPP(B,A,C,D). [copy(1801),flip(a)].
% 10.64/10.82 1833 hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),bot_bot(fun(A,bool))) = hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(A,fun(A,bool),fequal(A),B)) # label(fact_12_singleton__conv2) # label(axiom). [clausify(80)].
% 10.64/10.82 1889 hAPP(fun(A,bool),A,the_elem(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_41_the__elem__eq) # label(axiom). [clausify(109)].
% 10.64/10.82 1890 ti(A,B) = hAPP(fun(A,bool),A,the_elem(A),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(A,fun(A,bool),fequal(A),B))). [copy(1889),rewrite([1833(18)]),flip(a)].
% 10.64/10.82 1906 hBOOL(hAPP(state,bool,hAPP(A,fun(state,bool),B,f20(A,C,D,E,B)),f21(A,C,D,E,B))) | hBOOL(hAPP(fun(hoare_2118899576triple(A),bool),bool,hAPP(fun(hoare_2118899576triple(A),bool),fun(fun(hoare_2118899576triple(A),bool),bool),hoare_1301688828derivs(A),D),hAPP(fun(hoare_2118899576triple(A),bool),fun(hoare_2118899576triple(A),bool),hAPP(hoare_2118899576triple(A),fun(fun(hoare_2118899576triple(A),bool),fun(hoare_2118899576triple(A),bool)),insert(hoare_2118899576triple(A)),hAPP(fun(A,fun(state,bool)),hoare_2118899576triple(A),hAPP(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)),hAPP(fun(A,fun(state,bool)),fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),hoare_759811442triple(A),B),E),C)),bot_bot(fun(hoare_2118899576triple(A),bool))))) # label(fact_51_conseq) # label(axiom). [clausify(119)].
% 10.64/10.82 1907 hBOOL(hAPP(state,bool,hAPP(A,fun(state,bool),B,f20(A,C,D,E,B)),f21(A,C,D,E,B))) | hBOOL(hAPP(fun(hoare_2118899576triple(A),bool),bool,hAPP(fun(hoare_2118899576triple(A),bool),fun(fun(hoare_2118899576triple(A),bool),bool),hoare_1301688828derivs(A),D),hAPP(fun(hoare_2118899576triple(A),bool),fun(hoare_2118899576triple(A),bool),collect(hoare_2118899576triple(A)),hAPP(hoare_2118899576triple(A),fun(hoare_2118899576triple(A),bool),fequal(hoare_2118899576triple(A)),hAPP(fun(A,fun(state,bool)),hoare_2118899576triple(A),hAPP(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A)),hAPP(fun(A,fun(state,bool)),fun(com,fun(fun(A,fun(state,bool)),hoare_2118899576triple(A))),hoare_759811442triple(A),B),E),C))))). [copy(1906),rewrite([1833(74)])].
% 10.64/10.82 1988 hAPP(fun(A,bool),A,the(A),hAPP(A,fun(A,bool),fequal(A),B)) = ti(A,B) # label(fact_88_the__sym__eq__trivial) # label(axiom). [clausify(156)].
% 10.64/10.82 1989 hAPP(fun(A,bool),A,the_elem(A),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(A,fun(A,bool),fequal(A),B))) = hAPP(fun(A,bool),A,the(A),hAPP(A,fun(A,bool),fequal(A),B)). [copy(1988),rewrite([1890(9)]),flip(a)].
% 10.64/10.82 2862 hAPP(A,A,combi(A),B) = ti(A,B) # label(help_COMBI_1_1_U) # label(axiom). [clausify(1076)].
% 10.64/10.82 2863 hAPP(fun(A,bool),A,the(A),hAPP(A,fun(A,bool),fequal(A),B)) = hAPP(A,A,combi(A),B). [copy(2862),rewrite([1890(3),1989(16)]),flip(a)].
% 10.64/10.82 2864 hAPP(A,B,hAPP(B,fun(A,B),combk(B,A),C),D) = ti(B,C) # label(help_COMBK_1_1_U) # label(axiom). [clausify(1077)].
% 10.64/10.82 2865 hAPP(A,B,hAPP(B,fun(A,B),combk(B,A),C),D) = hAPP(B,B,combi(B),C). [copy(2864),rewrite([1890(5),1989(18),2863(12)])].
% 10.64/10.82 2873 -hBOOL(fFalse) # label(help_fFalse_1_1_U) # label(axiom). [assumption].
% 10.64/10.82 2883 -hBOOL(hAPP(fun(hoare_2118899576triple(x_a),bool),bool,hAPP(fun(hoare_2118899576triple(x_a),bool),fun(fun(hoare_2118899576triple(x_a),bool),bool),hoare_1301688828derivs(x_a),g),hAPP(fun(hoare_2118899576triple(x_a),bool),fun(hoare_2118899576triple(x_a),bool),hAPP(hoare_2118899576triple(x_a),fun(fun(hoare_2118899576triple(x_a),bool),fun(hoare_2118899576triple(x_a),bool)),insert(hoare_2118899576triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hoare_759811442triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_2118899576triple(x_a),bool))))) # label(conj_0) # label(negated_conjecture). [assumption].
% 10.64/10.82 2884 -hBOOL(hAPP(fun(hoare_2118899576triple(x_a),bool),bool,hAPP(fun(hoare_2118899576triple(x_a),bool),fun(fun(hoare_2118899576triple(x_a),bool),bool),hoare_1301688828derivs(x_a),g),hAPP(fun(hoare_2118899576triple(x_a),bool),fun(hoare_2118899576triple(x_a),bool),collect(hoare_2118899576triple(x_a)),hAPP(hoare_2118899576triple(x_a),fun(hoare_2118899576triple(x_a),bool),fequal(hoare_2118899576triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_2118899576triple(x_a))),hoare_759811442triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b))))))). [copy(2883),rewrite([1833(303)])].
% 10.64/10.82 3981 hAPP(A,A,combi(A),hAPP(B,A,C,D)) = hAPP(B,A,C,D). [back_rewrite(1802),rewrite([1890(2),1989(15),2863(9)])].
% 10.64/10.82 3990 hAPP(bool,bool,combi(bool),fFalse) = fFalse. [back_rewrite(1791),rewrite([1890(3),1989(24),2863(15)])].
% 10.64/10.82 9799 $F. [resolve(2884,a,1907,b),rewrite([2865(252),3981(22),2865(234),3990(6)]),unit_del(a,2873)].
% 10.64/10.82
% 10.64/10.82 % SZS output end Refutation
% 10.64/10.82 ============================== end of proof ==========================
% 10.64/10.82
% 10.64/10.82 ============================== STATISTICS ============================
% 10.64/10.82
% 10.64/10.82 Given=625. Generated=14380. Kept=7428. proofs=1.
% 10.64/10.82 Usable=619. Sos=6264. Demods=622. Limbo=0, Disabled=2932. Hints=0.
% 10.64/10.82 Megabytes=88.71.
% 10.64/10.82 User_CPU=8.46, System_CPU=0.04, Wall_clock=9.
% 10.64/10.82
% 10.64/10.82 ============================== end of statistics =====================
% 10.64/10.82
% 10.64/10.82 ============================== end of search =========================
% 10.64/10.82
% 10.64/10.82 THEOREM PROVED
% 10.64/10.82 % SZS status Theorem
% 10.64/10.82
% 10.64/10.82 Exiting with 1 proof.
% 10.64/10.82
% 10.64/10.82 Process 29149 exit (max_proofs) Sat Jun 4 18:21:03 2022
% 10.64/10.82 Prover9 interrupted
%------------------------------------------------------------------------------